Percent Solution Calculator with Steps (Free)

Percent Solution Calculator

Make any % w/v, % w/w or % v/v solution, find the mass percent of a solution (one solute or several), convert percent to molarity and back, dilute a percent solution and mix two strengths by alligation, with every step, the uncertainty, a figure and four charts.

By StatsUnlock Team · Checked against USP percent definitions, ASTM E288 flask tolerances, Tanaka water densities and JCGM 100:2008 · Last updated: October 30, 2026

LabSolution PrepStep by StepWith UncertaintyAP ChemistryPharmacyBiologyFree

⚡ 0. Quick Answer

A percent solution calculator uses grams of solute per 100 mL (% w/v), per 100 g (% w/w) or mL per 100 mL (% v/v). For 250.0 mL of 10% w/v NaCl, mass = 10 × 250.0 ÷ 100 = 25.00 g, made up to 250.0 mL. With a ±0.01 g balance and a Class A flask it is 10.0000 ± 0.0072% w/v (k = 2).

mass (g) = % w/v × volume (mL) ÷ 100 · mass % = m_solute ÷ m_solution × 100

Rule of thumb: always say which percent you mean. 10% w/w NaCl is about 10.7% w/v, and to turn any percent into molarity you need the solution density: M = % w/w × ρ × 10 ÷ MW.

⭐ Key Takeaways

A percent solution calculator turns a percent into a recipe: 25.00 g of NaCl made up to 250.0 mL is 10% w/v.
Mass percent divides by the whole solution: 4.20 g KCl in 50.0 g water is 4.20 ÷ 54.2 × 100 = 7.749%, not 8.40%.
Percent to molarity needs the density: 37.3% w/w HCl at 1.18 g/mL is 12.07 M; 10.0% w/w NaCl at 1.0707 g/mL is 1.832 M.
For 500.0 mL of 70% v/v ethanol from 95%, measure 368.4 mL and make up to the mark, because ethanol and water shrink on mixing.
Alligation: mix 75 mL of 30% with 25 mL of 10% for 100 mL of 25% (parts 15 : 5).

📚 1. What Is a Percent Solution Calculator?

A percent solution states how much solute is in 100 parts of solution. There are three kinds, and the United States Pharmacopeia defines each one: % w/w (weight in weight) is grams of solute in 100 g of solution; % w/v (weight in volume) is grams of solute in 100 mL of solution; and % v/v (volume in volume) is milliliters of the pure liquid solute in 100 mL of solution. A percent solution calculator turns any of them into a recipe, works out the mass percent of a solution you already made, converts percent to molarity, molality, ppm and g/L, dilutes a percent solution and mixes two strengths.

A worked one-liner: mass = % × volume ÷ 100 = 10 × 250.0 ÷ 100 = 25.00 g of NaCl, made up to 250.0 mL. With a balance read to ±0.01 g and a Class A 250 mL flask (±0.12 mL, ASTM E288), the solution is 10.0000 ± 0.0072% w/v at k = 2.

Who uses it: AP Chemistry and general chemistry students solving mass percent problems; biology labs making agarose gels, saline, sucrose and ethanol; pharmacy students and technicians using alligation; QC and food labs converting label percent to molarity; and anyone preparing a stock from a concentrated reagent bottle. One page replaces separate "mass percent", "percent to molarity", "w/v", "v/v" and "alligation" calculators.

Quick answers to the questions people ask most

How do you make a percent solution?

Multiply the percent by the amount of solution and divide by 100. For % w/v, that gives grams per the volume: 5% w/v in 200 mL needs 5 × 200 ÷ 100 = 10.0 g, dissolved and made up to 200 mL. For % w/w, weigh solute and solvent; for % v/v, measure the liquid and make up to volume.

How do you calculate the mass percent of a solution?

Divide the mass of solute by the mass of the whole solution and multiply by 100. The solution mass is solute plus solvent. For 4.20 g of KCl in 50.0 g of water: 4.20 ÷ (4.20 + 50.0) × 100 = 7.749% by mass. Dividing by the water alone (8.40%) is the most common mistake.

How do you calculate mass percent given the density?

Use the density to turn a volume into a mass. If the solvent is 250.0 mL of water at 25 °C (0.99705 g/mL), its mass is 249.26 g. With 15.0 g of sugar, mass percent = 15.0 ÷ (15.0 + 249.26) × 100 = 5.676%. Otherwise, mass % = % w/v ÷ solution density.

How do you calculate molarity from a percent solution?

Use M = (% w/w × density × 10) ÷ molar mass, with density in g/mL. For 37.3% HCl at 1.18 g/mL: 37.3 × 1.18 × 10 ÷ 36.458 = 12.07 M. For a % w/v solution no density is needed: M = % w/v × 10 ÷ molar mass, so 0.9% saline is 0.154 M.

How do you calculate volume percent of a solution?

Divide the volume of the pure liquid solute by the final volume of the solution and multiply by 100. 70 mL of ethanol made up to 100 mL with water is 70% v/v. Use the final volume, not the sum of the two liquids, because many pairs, like ethanol and water, shrink when mixed.

What is the difference between w/v, w/w and v/v?

% w/v is grams per 100 mL of solution and suits solids in water. % w/w is grams per 100 g of solution and is used for concentrated acids, creams and syrups. % v/v is mL per 100 mL and is used for liquids such as ethanol. They agree only when the density is 1 g/mL.

Bench note from the StatsUnlock Team: most percent solution errors are not arithmetic. They are using the solvent mass instead of the solution mass, mixing up w/v and w/w for a dense solution, and adding a measured volume of solvent instead of making up to the mark. Research on students shows that solution concentration, and percent in particular, is where many misconceptions sit (Raviolo et al., 2021), which is why this percent solution calculator shows every step and labels each percent by type.

The three USP percent types. Always write w/w, w/v or v/v after the number.

Term	What it means	10% example	Watch out for
% w/w (mass percent)	g solute per 100 g solution	10 g + 90 g water	Divide by solution mass, not solvent
% w/v	g solute per 100 mL solution	10 g made up to 100 mL	Same as g/dL; × 10 = g/L
% v/v	mL pure solute per 100 mL solution	10 mL made up to 100 mL	Volumes do not always add
ppm (w/w)	g per 10⁶ g solution	100 000 ppm	1% w/w = 10 000 ppm
Molarity (M)	mol per liter of solution	10% w/v NaCl = 1.711 M	Needs the molar mass

🧮 2. Enter Your Percent Solution

What do you want to calculate?

Make a percent solution Mass percent of a solution Percent to molarity and back Dilute a percent solution Mix two solutions (alligation)

Sample problem Significant figures

Type of percent

Percent wanted

Final volume of solution

Solute name

Purity or assay of the material, %

Weighing a hydrate for an anhydrous percent?

⚖️ Uncertainty inputs (tolerances, ±)

Balance tolerance ± (g)

Class A flask (ASTM E288) fills the tolerance

Flask tolerance ± (mL)

Purity uncertainty ± (%)

Each ±a is a rectangular distribution, u = a/√3; they combine in quadrature and U = 2u (JCGM 100:2008). A graduated cylinder is about ±1% of its volume; a 250 mL Class A flask is ±0.12 mL.

📊 3. Results and Step-by-Step Working

Load a sample or type your values above, then press Calculate Percent Solution. The answer with its uncertainty, the working, every step, a figure, four charts and the exports will appear here.

🧠 4. Understanding Your Percent Solution Result, In Detail

4.1 What the result means

___

4.2 How sure you can be

___

4.3 Which percent is this?

___

4.4 The detail that changes the answer

___

4.5 What to do next

___

4.6 Why % w/w and % w/v differ for the same solution

% w/v = % w/w × density. A 10.0% w/w NaCl solution has a density of 1.0707 g/mL at 20 °C, so it holds 10.0 × 1.0707 = 10.71 g per 100 mL, which is 10.71% w/v. For 37.3% HCl (1.18 g/mL) the gap is bigger: 44.0% w/v. Only for dilute solutions with a density near 1 g/mL, such as 0.9% saline, are the two close enough to swap. The percent solution calculator converts between them in Section 2 when you give the density (Rogers and Pitzer, 1982).

4.7 Which input usually dominates the uncertainty

For the headline 10% w/v NaCl (25.00 g in 250.0 mL), the flask (±0.12 mL) and the balance (±0.01 g) both matter, and the result is good to about 0.07% relative. Make the same solution in a graduated cylinder (±1%) and the cylinder dominates, giving roughly ±0.1% w/v at k = 2. For mass percent, everything is weighed, so the balance tolerance and the size of the smallest mass decide it.

4.8 Volume percent and shrinkage

For % v/v the volume of the pure liquid is measured before mixing. Ethanol and water shrink by up to about 4% when mixed, so 70 mL of ethanol plus 30 mL of water is about 97 mL, not 100 mL. Always make up to the final volume in a flask; never add the two volumes. Alcohol strength for tax and labeling is defined at 20 °C for the same reason.

✍ 5. How to Write a Percent Solution in a Report: Detailed Results

A percent on its own ("10% NaCl") is not a result. A detailed result states the type of percent, the amounts that produced it, the equivalent concentrations a reader may need (g/L, molarity), the uncertainty with its coverage factor, and how the number was checked. The seven write-ups below are filled from the percent solution calculator; they show the headline example until you press Calculate.

