Molar Mass Calculator with Steps | StatsUnlock

To calculate molar mass, multiply the atomic weight of each element by the number of its atoms in the formula and add the results; the answer is in grams per mole. For water, H₂O:

Rule of thumb: count every atom, including those inside brackets and the water in a hydrate. Ca(OH)₂ has two O and two H, so M = 40.078 + 2 × 15.999 + 2 × 1.008 = 74.092 g/mol, not 57.085.

Molar mass (symbol M) is the mass of one mole of a substance, measured in grams per mole (g/mol). One mole is exactly 6.022 140 76 × 10²³ particles, so molar mass is also the mass of that many molecules, atoms or formula units. Because a mole of carbon-12 atoms weighs 12 g, the molar mass of any substance in g/mol is the same number as its relative formula mass (M_r) with no unit.

A molar mass calculator reads a chemical formula, counts the atoms of each element, multiplies each count by the element’s standard atomic weight and adds the products. This one also accepts names such as water or acetone, suggests the right capital letters when a formula is typed in lower case, shows the mass percent of each element, and converts between grams and moles in the same step.

A worked one-liner: what is the molar mass of sodium chloride? M(NaCl) = 22.990 + 35.45 = 58.440 g/mol, which is 58.44 g/mol to two decimal places.

Who uses it: CBSE and ICSE students meet molar mass in NCERT Class 9 (“Atoms and Molecules”) and Class 11 (“Some Basic Concepts of Chemistry”); JEE and NEET use it in nearly every numerical; GCSE, IGCSE, A level, AP Chemistry and IB courses call it relative formula mass or molar mass. In the lab it is how you weigh out a reagent, make a solution of known molarity, or identify an unknown from its mass and moles; in biochemistry it is how a protein’s mass in kDa is estimated from its sequence.

What this free online molar mass calculator solves

One tool covers every molar mass calculation in a typical course, and it doubles as a mass to moles calculator, a moles to mass calculator and an average molar mass calculator. Press Try it to load an example into the calculator, then press Calculate to see the full working.

Free, with no sign-up. Everything runs in your browser: nothing you type is sent to a server or stored.

How accurate is this molar mass calculator?

Atomic weights are the CIAAW 2024 standard atomic weights for all 118 elements (Prohaska et al., 2022), or rounded exam values if you choose them. Each subtotal is kept to full precision and only the final molar mass is rounded. The answer is checked two ways before it gets the Verified badge: the element subtotals must add back to M, and the mass percents must add to exactly 100%. An approximate uncertainty is shown, combined from the CIAAW uncertainty of each atomic weight; for water it is about ± 0.001 g/mol. The R and Python scripts in Sections 10 and 11 return the same 18.015 g/mol for water.

Studies of how students learn the mole find that most errors come from reading the formula, not the arithmetic: missed brackets, forgotten hydrate water and confusing subscripts with coefficients (Furió et al., 2002; Pekdağ & Azizoğlu, 2013). That is why every result shows the atom count first, then each multiplication, then the sum.

4.1 Molar mass is a conversion factor between grams and moles

18.015 g/mol for water means 18.015 g of water is exactly one mole, 6.022 × 10²³ molecules. Read as a fraction, it converts both ways: grams ÷ M gives moles, and moles × M gives grams. That is all you need to calculate mass from moles or moles from mass: 25.0 g of water is 25.0 ÷ 18.015 = 1.39 mol, and 0.800 mol of H₂CO₃ is 0.800 × 62.024 = 49.6 g.

4.2 Molar mass, molecular mass and molecular weight

They are the same number in different units. The molar mass of water is 18.015 g/mol; its relative molecular mass (M_r, often called molecular weight) is 18.015 with no unit; one water molecule weighs 18.015 u (daltons), or 2.991 × 10⁻²³ g. For ionic compounds such as NaCl, which have no molecules, say formula mass rather than molecular mass.

4.3 Reading the mass percent column

Each element’s subtotal divided by M is its percent by mass. Hydrogen is two of the three atoms in water but only 11.19% of the mass, because an oxygen atom is almost 16 times heavier. The “% of atoms” column shows the contrast. Mass percent is what combustion analysis measures, which is why the percent composition mode in this calculator can run the calculation backwards to find a formula.

4.4 How many decimal places should a molar mass have?

Use what your course expects. Most textbooks and exam boards give atomic weights to one or two decimals (H 1.01, O 16.00, Cl 35.45), giving 18.02 g/mol for water; CBSE, GCSE and IGCSE papers often use whole numbers (H 1, O 16), giving 18 g/mol. This calculator shows three decimals from the CIAAW 2024 values and the same result rounded to two and one decimal. In a calculation, the molar mass is rarely what limits the significant figures: your measured mass or volume is.