Showing the headline example (10% w/v NaCl, 250.0 mL). Press Calculate above to fill all seven write-ups with your own result.

5.1 What a detailed result must contain

Element	Why it matters	Headline example
Percent and its type	w/w, w/v and v/v differ by the density	10% w/v
Solute identity, grade and lot	Purity and hydrate change the mass weighed	NaCl, ACS reagent, lot 2610-B
Amounts used	Lets a reader repeat or audit the prep	25.00 g made up to 250.0 mL
Solvent and temperature	Volumes and densities depend on temperature	Deionized water, 20 °C
Equivalent units	Readers often need g/L or molarity	100.0 g/L; 1.711 M
Uncertainty and k	Shows how good the number is (JCGM 100:2008)	±0.0072% w/v, k = 2
Largest uncertainty source	Tells you what to improve	Flask (59% of u²)
Verification	Proves the arithmetic	25.00 g ÷ 250.0 mL × 100 = 10.00%

5.2 Weak vs detailed

Weak

"A 10% salt solution was made."

No type, no amounts, no uncertainty: a reader cannot tell if it is 10.0 or 10.7 g per 100 mL.

Detailed

"10.0000 ± 0.0072% w/v NaCl (k = 2): 25.00 g made up to 250.0 mL with deionized water at 20 °C (100.0 g/L, 1.711 M)."

Type, amounts, equivalents, uncertainty and conditions in one sentence.

5.3 Seven ready-to-copy write-ups

1. Lab report: methods and results sentence

A 10.00% w/v solution of NaCl was prepared by dissolving 25.00 g of NaCl and making up to 250.0 mL. Concentration 10.0000 ± 0.0072% w/v (k = 2). Summary: 25.00 g NaCl, made up to 250.0 mL → 10.00% w/v.

📌 Conventions

Always add w/w, w/v or v/v after the percent.
Name the solvent and the final volume or mass.
Give U with k; round U to two significant figures and the value to the same decimal place.

2. Reagent label or QC record

SOLUTION: NaCl RESULT: 25.00 g NaCl, made up to 250.0 mL → 10.00% w/v KEY VALUE: Mass of NaCl for 250.0 mL of 10.00% w/v: Weigh 25.00 g of NaCl UNCERTAINTY: Solution made: 10.0000 ± 0.0072% w/v (k = 2, about 95%) from the tolerances entered METHOD: Make a percent solution (USP percent definition); StatsUnlock Percent Solution Calculator CHECK: m ÷ amount × 100 = 10% w/v ✓ Lot: ______ Balance ID: ______ Flask ID: ______ Temperature: ______ °C Prepared by: ______ Date: ______ Expiry: ______ Storage: ______

📌 Conventions

Label with name, percent and type, date made, expiry and initials (GLP; FDA 21 CFR 211.194 for records).
Record the solute lot and the balance and flask IDs.

3. Method validation and uncertainty statement

Percent concentrations follow the USP definitions (% w/w, g per 100 g; % w/v, g per 100 mL; % v/v, mL per 100 mL). Result: 25.00 g NaCl, made up to 250.0 mL → 10.00% w/v. Standard uncertainty was evaluated per JCGM 100:2008 with rectangular tolerances (u = a/√3) combined in quadrature: Solute mass (balance) ± 0.01 g (41.0% of u²); Final volume (flask) ± 0.12 mL (59.0% of u²). Combined relative standard uncertainty 0.0361%, expanded U (k = 2) 0.0721% relative; the largest contribution was final volume (flask). The result was verified by back-calculation (m ÷ amount × 100 = 10% w/v ✓).

📌 Conventions

Cite the definition (USP General Notices) and the glassware standard (ASTM E288).
State that tolerances were treated as rectangular and name the dominant contributor.

4. Exam or practical answer, fully worked

Given: 10% w/v, 250.0 mL Required: Mass of NaCl Equation: m = % × amount ÷ 100 Substitute: 10 × 250 ÷ 100 Solve: 25.00 g Working: 1. Write what the percent means: % w/v = grams of solute per 100 mL of solution 2. Amount of pure solute: m = 10/100 × 250.0 mL = 25 g 3. Make up to volume: dissolve, then add solvent to the 250.0 mL mark 4. Uncertainty of the percent made: u/% = √[(u_solute/solute)² + (u_total/total)² + (u_purity/purity)²] = 0.0361%; U = 0.0072% w/v 5. Check: m ÷ amount × 100 = 10% w/v ✓ Answer: Weigh 25.00 g of NaCl

📌 Conventions

Write the definition, substitute with units, then answer.
For mass percent, show solute + solvent = solution.

5. Plain text for chat or a forum

25.00 g NaCl, made up to 250.0 mL → 10.00% w/v. Solution made: 10.0000 ± 0.0072% w/v (k = 2, about 95%) from the tolerances entered.

6. Detailed results paragraph (thesis or paper)

Results. 25.00 g NaCl, made up to 250.0 mL → 10.00% w/v. Mass of NaCl for 250.0 mL of 10.00% w/v: Weigh 25.00 g of NaCl. Uncertainty: Solution made: 10.0000 ± 0.0072% w/v (k = 2, about 95%) from the tolerances entered. Supporting values: Solute to weigh: 25.00 g (NaCl); Pure solute: 25.00 g (percent × amount ÷ 100); Final volume: 250.0 mL (make up to the mark); Percent: 10.00% w/v; Per 100 mL: 10.000 g (the definition); In US units: 8.454 US fl oz total; Also: 100.00 g/L = 100.00 mg/mL (% w/v × 10). The largest source of uncertainty was final volume (flask) (59.0% of the variance). The calculation was checked by back-substitution (m ÷ amount × 100 = 10% w/v ✓).

📌 Conventions

Report the value first, then its uncertainty, then the supporting quantities.
Keep the number of digits consistent with the uncertainty.

7. Results table (tab-separated, pastes into Excel or Word)

Quantity Value Note Solute to weigh 25.00 g NaCl Pure solute 25.00 g percent × amount ÷ 100 Final volume 250.0 mL make up to the mark Percent 10.00% w/v Per 100 mL 10.000 g the definition In US units 8.454 US fl oz total Also 100.00 g/L = 100.00 mg/mL % w/v × 10 Uncertainty input Tolerance Share of u² Solute mass (balance) ± 0.01 g 41.0% Final volume (flask) ± 0.12 mL 59.0% Expanded U (k = 2) 0.0721% relative

📌 Conventions

Paste into Excel: each tab becomes a new column.
In Word, use Insert, Table, Convert Text to Table, separated by tabs.

∑ 6. What Is the Percent Solution Formula? All Formulas Used

①

The three percent definitions

% w/w = m_solute ÷ m_solution × 100 · % w/v = m_solute(g) ÷ V_solution(mL) × 100 · % v/v = V_solute ÷ V_solution × 100

m_solutionSolute plus solvent, in grams

Example4.20 g KCl in 50.0 g water: 4.20 ÷ 54.20 × 100 = 7.749% w/w

②

Recipe for a percent solution

m = % × amount ÷ 100 ÷ (purity/100) × (MW_hydrate ÷ MW_anhydrous)

AmountmL of solution for w/v and v/v; g of solution for w/w

Example10% w/v in 250.0 mL: 25.00 g; for 20% w/w in 500.0 g, 100.0 g solute + 400.0 g water

③

Percent to molarity and back

M = % w/w × ρ × 10 ÷ MW · M = % w/v × 10 ÷ MW · % w/w = M × MW ÷ (10ρ)

ρDensity of the solution, g/mL

Example37.3% HCl, 1.18 g/mL: 37.3 × 1.18 × 10 ÷ 36.458 = 12.07 M

④

Molality, mole fraction, ppm and % v/v

b = 1000 M ÷ (1000ρ − M·MW) · ppm = % w/w × 10⁴ · % w/v = % v/v × ρ_solute

bMolality, mol per kg of solvent

Example10.0% w/w NaCl at 1.0707 g/mL: 1.832 M, 1.901 mol/kg

⑤

Diluting a percent solution

C₁V₁ = C₂V₂ (w/v, v/v) · C₁m₁ = C₂m₂ (w/w)

RuleKeep the same kind of percent on both sides

Example70% v/v from 95%: 70 × 500.0 ÷ 95 = 368.4 mL, made up to 500.0 mL

⑥

Mixing and alligation

C_mix = (C₁A₁ + C₂A₂) ÷ (A₁ + A₂) · parts strong = C_t − C_weak; parts weak = C_strong − C_t

Example30% and 10% to 25%: 15 : 5 parts, so 75 mL + 25 mL for 100 mL

⑦

Uncertainty of a percent solution

u(%)/% = √[(u_m/m)² + (u_V/V)² + (u_P/P)²] · u = a/√3 · U = 2u

aA ± tolerance (balance, flask, purity), rectangular

Example±0.01 g on 25.00 g and ±0.12 mL on 250.0 mL: u/% = 0.036%; U = 0.0072% w/v

🔀 7. How Do You Calculate a Percent Solution? Flowchart, Step by Step

The same worked problem as Sections 0, 9, 10, 11 and 14: make 250.0 mL of 10% w/v NaCl, with a ±0.01 g balance and a Class A 250 mL flask.

Start or resultData stepCalculation stepYes or no check

StartA percent and an amountWant 10% NaCl, 250.0 mL

CheckWhich percent: w/v, w/w or v/v?

w/vA solid in a volume: grams per 100 mL.

w/w or v/vWeigh the total (w/w) or measure the liquid (v/v).

Mass of solutem = % × V ÷ 10010 × 250.0 ÷ 100 = 25.00 g

CheckIs the material pure and anhydrous?

YesNaCl, 99.5% or better: weigh 25.00 g.

NoDivide by purity; multiply by MW hydrate ÷ MW anhydrous.

Weigh, dissolve, make up25.00 g into about 200 mL water, dissolve, transfer to a 250 mL flask, fill to the mark at 20 °C, invert 15 times

Uncertaintyu/% = √[(0.01/√3/25.00)² + (0.12/√3/250.0)²]u/% = 0.036%; U = 2u = 0.0072% w/v

CheckDoes 25.00 g ÷ 250.0 mL × 100 give 10%?

Yes10.00% w/v. Verified.

NoA unit slipped (L vs mL); recheck step 1.

Result10.0000 ± 0.0072% w/v NaCl25.00 g made up to 250.0 mL (k = 2); also 100.0 g/L and 1.711 M

📝 8. How to Use This Percent Solution Calculator

Pick what you want to calculate. Choose a mode in Section 2: make a percent solution, mass percent of a solution, percent to molarity and back, dilute a percent solution, or mix two solutions.
Load a sample or start from your numbers. Ten worked problems are in the sample menu. Sample 1 is the headline problem. Nothing is calculated until you press Calculate.
Say which percent you mean. Choose % w/v (g per 100 mL), % w/w (g per 100 g) or % v/v (mL per 100 mL). The units of the amount change to match.
Enter the percent and the amount. Type the percent and the final volume or mass in mL, L, US gallons, US fluid ounces, g, kg, oz or lb.
Correct for purity and hydrates. Enter the assay percent of your material, and the two molar masses if you weigh a hydrate for an anhydrous percent.
Add the tolerances. Give the balance tolerance and pick your Class A flask. The page combines them by the GUM rule and reports U at k = 2.
Press Calculate Percent Solution. Press the button or Enter. The answer, a Verified badge, the working, every step and a results table appear in Section 3.
Read the figure and charts. The figure is drawn from your numbers; the four charts show the relationship, a comparison, the amounts and the uncertainty or composition.
Copy the write-up. Section 5 fills five ready sentences for a lab report, label, method, exam and chat; Section 20 fills a methods sentence.
Export or run a batch. Download Doc or PDF, or use the Batch tab for many recipes at once, typed or from a CSV or Excel file.

📈 9. How to Calculate a Percent Solution in Excel

Excel has no PERCENT SOLUTION function, but you can rebuild this percent solution calculator in one row of cells. The sheet repeats the headline problem (10% w/v NaCl, 250.0 mL) with the uncertainty, so the numbers match Sections 0, 7, 10, 11 and 14.

The whole thing in one cell: with the percent in A2 and the final volume in mL in B2, type =A2*B2/100. It returns 25.

9.1 The formulas you need

You want	Excel formula	Note
Grams for % w/v	`=A2*B2/100`	% × mL ÷ 100
Mass percent (w/w)	`=A2/(A2+B2)*100`	solute ÷ (solute + solvent)
Solvent mass from volume	`=C2*D2`	mL × g/mL (water 0.99705 at 25 °C)
g/L from % w/v	`=A2*10`	Same number as mg/mL
Molarity from % w/v	`=A2*10/58.44`	Molar mass in the denominator
Molarity from % w/w	`=A2E210/F2`	E2 density, F2 molar mass
% w/w from molarity	`=G2F2/(10E2)`	M × MW ÷ (10ρ)
Dilute a percent	`=C2*V2/C1`	Stock volume, C₁V₁ = C₂V₂
Alligation, strong part	`=T*(Ct-Cl)/(Ch-Cl)`	T = total amount
Relative uncertainty	`=SQRT((0.01/SQRT(3)/C2)^2+(0.12/SQRT(3)/B2)^2)`	Balance and flask

9.2 Step by step

1 Enter the percent and the final volume

Percent in A2, final volume in mL in B2. Numbers only.

Row 2 holds 10 and 250.0.

2 Grams of solute

In C2 type the percent times the volume, divided by 100.

C2 shows 25.00 g.

3 Grams per liter and molarity

In D2 type =A2*10; in E2 type =D2/58.44 for NaCl.

D2 shows 100 g/L; E2 shows 1.711 M.

4 Uncertainty of the solution

In F2 combine the balance (0.01 g) and the flask (0.12 mL); in G2 take 2 × F2 × A2.

F2 shows 0.0361%; G2 shows U = 0.0072% w/v at k = 2.

9.3 Mass percent of several solutes

Put solute names in column A and masses in column B, the solvent last. In C2 type =B2/SUM($B$2:$B$4)*100 and fill down. For 2.50 g NaCl, 1.20 g KCl and 100.0 g water, C2 to C4 show 2.411%, 1.157% and 96.43%, and they add to 100%.

9.4 Why Excel may differ from R or Python

Situation	What happens	Fix
Rounding	Excel ROUND is half away from zero; R and Python round half to even	Round only the final answer
Percent format	Formatting a cell as % multiplies its display by 100	Keep the percent as a plain number (10, not 10%)
Display	Cell format hides digits but keeps them	Not an error

9.5 Charting the recipe

Fill A2:A21 with 1 to 20 (% w/v) and B2:B21 with =A2*250/100. Insert a Scatter chart with straight lines: grams rise in a straight line with the percent, 2.5 g for every 1% in 250 mL.

9.6 Errors you may see

#DIV/0!: the solution mass or molar mass cell is empty.
#VALUE!: a unit typed in a number cell ("25 g").
A result 100 times too small: the percent cell was formatted as %, so 10% is stored as 0.1.

📈 10. How to Calculate a Percent Solution in R

A complete, copy-and-run script that reproduces the percent solution calculator for the headline problem. It prints the recipe, the uncertainty of the solution made, a mass percent, a percent to molarity conversion, a dilution and an alligation, and saves one 300 dpi figure.

No packages needed. Base R covers every step.

10.1 The complete script

R, base only, saves percent_solution.png

# Percent solution recipe with GUM uncertainty, mass percent, percent to molarity and alligation
# StatsUnlock - https://statsunlock.com/percent-solution-calculator/   Base R only.

# ---- 1. Inputs (units in the comments) ----
pct <- 10.0; V <- 250.0          # target % w/v and final volume, mL
tol_bal <- 0.01; tol_V <- 0.12   # balance g; Class A 250 mL flask mL (ASTM E288)

# ---- 2. The recipe: grams = % x mL / 100 ----
m <- pct * V / 100
cat(sprintf("Weigh %.2f g NaCl, make up to %.1f mL -> %g%% w/v (%g g/L)\n", m, V, pct, pct * 10))

# ---- 3. Uncertainty: rectangular tolerances, u = a / sqrt(3) ----
rel <- sqrt((tol_bal / sqrt(3) / m)^2 + (tol_V / sqrt(3) / V)^2)
cat(sprintf("Solution made: %.4f +/- %.4f %% w/v (k = 2), relative %.4f%%\n", pct, 2 * rel * pct, 100 * rel))
stopifnot(abs(m / V * 100 - pct) < 1e-12)
cat("Check: grams / mL x 100 = target. Verified.\n")

# ---- 4. Mass percent: 4.20 g KCl in 50.0 g water ----
m_kcl <- 4.20; m_w <- 50.0
w <- 100 * m_kcl / (m_kcl + m_w)
cat(sprintf("Mass percent KCl = %.2f / %.2f x 100 = %.3f%% w/w (not %.2f%%)\n", m_kcl, m_kcl + m_w, w, 100 * m_kcl / m_w))

# ---- 5. Percent to molarity: 37.3% w/w HCl, density 1.18 g/mL ----
ww <- 37.3; rho <- 1.18; MW <- 36.458
M <- ww * rho * 10 / MW
molal <- 1000 * M / (1000 * rho - M * MW)
cat(sprintf("HCl: M = %.2f M; molality %.2f mol/kg\n", M, molal))

# ---- 6. Dilute 95% to 70% v/v and alligation 30% + 10% -> 25% ----
cat(sprintf("Ethanol: %.1f mL of 95%%, made up to 500.0 mL\n", 70 * 500.0 / 95))
hi <- 30; lo <- 10; t <- 25; tot <- 100
cat(sprintf("Alligation: %.0f mL of %d%% + %.0f mL of %d%% (parts %d:%d)\n",
            tot * (t - lo) / (hi - lo), hi, tot * (hi - t) / (hi - lo), lo, t - lo, hi - t))

# ---- 7. One 300 dpi figure ----
p <- seq(0, 20, by = 0.5)
png("percent_solution.png", width = 6, height = 4, units = "in", res = 300)
plot(p, p * V / 100, type = "l", lwd = 2.5, col = "#2563eb", xlab = "% w/v", ylab = "Solute (g)",
     main = "Grams of solute for 250.0 mL")
points(pct, m, pch = 19, cex = 2, col = "#9333ea")
dev.off()

10.2 Output

Weigh 25.00 g NaCl, make up to 250.0 mL -> 10% w/v (100 g/L)
Solution made: 10.0000 +/- 0.0072 % w/v (k = 2), relative 0.0361%
Check: grams / mL x 100 = target. Verified.
Mass percent KCl = 4.20 / 54.20 x 100 = 7.749% w/w (not 8.40%)
HCl: M = 12.07 M; molality 16.32 mol/kg
Ethanol: 368.4 mL of 95%, made up to 500.0 mL
Alligation: 75 mL of 30% + 25 mL of 10% (parts 15:5)

10.3 Traps

round() rounds half to even; format with sprintf.
In sprintf, a literal percent sign is written %%.
Keep the percent as 10, not 0.10, or every result is 100 times too small.