4.5 The uncertainty shown with the answer

CIAAW gives each standard atomic weight with an uncertainty that reflects natural variation in isotope abundances: hydrogen is 1.0080 ± 0.0002, oxygen 15.999 ± 0.001, chlorine 35.45 ± 0.01. The calculator combines these into an approximate uncertainty for M; for water it is about ± 0.001 g/mol, for NaCl about ± 0.01 g/mol because of chlorine. For almost all school and lab work it is far smaller than the uncertainty of the balance.

4.6 Molar mass of a gas, and density

For an ideal gas, density and molar mass are tied together by ρ = PM ÷ RT. A heavier gas is denser at the same temperature and pressure: at 0 °C and 1 bar, hydrogen (2.016 g/mol) is 0.0888 g/L and carbon dioxide (44.009 g/mol) is 1.938 g/L. The results table shows this density for any formula; the gas mode runs it backwards to find M from a measured density.

4.7 Average molar mass of a mixture

A mixture has an average molar mass weighted by mole fraction: M̄ = Σ x_iM_i. Dry air (78.08% N₂, 20.95% O₂, 0.93% Ar, 0.04% CO₂ by moles) comes out at 28.97 g/mol. The same sum over isotope masses and abundances gives an element’s atomic weight: chlorine-35 (75.76%) and chlorine-37 (24.24%) average 35.453.

4.8 A field note on where molar mass goes wrong

In checking hundreds of student answers, nearly every wrong molar mass traces back to reading the formula, not to the addition. The usual culprits are Ca(OH)₂ counted as one O and one H, hydrate water left out, O instead of O₂ for oxygen gas, and Co typed for CO. Research on the mole concept reports the same: students can apply n = m ÷ M yet struggle to connect the formula to the atoms it stands for (Gabel & Sherwood, 1984; Staver & Lumpe, 1995). The calculator therefore shows the atom count before any arithmetic.

4.9 Where molar mass leads next

Molar mass is the first step of almost every quantitative chemistry problem: grams to moles, moles to particles, solution concentrations, gas volumes, stoichiometry with mole ratios, limiting reagent and percent yield, and empirical and molecular formulas.

▶ Calculate a molar mass above to fill all five cards with your own answer.

The formula for calculating molar mass is M = Σ (atoms × atomic weight). This section lists it with every other molar mass calculation formula the calculator uses, each with a worked number.

This flowchart shows how to calculate the molar mass of a compound, on the same example used in the Excel, R, Python and by-hand sections: what is the molar mass of water, H₂O?

Check any box yourself: the Excel sheet in Section 9, the R script in Section 10 and the Python script in Section 11 all return 18.015 g/mol for water.

1. Choose what you want to find. Pick molar mass from a formula, or one of the data modes: mass and moles, gas, titration, percent composition, mixture, solution or protein sequence.
2. Type the formula or the name. Write it as H2O, Ca(OH)2 or CuSO4.5H2O, type a name such as acetone, or tap a common compound.
3. Check the capital letters. Each element symbol starts with a capital: Co is cobalt and CO is carbon monoxide. If you type in lower case, the calculator suggests the right formula.
4. Use brackets and dots exactly as written. Ca(NO3)2 has two nitrate groups; a dot adds water of crystallisation; ^2- marks an ion charge.
5. Add a mass or moles if you want a conversion. Type grams to get moles, or moles to get grams, with the unit you need.
6. For the data modes, enter your measurements. Type them exactly as measured, including trailing zeros, because they set the significant figures.
7. Choose the atomic weights. Keep CIAAW 2024 values or switch to rounded exam values such as C 12 and O 16.
8. Press Calculate Molar Mass. Nothing is calculated before you press it, and changing any input clears the old answer.
9. Read the element table and the steps. The Verified badge means the subtotals add back to M and the mass percents add to 100%.
10. Copy, share or batch. Copy the answer or the working, share a link, download a report, or calculate a whole list on the Batch tab.

Excel cannot read a chemical formula, so you lay the formula out as a small table: one row per element with its atom count and atomic weight. SUMPRODUCT then gives the molar mass, and one more column gives the mass percent. The sheet below uses the headline example, water, so it must return 18.015 g/mol, the same as the molar mass calculator above.