10.4 What each part does

Block	Purpose
1. Inputs	Target percent, final volume and the two tolerances
2. Recipe	grams = % × mL ÷ 100
3. Uncertainty	Each ± tolerance becomes a/√3, combined in quadrature; U = 2u
Middle blocks	Mass percent of KCl (dividing by the solution, not the water), molarity and molality of 37.3% HCl, a 95% to 70% ethanol dilution and an alligation
Last block	Grams against percent with the headline solution marked, saved at 300 dpi

10.5 Adapting it

Change pct and V for your solution. For % w/w, use the total mass in g for V. For another acid or salt, change the percent, density and molar mass in the molarity block.

📈 11. How to Calculate a Percent Solution in Python

numpymatplotlib

Install once: pip install numpy matplotlib

11.1 The complete script

Python with NumPy and Matplotlib, saves percent_solution.png

# Percent solution recipe with GUM uncertainty, mass percent, percent to molarity and alligation
# StatsUnlock - https://statsunlock.com/percent-solution-calculator/
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

# ---- 1. Inputs (units in the comments) ----
pct, V = 10.0, 250.0             # target % w/v and final volume, mL
tol_bal, tol_V = 0.01, 0.12      # balance g; Class A 250 mL flask mL (ASTM E288)

# ---- 2. The recipe: grams = % x mL / 100 ----
m = pct * V / 100
print(f"Weigh {m:.2f} g NaCl, make up to {V:.1f} mL -> {pct:g}% w/v ({pct * 10:g} g/L)")

# ---- 3. Uncertainty: rectangular tolerances, u = a/sqrt(3) ----
rel = np.sqrt((tol_bal / np.sqrt(3) / m) ** 2 + (tol_V / np.sqrt(3) / V) ** 2)
print(f"Solution made: {pct:.4f} +/- {2 * rel * pct:.4f} % w/v (k = 2), relative {100 * rel:.4f}%")

# ---- 4. Monte Carlo check (JCGM 101), 100 000 draws ----
rng = np.random.default_rng(1)
sim = 100 * rng.uniform(m - tol_bal, m + tol_bal, 100_000) / rng.uniform(V - tol_V, V + tol_V, 100_000)
print(f"Monte Carlo: SD = {sim.std(ddof=1):.5f} % w/v, 95% interval {np.percentile(sim, 2.5):.4f} to {np.percentile(sim, 97.5):.4f}")
assert abs(m / V * 100 - pct) < 1e-12
print("Check: grams / mL x 100 = target. Verified.")

# ---- 5. Mass percent: 4.20 g KCl in 50.0 g water ----
m_kcl, m_w = 4.20, 50.0
w = 100 * m_kcl / (m_kcl + m_w)
print(f"Mass percent KCl = {m_kcl} / {m_kcl + m_w:.2f} x 100 = {w:.3f}% w/w (not {100 * m_kcl / m_w:.2f}%)")

# ---- 6. Percent to molarity: 37.3% w/w HCl, density 1.18 g/mL ----
ww, rho, MW = 37.3, 1.18, 36.458
M = ww * rho * 10 / MW
molal = 1000 * M / (1000 * rho - M * MW)
print(f"HCl: M = {ww} x {rho} x 10 / {MW} = {M:.2f} M; molality {molal:.2f} mol/kg")

# ---- 7. Dilute 95% to 70% v/v (500.0 mL) and alligation 30% + 10% -> 25% ----
print(f"Ethanol: {70 * 500.0 / 95:.1f} mL of 95%, made up to 500.0 mL")
hi, lo, t, tot = 30, 10, 25, 100
print(f"Alligation: {tot * (t - lo) / (hi - lo):.0f} mL of {hi}% + {tot * (hi - t) / (hi - lo):.0f} mL of {lo}% (parts {t - lo}:{hi - t})")

# ---- 8. One 300 dpi figure: grams for 250.0 mL vs % w/v ----
p = np.linspace(0, 20, 41)
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(p, p * V / 100, color="#2563eb", lw=2.5, label="g needed for 250.0 mL")
ax.plot(pct, m, "o", color="#9333ea", ms=11, label=f"{pct:g}% w/v: {m:.2f} g")
ax.set_xlabel("% w/v"); ax.set_ylabel("Solute (g)"); ax.legend(frameon=False)
fig.tight_layout(); fig.savefig("percent_solution.png", dpi=300)

11.2 Output

Weigh 25.00 g NaCl, make up to 250.0 mL -> 10% w/v (100 g/L)
Solution made: 10.0000 +/- 0.0072 % w/v (k = 2), relative 0.0361%
Monte Carlo: SD = 0.00361 % w/v, 95% interval 9.9932 to 10.0068
Check: grams / mL x 100 = target. Verified.
Mass percent KCl = 4.2 / 54.20 x 100 = 7.749% w/w (not 8.40%)
HCl: M = 37.3 x 1.18 x 10 / 36.458 = 12.07 M; molality 16.32 mol/kg
Ethanol: 368.4 mL of 95%, made up to 500.0 mL
Alligation: 75 mL of 30% + 25 mL of 10% (parts 15:5)

11.3 Traps

round() rounds half to even; format with f-strings.
Integer division: 10 // 3 is 3; use / for percents.
numpy.std() defaults to ddof=0; use ddof=1 for replicates.

11.4 What each part does

Block	Purpose
1. Inputs	Target percent, final volume and the two tolerances
2. Recipe	grams = % × mL ÷ 100
3. Uncertainty	Each ± tolerance becomes a/√3, combined in quadrature; U = 2u
Middle blocks	A 100 000-draw Monte Carlo (JCGM 101) agrees with the GUM result; then mass percent, molarity, dilution and alligation
Last block	Grams against percent with the headline solution marked, saved at 300 dpi

11.5 Adapting it

Change pct and V for your solution. For % w/w, use the total mass in g for V. For another acid or salt, change the percent, density and molar mass in the molarity block.

📋 12. Percent Solution Reference Tables: Recipes, Densities and Conversions

12.1 Common percent solutions and their molarity

Solution	Solute	Percent	Per 100 mL	Per 1 L	Molarity
Normal saline	NaCl	0.9% w/v	0.9 g	9 g	0.154 M
Hypertonic saline	NaCl	3% w/v	3 g	30 g	0.5133 M
Dextrose (glucose) 5%	C₆H₁₂O₆	5% w/v	5 g	50 g	0.2775 M
SDS 10%	C₁₂H₂₅NaO₄S	10% w/v	10 g	100 g	0.3468 M
Sodium bicarbonate 8.4%	NaHCO₃	8.4% w/v	8.4 g	84 g	0.9999 M
Sucrose 20%	C₁₂H₂₂O₁₁	20% w/v	20 g	200 g	0.5843 M
Agarose gel 1%	agarose	1% w/v	1 g	10 g	not used
Ethanol 70%	C₂H₅OH	70% v/v	70 mL	700 mL	12 M

Molarity = % w/v × 10 ÷ molar mass (IUPAC 2021 atomic weights); ethanol uses 0.78945 g/mL at 20 °C for the pure liquid. Saline composition as in Reddy et al. (2016). Last checked: October 2026.

12.2 Sodium chloride: % w/w, density, % w/v and molarity at 20 °C

% w/w	Density (g/mL)	% w/v	g/L	Molarity (M)	Molality (mol/kg)
1	1.0053	1.005	10.1	0.1720	0.1728
2	1.0125	2.025	20.2	0.3465	0.3492
4	1.0268	4.107	41.1	0.7028	0.7130
6	1.0413	6.248	62.5	1.0691	1.0922
8	1.0559	8.447	84.5	1.4454	1.4880
10	1.0707	10.707	107.1	1.8321	1.9013
12	1.0857	13.028	130.3	2.2294	2.3334
16	1.1162	17.859	178.6	3.0560	3.2593
20	1.1478	22.956	229.6	3.9281	4.2779
26	1.1972	31.127	311.3	5.3264	6.0122

Densities from the volumetric property compilation of Rogers and Pitzer (1982) as tabulated by standard handbooks; 26% is close to saturation (about 26.4% w/w at 20 °C). Last checked: October 2026.

12.3 Concentrated reagents: label percent to molarity

Reagent	Formula	Assay (% w/w)	Density (g/mL)	% w/v	Molarity (M)	mL for 1 L of 1 M
Hydrochloric acid	HCl	37.3	1.18	44.0	12.07	82.8
Nitric acid	HNO₃	70.0	1.41	98.7	15.66	63.8
Sulfuric acid	H₂SO₄	96.5	1.84	177.6	18.11	55.2
Phosphoric acid	H₃PO₄	85.0	1.685	143.2	14.62	68.4
Acetic acid, glacial	CH₃COOH	99.7	1.05	104.7	17.43	57.4
Ammonia solution	NH₃	29.0	0.9	26.1	15.32	65.3
Hydrogen peroxide	H₂O₂	30.0	1.11	33.3	9.79	102.1

Typical label values; read your bottle, because lots vary. Molarity = % w/w × density × 10 ÷ molar mass. Last checked: October 2026.

12.4 Density of water (for mass percent with a solvent volume)

Temperature (°C)	Density (g/mL)	Mass of 100.0 mL (g)	Mass of 250.0 mL (g)
4	0.99997	99.997	249.99
15	0.99910	99.910	249.78
18	0.99860	99.860	249.65
20	0.99821	99.821	249.55
22	0.99777	99.777	249.44
25	0.99705	99.705	249.26
30	0.99565	99.565	248.91
37	0.99333	99.333	248.33

Air-free water, from the formula of Tanaka et al. (2001). Last checked: October 2026.

12.5 Unit conversions for percent solutions

From	To	Multiply by	Example
% w/v	g/L (= mg/mL)	10	0.9% = 9 g/L
% w/v	mg/L (dilute water)	10 000	0.001% = 10 mg/L
% w/w	ppm by mass	10 000	0.5% = 5000 ppm
% w/w	% w/v	density (g/mL)	10% NaCl × 1.0707 = 10.71%
% w/v	M	10 ÷ molar mass	10% NaCl: 1.711 M
% v/v	% w/v	density of pure solute	70% ethanol × 0.7893 = 55.25%
US fl oz	mL	29.5735	8 fl oz = 236.6 mL
US gallon	mL	3785.41	1 gal of 10% w/v = 378.5 g

US customary units from NIST Handbook 44, Appendix C (exact definitions). Last checked: October 2026.

12.6 Class A volumetric flasks

Capacity (mL)	Tolerance (± mL)	Relative	u = a/√3 (mL)
25	0.03	0.120%	0.0173
50	0.05	0.100%	0.0289
100	0.08	0.080%	0.0462
250	0.12	0.048%	0.0693
500	0.20	0.040%	0.1155
1000	0.30	0.030%	0.1732

Source: ASTM E288 Class A, as listed by DWK Life Sciences. Calibrated to contain at 20 °C. Last checked: October 2026.

📈 13. Percent Solution Example Results: Worked Problems

Eight worked problems that cover what a percent solution calculator meets: a textbook mass percent, several solutes, a given density, percent to molarity, clinical saline, a biology gel, pharmacy alligation and an impossible request. Each number was checked in Python.

TEXTBOOK CASE

Calculate the mass percent of KCl in the solution

Divide by the solution, not the water.

4.20 g of KCl is dissolved in 50.0 g of water. What is the mass percent of KCl?

KCl 4.20 gwater 50.0 gsolution 54.20 g7.749%not 8.40%

Quantity	Value	Note
Solution mass	54.20 g	4.20 + 50.0
Mass percent KCl	7.749% w/w	4.20 ÷ 54.20 × 100
If divided by water	8.40%	wrong: 4.20 ÷ 50.0 × 100

Using the water mass overstates the percent by 8%.

What it means: Every 100 g of this solution holds 7.749 g of KCl.

How to write it: "The solution was 7.749% w/w KCl (4.20 g KCl in 54.20 g of solution)."

SEVERAL SOLUTES

Concentration of each solute in mass percent

One total, several shares.

2.50 g of NaCl and 1.20 g of KCl are dissolved in 100.0 g of water. Give the mass percent of each.

NaCl 2.50 gKCl 1.20 gwater 100.0 gtotal 103.70 gsum 100%

Quantity	Value	Note
NaCl	2.411% w/w	2.50 ÷ 103.70 × 100
KCl	1.157% w/w	1.20 ÷ 103.70 × 100
Water	96.43% w/w	100.0 ÷ 103.70 × 100

Each solute is a share of the same total mass.

What it means: The three percents add to 100%, a quick check on any mass percent problem.

How to write it: "The solution contained 2.411% w/w NaCl and 1.157% w/w KCl."

GIVEN DENSITY

Mass percent when the solvent is measured by volume

Volume × density = mass.

15.0 g of sucrose is dissolved in 250.0 mL of water at 25 °C (0.99705 g/mL). What is the mass percent?

sucrose 15.0 gwater 250.0 mLρ 0.99705 g/mLwater 249.26 g5.676%

Quantity	Value	Note
Water mass	249.26 g	250.0 × 0.99705
Solution mass	264.26 g	15.0 + 249.26
Mass percent	5.676% w/w	15.0 ÷ 264.26 × 100

Convert the water volume to grams first.

What it means: With water at 1.000 g/mL you would get 5.660%; the density matters in the third figure.

How to write it: "The sucrose solution was 5.676% w/w (15.0 g in 250.0 mL of water at 25 °C)."

PERCENT TO MOLARITY

10.0% w/w NaCl to % w/v and molarity

Density turns w/w into w/v.

A 10.0% w/w NaCl solution has a density of 1.0707 g/mL at 20 °C. Find % w/v, molarity and molality.

10.0% w/wρ 1.0707 g/mL10.71% w/v1.832 M1.901 mol/kg

Quantity	Value	Note
% w/v	10.71%	10.0 × 1.0707
Molarity	1.832 M	10.0 × 1.0707 × 10 ÷ 58.44
Molality	1.901 mol/kg	(10.0 ÷ 58.44) ÷ 0.0900 kg

% w/v is larger than % w/w because the density is above 1.

What it means: Treating 10% w/w as 10% w/v would understate the molarity by 7%.

How to write it: "The 10.0% w/w NaCl solution (1.0707 g/mL, 20 °C) is 1.832 M."

CLINICAL

Normal saline: 0.9% w/v in mmol/L

Percent to molarity without a density.

Normal saline is labeled 0.9% w/v sodium chloride. How many grams per liter and mmol/L of sodium?

0.9% w/v9.0 g/L58.44 g/mol0.154 M154 mmol/L Na⁺

Quantity	Value	Note
Grams per liter	9.0 g/L	0.9 × 10
Molarity	0.154 M	9.0 ÷ 58.44
Sodium and chloride	154 mmol/L each	NaCl gives one of each

Saline carries more sodium and chloride than plasma.

What it means: That is why large volumes of saline can raise chloride, as reviewed by Reddy et al. (2016).

How to write it: "Normal saline (0.9% w/v NaCl) contains 154 mmol/L each of Na⁺ and Cl⁻."

BIOLOGY LAB

A 1.0% agarose gel in 50 mL

Percent w/v in a molecular biology lab.

A student needs 50.0 mL of 1.0% w/v agarose in 1X TAE for a DNA gel.

1.0% w/v50.0 mL0.50 gboil until cleartop up water

Quantity	Value	Note
Agarose	0.50 g	1.0 × 50.0 ÷ 100
Buffer	50.0 mL 1X TAE	weigh the flask before heating
After boiling	top up to the start mass	water lost raises the percent

Grams rise in step with the gel volume.

What it means: Gels from 0.7% to 2% separate different DNA sizes (Lee et al., 2012).

How to write it: "DNA was separated on a 1.0% w/v agarose gel (0.50 g in 50.0 mL 1X TAE)."

PHARMACY

Alligation: 15% zinc oxide ointment from 20% and base

Parts from the cross.

A pharmacy needs 100 g of 15% w/w zinc oxide ointment from 20% ointment and plain petrolatum (0%).

strong 20%weak 0%target 15%parts 15 : 575 g + 25 g

Quantity	Value	Note
20% ointment	75 g	15 parts of 20
Petrolatum	25 g	5 parts of 20
Check	15% w/w	(20 × 75 + 0 × 25) ÷ 100

Three quarters strong, one quarter base.

What it means: Alligation is exact by mass, which suits ointments and creams.

How to write it: "100 g of 15% w/w zinc oxide ointment was compounded from 75 g of 20% ointment and 25 g of petrolatum."

IMPOSSIBLE

A 40% w/w sodium chloride solution

Past the solubility limit.

A student is asked to make 100 g of 40% w/w NaCl in water at 20 °C.

target 40% w/wsaturation about 26.4%40 g in 60 g waterneeds 66.7 g/100 gnot possible

Quantity	Value	Note
Salt per 100 g water	66.7 g	40 ÷ 60 × 100
Solubility at 20 °C	about 36 g per 100 g water	about 26.4% w/w
Verdict	Impossible	solid will not dissolve

The request is well past saturation.

What it means: Arithmetic alone does not catch this. Check solubility before you weigh.

How to write it: "A 40% w/w NaCl solution cannot be made at 20 °C; saturation is about 26.4% w/w."

✏️ 14. How Do You Make a Percent Solution in the Lab? Steps (SOP)

The written method, calculator keys and a short standard operating procedure for the headline problem: prepare 250.0 mL of 10% w/v sodium chloride. School students do this under a teacher's supervision and the school's own risk assessment.

14.1 The written method

Name the percent. 10% w/v means 10 g per 100 mL of solution.
Check units. Grams and milliliters.
Formula. m = % × V ÷ 100.
Substitute. m = 10 × 250.0 mL ÷ 100 = 25.00 g.
Also. 100.0 g/L; 100.0 ÷ 58.44 = 1.711 M.
Check. 25.00 g ÷ 250.0 mL × 100 = 10.00% ✓

14.2 On a scientific calculator

Step	Casio fx-991EX / fx-82 and TI-30XS keys	Display
Grams for % w/v	10×250÷100=	25
Mass percent KCl	4.2÷(4.2+50)×100=	7.749077491
Molarity of 37.3% HCl	37.3×1.18×10÷36.458=	12.07252181
Ethanol 95% to 70%	70×500÷95=	368.4210526

14.3 The lab SOP

Purpose

Prepare 250.0 mL of 10% w/v NaCl and record its concentration with uncertainty.

Equipment

Top-loading or analytical balance readable to 0.01 g; weighing boat; Class A 250 mL volumetric flask (±0.12 mL, ASTM E288) with stopper; beaker; glass funnel; wash bottle; dropper.

Reagents

Sodium chloride, ACS reagent grade (99.0% or better); deionized water (ASTM Type II or better).

Hazards and controls

Sodium chloride is not classified as hazardous on typical supplier safety data sheets; read the current SDS. Wear safety goggles. If you prepare percent solutions from concentrated acids or bases, they are corrosive (GHS skin corrosion category 1): work in a fume hood with gloves and always add acid to water.

Procedure

Tare the weighing boat and weigh 25.00 g of NaCl.
Transfer to a beaker with about 150 mL of water; rinse the boat into the beaker.
Stir until fully dissolved.
Pour through a funnel into the 250 mL flask; rinse the beaker and funnel into the flask three times.
Add water to about 1 cm below the mark, then dropwise to the mark at 20 °C.
Stopper and invert 15 to 20 times.
Label with name, percent and type (w/v), date and initials.

Record sheet

Item	Value	Unit
NaCl mass and lot	25.00 (lot 2610-B)	g
Balance ID	BAL-02 (±0.01 g)
Flask volume and ID	250.0 (VF-07)	mL
Temperature	20.5	°C
Percent made	10.0000 ± 0.0072	% w/v (k = 2)

Calculation

% w/v = 25.00 g ÷ 250.0 mL × 100 = 10.00%; u/% = √[(0.01/√3/25.00)² + (0.12/√3/250.0)²] = 0.0361%; U = 0.0072% w/v.

Acceptance criteria

Mass within ±0.02 g of target; Class A flask within tolerance (Section 12.6); relative expanded uncertainty under 0.5%; meniscus on the mark at eye level. These are teaching-lab criteria; follow your course or SOP limits where they differ.

Sources of error and their direction

Solid left in the weighing boat or beaker: percent low.
Damp or caked salt (absorbed water): percent low.
Overshooting the mark: percent low.
Making up warm, then cooling: percent high.
Not mixing after making up: uneven concentration.

14.4 Practice problems

1. How many grams of glucose for 500.0 mL of 5.0% w/v?

5.0 × 500.0 ÷ 100 = 25 g

2. 12.0 g of NaOH is dissolved in 88.0 g of water. Mass percent?

12.0 ÷ 100.0 × 100 = 12.0% w/w

3. 25.0 g of sugar in 125.0 g of water. Mass percent?

25.0 ÷ 150.0 × 100 = 16.7% w/w

4. What volume of ethanol is in 750 mL of 40% v/v?

40 × 750 ÷ 100 = 300 mL

5. How much water and salt for 200.0 g of 15.0% w/w NaCl?

30.0 g NaCl + 170.0 g water

6. Molarity of 70.0% w/w HNO₃, density 1.41 g/mL?

70.0 × 1.41 × 10 ÷ 63.012 = 15.7 M

7. Percent w/v of 0.500 M KCl (74.55 g/mol)?

0.500 × 74.55 ÷ 10 = 3.73% w/v

8. Stock volume for 250 mL of 2% from 10% w/v?

2 × 250 ÷ 10 = 50 mL, made up to 250 mL

9. Mix 60 mL of 50% with 40 mL of 20%. Final percent?

(50 × 60 + 20 × 40) ÷ 100 = 38%

10. Grams of CuSO₄·5H₂O for 100 mL of 2.0% w/v anhydrous CuSO₄?

2.0 × 249.68 ÷ 159.60 = 3.13 g

14.5 Mistakes that lose marks or fail an audit

Dividing by the solvent mass instead of the solution mass.
Leaving out w/w, w/v or v/v after the percent.
Treating % w/w as % w/v for a dense solution.
Adding 100 mL of water instead of making up to 100 mL.
Weighing a hydrate as if it were anhydrous.
Formatting the percent as 0.10 in one place and 10 in another.
Water into acid instead of acid into water.

14.6 Pre-Lab and Post-Lab Questions

Pre-lab: Why is a w/v solution made up to the mark instead of adding a measured volume of water?

The solute takes up volume. Making up to the mark fixes the final volume, which is what % w/v divides by.

Pre-lab: How many grams of NaCl for 250.0 mL of 10% w/v?

10 × 250.0 ÷ 100 = 25.00 g.

Pre-lab: Why weigh by difference or tare the weighing boat?

So the mass recorded is only the solute, not the container.

Pre-lab: What is this solution in molarity?

100.0 g/L ÷ 58.44 g/mol = 1.711 M.

Post-lab: You weighed 25.08 g instead of 25.00 g. What percent did you make?

25.08 ÷ 250.0 × 100 = 10.03% w/v.

Post-lab: You overshot the mark by 1.0 mL. Effect?

25.00 ÷ 251.0 × 100 = 9.96% w/v, slightly low.

Post-lab: Which input dominated the uncertainty?

The flask and the balance shared it: 0.12/250 is 0.048% and 0.01/25 is 0.040%, so the flask was slightly larger (59% of the variance).

Post-lab: Why would 10% w/w NaCl not be 10 g per 100 mL?

Its density is 1.0707 g/mL, so 100 mL weighs 107.07 g and holds 10.71 g of NaCl.

✅ 15. Which Percent Should You Use?

You have	You want	Percent solution calculator mode	Real example
A solid and a volume	Grams to weigh	Make a percent solution (w/v)	10% NaCl, 250.0 mL: 25.00 g
A cream, syrup or dense solution	Grams of solute and solvent	Make a percent solution (w/w)	20% sucrose, 500.0 g: 100.0 g + 400.0 g
A liquid solute	mL to measure	Make a percent solution (v/v)	70% ethanol from pure, 100 mL: 70 mL
Masses of solute and solvent	Mass percent	Mass percent of a solution	4.20 g KCl + 50.0 g water: 7.749%
Several solutes	Mass percent of each	Mass percent (add rows)	NaCl 2.411%, KCl 1.157%
A reagent bottle label	Molarity	Percent to molarity	37.3% HCl: 12.07 M
A molarity	Percent w/w or w/v	Percent to molarity (M in)	1.832 M NaCl: 10.0% w/w
A strong percent stock	A weaker percent	Dilute a percent solution	95% to 70% ethanol: 368.4 mL in 500.0 mL
Two strengths on the shelf	A strength in between	Mix (alligation)	30% + 10% to 25%: 75 + 25

Use % w/v when

Dissolving a solid in water for lab or pharmacy use.
The solution is dilute (under about 10%).
You will dispense it by volume.

Use % w/w when

The solution is dense (acids, syrups, brines).
Temperature changes the volume.
You need molality or a gravimetric standard.

🔧 16. Common Percent Solution Mistakes and Troubleshooting

Studies of chemistry students find that concentration, including percent and its link to molarity, is one of the most error-prone topics (Raviolo et al., 2021; Vaccaro et al., 2022). The percent solution calculator guards against each mistake below.

Symptom	Cause	Fix
Mass percent too high (8.40% instead of 7.749%)	Divided by the solvent instead of the solution	Divide by solute + solvent
Molarity off by about 7% for 10% NaCl	Treated w/w as w/v	Multiply % w/w by the density
Answer 10 times or 1000 times off	L and mL, or g and mg, mixed	% w/v uses g and mL; g/L = % w/v × 10
70% ethanol short of volume	Volumes added, not made up	Make up to the mark in a flask
Solution weaker than expected	Hydrate weighed as if anhydrous	Use the hydrate correction
Solution weaker than expected	Low-purity material	Enter the assay %; the calculator weighs more
Solid will not dissolve	Above the solubility (NaCl about 26% w/w at 20 °C)	Warm, or choose a lower percent
Agarose gel too soft or too firm	Water lost on boiling	Weigh the flask before and after; top up with water
Alligation gives an error	Target not between the two strengths	A mixture always lies between them
Excel gives #VALUE!	Units typed into number cells	Numbers only; units in the header

⚠️ 17. Assumptions and Limitations

Assumption	How to check	If it fails, the error goes
Percent type is stated correctly	Label, protocol or exam wording	w/w read as w/v: off by the density
The density is of the solution at the stated temperature	Supplier sheet or a density meter	Molarity and % w/w off in proportion
The solute dissolves completely	Clear solution, no residue	Real percent lower than calculated
Final volume is made up to the mark	Volumetric flask, not a beaker	Adding a fixed volume: % off by the volume change
Volumes add in mixing and alligation by volume	Dilute water solutions only	Ethanol, acids: mix by mass instead
Tolerances are rectangular and independent	Eurachem QUAM uses triangular for glassware	Rectangular gives a larger, safer U
Molar mass and purity are right	Certificate of analysis	Same relative error in molarity
ppm equals mg/L	Only when the density is near 1 g/mL	Use the density to convert

Better methods for the highest accuracy: prepare by mass (gravimetric) and correct for air buoyancy, measure the density with an oscillating U-tube meter, and verify with an independent assay such as titration or refractometry.

🎯 18. Conclusion

Your result

___

What the percent solution calculator does for the bench

Percent looks simple, but three definitions share one symbol, density links them, and purity, hydrates and shrinkage change what you weigh. This percent solution calculator keeps the type of percent visible at every step, converts to molarity and molality with the density, handles several solutes, dilutes and mixes, and puts an uncertainty on the solution you make.

Watch out for

Dividing by the solvent instead of the solution.
Swapping w/w and w/v for dense solutions.
Hydrates and low-purity materials.
Adding volumes instead of making up to the mark.
A target outside the two strengths in alligation.

Next steps

Check a batch by measurement and record replicate readings. The mean calculator and standard deviation calculator summarize repeats, and the coefficient of variation calculator gives the precision. Whatever the percent, start and finish with the percent solution calculator.

❓ 19. Frequently Asked Questions

Q1. How do you calculate a percent solution?

Multiply the percent by the amount of solution and divide by 100. For % w/v the amount is the final volume in mL and the answer is grams: 10% w/v in 250.0 mL needs 10 × 250.0 ÷ 100 = 25.00 g of solute, dissolved and made up to 250.0 mL. For % w/w, use the total mass of solution instead.

Q2. What is the formula for percent solution?

There are three formulas. % w/w = grams of solute ÷ grams of solution × 100. % w/v = grams of solute ÷ mL of solution × 100. % v/v = mL of pure solute ÷ mL of solution × 100. The United States Pharmacopeia defines all three, so always write w/w, w/v or v/v after the number.

Q3. How do you calculate the mass percent of a solution?

Divide the mass of the solute by the mass of the whole solution, then multiply by 100. The solution mass is the solute plus the solvent. For 4.20 g of KCl in 50.0 g of water, mass percent = 4.20 ÷ 54.20 × 100 = 7.749%. Dividing by the 50.0 g of water alone gives 8.40%, a common mistake.

Q4. How do you calculate mass percent given density?

Use the density to turn a volume into a mass, then divide as usual. Water at 25 °C is 0.99705 g/mL, so 250.0 mL weighs 249.26 g. Dissolving 15.0 g of sugar gives 15.0 ÷ (15.0 + 249.26) × 100 = 5.676% by mass. If you know % w/v and the solution density instead, % w/w = % w/v ÷ density.

Q5. How do you calculate molarity from a percent solution?

For a % w/w solution, use M = (% × density × 10) ÷ molar mass, with density in g/mL. Concentrated hydrochloric acid at 37.3% and 1.18 g/mL gives 37.3 × 1.18 × 10 ÷ 36.458 = 12.07 M. For a % w/v solution no density is needed: M = % × 10 ÷ molar mass, so 0.9% saline is 0.154 M.

Q6. How do you convert molarity to percent?

Multiply molarity by molar mass to get grams per liter, then divide by 10 for % w/v. A 1.711 M NaCl solution holds 1.711 × 58.44 = 100.0 g/L, which is 10.00% w/v. For % w/w, divide the % w/v by the solution density: 1.832 M NaCl at 1.0707 g/mL is 10.71 ÷ 1.0707 = 10.0% w/w.

Q7. What is the difference between w/v, w/w and v/v percent?

Percent w/v is grams of solute per 100 mL of solution and suits solids dissolved in water. Percent w/w is grams per 100 g of solution and suits dense or concentrated mixtures such as acids and creams. Percent v/v is mL of liquid per 100 mL and suits liquids such as ethanol. They match only when the density is 1 g/mL.

Q8. How do you make a 10% w/v solution?

Weigh 10 g of solute for every 100 mL of final solution, dissolve it in less solvent than you need, then make up to the final volume in a volumetric flask. For 250.0 mL, weigh 25.00 g; for 1 L, weigh 100.0 g. Do not add 100 mL of water to 10 g, because the solute takes up volume too.

Q9. How do you calculate volume percent of a solution?

Divide the volume of the pure liquid solute by the final volume of the solution and multiply by 100. 70 mL of ethanol made up to 100 mL with water is 70% v/v. Use the final volume after mixing, not the sum of the two liquids, because ethanol and water shrink by a few percent when they are mixed together.

Q10. How do you calculate the concentration of each solute in mass percent?

Add up all the masses to get the total solution mass, then divide each solute mass by that total. For 2.50 g NaCl and 1.20 g KCl in 100.0 g of water, the total is 103.7 g, so NaCl is 2.411% and KCl is 1.157% by mass. The solutes and the water together always add to 100%.

Q11. How do you dilute a percent solution?

Use C1V1 = C2V2 with both percents of the same type. To make 500.0 mL of 70% v/v ethanol from 95%, take 70 × 500.0 ÷ 95 = 368.4 mL of the 95% and make up to 500.0 mL with water. For % w/w solutions, dilute by mass instead: C1m1 = C2m2, weighing both the stock and the final mixture.

Q12. How do you use alligation to mix two percent solutions?

Write the two strengths and the target. The parts of the strong solution equal target minus weak; the parts of the weak equal strong minus target. For 25% from 30% and 10%, use 15 parts of 30% and 5 parts of 10%. For 100 mL, that is 75 mL of 30% and 25 mL of 10%.

Q13. How much salt is in 0.9% saline?

Normal saline is 0.9% w/v sodium chloride, so it holds 0.9 g of NaCl per 100 mL, or 9.0 g per liter. That equals 9.0 ÷ 58.44 = 0.154 mol/L, which gives 154 mmol/L of sodium and 154 mmol/L of chloride. To make 1 L, dissolve 9.0 g of NaCl and make up to 1000 mL with water.

Q14. How do you make a 1% agarose gel?

A 1% agarose gel is 1% w/v, so weigh 1 g of agarose per 100 mL of buffer. For a 50 mL gel, add 0.50 g of agarose to 50 mL of TAE or TBE, heat until fully clear, and top up with water if some evaporated while boiling. Let it cool to about 55 °C before pouring.

Q15. How do you correct a percent solution for purity or a hydrate?

Divide the mass by the purity as a fraction, and multiply by the hydrate factor. For 5% w/v anhydrous copper sulfate made from the pentahydrate, multiply by 249.68 ÷ 159.60 = 1.564. For 100 mL, that is 5.00 g × 1.564 = 7.82 g of CuSO4·5H2O. A 99.0% pure salt needs 1.0101 times as much.

Q16. Is percent by mass the same as percent by weight?

Yes. In chemistry, percent by mass, mass percent, weight percent, wt% and % w/w all mean grams of solute in 100 g of solution. The older word weight is still used on reagent labels. Percent w/v is different, because it divides by the solution volume rather than its mass, so it needs the density to compare.

Q17. How do you convert percent to ppm?

For a % w/w solution, multiply by 10 000: 0.5% w/w is 5000 ppm by mass. For a dilute water solution, % w/v times 10 000 also gives mg/L, so 0.001% w/v is 10 mg/L, about 10 ppm. For dense or non-water solutions, use the density, because ppm by mass and mg/L then differ.

Q18. How do you calculate a percent solution in Excel?

Put the percent in A2 and the final volume in mL in B2, then type =A2*B2/100 to get the grams of solute. For mass percent, put the solute mass in A2 and the solvent mass in B2 and type =A2/(A2+B2)*100. Both give the same answers as this calculator. Keep units out of the number cells.

Q19. How do you calculate a percent solution in Python or R?

In Python, grams = pct * volume / 100; in R, grams <- pct * volume / 100. Both give 25 for 10% w/v in 250 mL. The complete scripts in Sections 10 and 11 also print the uncertainty of the solution made, the mass percent of KCl, the molarity of 37.3% HCl, an ethanol dilution and an alligation.

Q20. Why does my percent solution come out wrong?

The usual causes are dividing by the solvent instead of the solution, treating % w/w as % w/v for a dense solution, weighing a hydrate as if it were anhydrous, and adding a fixed volume of water instead of making up to the mark. Check the label for purity, state the percent type, and use a volumetric flask.

📑 20. Cite This Tool

APA 7th edition

StatsUnlock. (2026). Percent solution calculator [Interactive laboratory tool]. https://statsunlock.com/percent-solution-calculator/

BibTeX

@misc{statsunlock_percent_solution_2026, title={Percent Solution Calculator}, author={{StatsUnlock Team}}, year={2026}, note={Interactive laboratory tool}, url={https://statsunlock.com/percent-solution-calculator/}}

Methods sentence (fills from your last calculation)

A 10% w/v NaCl solution was prepared by dissolving 25.00 g of NaCl and making up to 250.0 mL (10.0000 ± 0.0072% w/v, k = 2, JCGM 100:2008), using the StatsUnlock Percent Solution Calculator (2026).

🔗 21. Related Tools

descriptive statistics

Mean Calculator

Average replicate weighings or assay results for a batch.

descriptive statistics

Standard Deviation Calculator

Spread of repeated preparations, with the n − 1 formula.

descriptive statistics

Coefficient of Variation Calculator

Batch-to-batch precision of a percent solution as %CV.

descriptive statistics

Standard Error of the Mean Calculator

How precise the average of replicate assays is.

descriptive statistics

Confidence Interval Calculator

A t-based interval for a measured percent or molarity.

descriptive statistics

Descriptive Statistics Calculator

Every summary of a set of QC results in one table.

statistical models

Simple Linear Regression Calculator

Fit density or refractive index against percent to check a batch.

lab and chemistry

Dilution Calculator

Dilute any stock with C₁V₁ = C₂V₂, serial dilutions and acids.

Use these to dilute your solution and to report the statistics behind it: replicate spread, precision and calibration.

📖 22. Glossary of Terms

Term	Plain-English meaning
Alligation	A pharmacy method for finding the parts of two strengths to mix to a target strength.
Anhydrous	Without water of crystallization (CuSO₄ rather than CuSO₄·5H₂O).
Assay (purity)	The percent of the named substance in the material, from the label or certificate.
Density (ρ)	Mass per volume of the solution, in g/mL; links % w/w and % w/v.
g/L	Grams per liter; equals % w/v × 10 and the same number as mg/mL.
Hydrate	A salt with water in its crystal; weigh more of it for the same anhydrous percent.
Make up to the mark	Fill a volumetric flask until the meniscus sits on the line.
Mass percent (% w/w)	Grams of solute per 100 g of solution; also weight percent, wt%.
Molality	Moles of solute per kilogram of solvent.
Molarity (M)	Moles of solute per liter of solution.
Mole fraction	Moles of one component divided by the total moles.
Normal saline	0.9% w/v sodium chloride, 154 mmol/L.
ppm	Parts per million; 1% w/w = 10 000 ppm by mass.
Saturated solution	A solution holding as much solute as can dissolve at that temperature.
Solute	The substance dissolved (salt, sugar, ethanol).
Solution	Solute plus solvent; the whole mixture.
Solvent	The liquid that dissolves the solute, usually water.
Uncertainty (U)	The ± range on a result; U = 2u gives about 95% coverage.
Volume percent (% v/v)	mL of pure liquid solute per 100 mL of solution.
Weight in volume (% w/v)	Grams of solute per 100 mL of solution.

📚 23. References

Peer-reviewed sources behind this percent solution calculator: solution densities, water density, ethanol and water mixing, atomic weights, saline and hand sanitizer composition, gel preparation, uncertainty, and research on how students learn concentration and pharmacy calculations. Standards (JCGM 100:2008, ASTM E288, USP General Notices, NIST Handbook 44) are named where they are used. Every DOI checked October 2026.

Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. BMJ, 331(7521), 903. https://doi.org/10.1136/bmj.331.7521.903
Chong, S. H. (2016). Wither the concepts of mole and concentration: Conceptual confusion in applying M₁V₁ = M₂V₂. Universal Journal of Educational Research, 4(5), 1158–1162. https://doi.org/10.13189/ujer.2016.040527
Cumming, G., Fidler, F., & Vaux, D. L. (2007). Error bars in experimental biology. Journal of Cell Biology, 177(1), 7–11. https://doi.org/10.1083/jcb.200611141
Dell, K. (2025). Evaluation of pharmaceutical calculations knowledge retention among pharmacy students. American Journal of Pharmaceutical Education, 89(11), 101635. https://doi.org/10.1016/j.ajpe.2025.101635
D’Souza, B., & Adunlin, G. (2023). Correlating students’ metacognitive monitoring with performance on calculations concepts. American Journal of Pharmaceutical Education, 87(8), 100258. https://doi.org/10.1016/j.ajpe.2023.100258
Gültepe, N., & Erdem, A. R. (2026). Diagnosing teacher candidates’ reasoning on solution concentration: A theoretical analysis of definitional and procedural difficulties. Chemistry Education Research and Practice, 27(3), 1073–1088. https://doi.org/10.1039/d5rp00422e
Golin, A. P., Choi, D., & Ghahary, A. (2020). Hand sanitizers: A review of ingredients, mechanisms of action, modes of delivery, and efficacy against coronaviruses. American Journal of Infection Control, 48(9), 1062–1067. https://doi.org/10.1016/j.ajic.2020.06.182
Kragten, J. (1994). Calculating standard deviations and confidence intervals with a universally applicable spreadsheet technique. Analyst, 119(10), 2161–2165. https://doi.org/10.1039/AN9941902161
Lee, P. Y., Costumbrado, J., Hsu, C.-Y., & Kim, Y. H. (2012). Agarose gel electrophoresis for the separation of DNA fragments. Journal of Visualized Experiments, (62), e3923. https://doi.org/10.3791/3923
Marsh, K. N., & Richards, A. E. (1980). Excess volumes for ethanol + water mixtures at 10-K intervals from 278.15 to 338.15 K. Australian Journal of Chemistry, 33(10), 2121–2132. https://doi.org/10.1071/CH9802121
McGlashan, M. L. (1995). Amount of substance and the mole. Metrologia, 31(6), 447–455. https://doi.org/10.1088/0026-1394/31/6/004
Meija, J., Coplen, T. B., Berglund, M., Brand, W. A., De Bièvre, P., Gröning, M., Holden, N. E., Irrgeher, J., Loss, R. D., Walczyk, T., & Prohaska, T. (2016). Atomic weights of the elements 2013 (IUPAC Technical Report). Pure and Applied Chemistry, 88(3), 265–291. https://doi.org/10.1515/pac-2015-0305
Prohaska, T., Irrgeher, J., Benefield, J., Böhlke, J. K., Chesson, L. A., Coplen, T. B., Ding, T., Dunn, P. J. H., Gröning, M., Holden, N. E., Meijer, H. A. J., Moossen, H., Possolo, A., Takahashi, Y., Vogl, J., Walczyk, T., Wang, J., Wieser, M. E., Yoneda, S., Zhu, X.-K., & Meija, J. (2022). Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure and Applied Chemistry, 94(5), 573–600. https://doi.org/10.1515/pac-2019-0603
Raviolo, A., Farré, A. S., & Traiman Schroh, N. (2021). Students’ understanding of molar concentration. Chemistry Education Research and Practice, 22(2), 486–497. https://doi.org/10.1039/d0rp00344a
Reddy, S., Weinberg, L., & Young, P. (2016). Crystalloid fluid therapy. Critical Care, 20(1), 59. https://doi.org/10.1186/s13054-016-1217-5
Rogers, P. S. Z., & Pitzer, K. S. (1982). Volumetric properties of aqueous sodium chloride solutions. Journal of Physical and Chemical Reference Data, 11(1), 15–81. https://doi.org/10.1063/1.555660
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Percent Solution Calculator with Steps (Free) | StatsUnlock

⚡ 0. Quick Answer

⭐ Key Takeaways

📚 1. What Is a Percent Solution Calculator?

Quick answers to the questions people ask most

How do you make a percent solution?

How do you calculate the mass percent of a solution?

How do you calculate mass percent given the density?

How do you calculate molarity from a percent solution?

How do you calculate volume percent of a solution?

What is the difference between w/v, w/w and v/v?

🧮 2. Enter Your Percent Solution

📊 3. Results and Step-by-Step Working

Working (Given, Required, Equation, Substitute, Solve)

Uncertainty budget

Step by step

Full results table

Your solution, drawn from the numbers

Charts

1.

2.

3.

4.

🧠 4. Understanding Your Percent Solution Result, In Detail

4.1 What the result means

4.2 How sure you can be

4.3 Which percent is this?

4.4 The detail that changes the answer

4.5 What to do next

4.6 Why % w/w and % w/v differ for the same solution

4.7 Which input usually dominates the uncertainty

4.8 Volume percent and shrinkage

✍ 5. How to Write a Percent Solution in a Report: Detailed Results

5.1 What a detailed result must contain

5.2 Weak vs detailed

5.3 Seven ready-to-copy write-ups

∑ 6. What Is the Percent Solution Formula? All Formulas Used

🔀 7. How Do You Calculate a Percent Solution? Flowchart, Step by Step

📝 8. How to Use This Percent Solution Calculator

📈 9. How to Calculate a Percent Solution in Excel

9.1 The formulas you need

9.2 Step by step

1 Enter the percent and the final volume

2 Grams of solute

3 Grams per liter and molarity

4 Uncertainty of the solution

9.3 Mass percent of several solutes

9.4 Why Excel may differ from R or Python

9.5 Charting the recipe

9.6 Errors you may see

📈 10. How to Calculate a Percent Solution in R

10.1 The complete script

10.2 Output

10.3 Traps

10.4 What each part does

10.5 Adapting it

📈 11. How to Calculate a Percent Solution in Python

11.1 The complete script

11.2 Output

11.3 Traps

11.4 What each part does

11.5 Adapting it

📋 12. Percent Solution Reference Tables: Recipes, Densities and Conversions

12.1 Common percent solutions and their molarity

12.2 Sodium chloride: % w/w, density, % w/v and molarity at 20 °C

12.3 Concentrated reagents: label percent to molarity

12.4 Density of water (for mass percent with a solvent volume)

12.5 Unit conversions for percent solutions

12.6 Class A volumetric flasks

📈 13. Percent Solution Example Results: Worked Problems

Calculate the mass percent of KCl in the solution

Concentration of each solute in mass percent

Mass percent when the solvent is measured by volume

10.0% w/w NaCl to % w/v and molarity

Normal saline: 0.9% w/v in mmol/L

A 1.0% agarose gel in 50 mL

Alligation: 15% zinc oxide ointment from 20% and base

A 40% w/w sodium chloride solution

✏️ 14. How Do You Make a Percent Solution in the Lab? Steps (SOP)

14.1 The written method