9.1 The functions you need

9.2 Step by step

9.3 Awkward cases

• Brackets. Count before typing: Ca(NO₃)₂ is 1 Ca, 2 N, 6 O.
• Hydrates. Add the water as extra atoms: CuSO₄·5H₂O has 9 O and 10 H.
• Condensed organic formulas. Add every C, H and O: CH₃COCH₃ is C₃H₆O.
• Average molar mass. Use =SUMPRODUCT(fractions,molar_masses)/SUM(fractions).

9.4 Why your Excel answer might differ from R, Python or this page

9.5 Charting in Excel

1. Select the element symbols and their subtotals (A2:A3, D2:D3).
2. Insert → Charts → Pie or Doughnut to show each element’s share of the molar mass, as in Chart 1 above.
3. For a mass-versus-moles line, make a column of moles (0 to 2), a column =moles*$D$4, then Insert → Scatter with Straight Lines.

9.6 Excel errors you will probably hit

This base R script reads a chemical formula, multiplies through brackets and hydrate dots, prints a table of atoms, atomic weights, subtotals and mass percents, checks that the percents add to 100, converts a mass to moles and saves one 300 dpi chart. For water it prints 18.015 g/mol, matching the molar mass calculator on this page.

10.1 The complete script

R, base only, saves molar_mass.png

# ============================================================
# Molar mass calculator in R: M = sum(atoms x atomic weight)
# StatsUnlock - https://statsunlock.com/molar-mass-calculator/
# Base R only. No packages to install.
# ============================================================

# ---- 1. Your formula ---------------------------------------------
formula <- "H2O"     # brackets and hydrates work: Ca(OH)2, Ca(NO3)2, CuSO4.5H2O
mass_g  <- 25.0      # optional: a mass to convert to moles (or NA)

# CIAAW 2024 standard atomic weights (g/mol); add any element you need
W <- c(H = 1.008, Li = 6.94, C = 12.011, N = 14.007, O = 15.999, F = 18.998,
       Na = 22.990, Mg = 24.305, Al = 26.982, Si = 28.085, P = 30.974,
       S = 32.06, Cl = 35.45, K = 39.098, Ca = 40.078, Mn = 54.938,
       Fe = 55.845, Cu = 63.546, Zn = 65.38, Br = 79.904, Ag = 107.87,
       I = 126.90, Ba = 137.33, Au = 196.97, Pb = 207.2)

# Count atoms, multiplying through brackets and the hydrate dot
parse_formula <- function(f) {
  total <- c()
  parts <- strsplit(f, "[.*]")[[1]]
  for (i in seq_along(parts)) {
    part <- parts[i]; mult <- 1
    if (i > 1 && grepl("^[0-9]+", part)) {
      mult <- as.numeric(sub("^([0-9]+).*", "\\1", part))
      part <- sub("^[0-9]+", "", part)
    }
    tok <- regmatches(part, gregexpr("[A-Z][a-z]?|[0-9]+|[][()]", part))[[1]]
    stack <- list(numeric(0)); j <- 1
    while (j <= length(tok)) {
      t <- tok[j]; j <- j + 1
      if (t %in% c("(", "[")) { stack[[length(stack) + 1]] <- numeric(0); next }
      n <- 1
      if (j <= length(tok) && grepl("^[0-9]+$", tok[j])) { n <- as.numeric(tok[j]); j <- j + 1 }
      top <- length(stack)
      if (t %in% c(")", "]")) {
        inner <- stack[[top]] * n; stack[[top]] <- NULL; top <- top - 1
        for (k in names(inner)) stack[[top]][k] <- sum(stack[[top]][k], inner[k], na.rm = TRUE)
      } else {
        stack[[top]][t] <- sum(stack[[top]][t], n, na.rm = TRUE)
      }
    }
    for (k in names(stack[[1]])) total[k] <- sum(total[k], stack[[1]][k] * mult, na.rm = TRUE)
  }
  total
}

# ---- 2. Molar mass, element by element ----------------------------
counts <- parse_formula(formula)
if (any(!names(counts) %in% names(W))) stop("Add the atomic weight of ", paste(setdiff(names(counts), names(W)), collapse = ", "))
sub_mass <- counts * W[names(counts)]
M <- sum(sub_mass)
print(data.frame(element = names(counts), atoms = as.vector(counts), Ar = as.vector(W[names(counts)]),
                 subtotal = round(as.vector(sub_mass), 3),
                 pct_mass = round(100 * as.vector(sub_mass) / M, 2)))
cat(sprintf("Molar mass M(%s) = %.3f g/mol  (%.2f to 2 d.p.)\n", formula, M, M))

# ---- 3. Check: the mass percents add to 100 ------------------------
stopifnot(abs(sum(100 * sub_mass / M) - 100) < 1e-9)
cat("Verdict: Verified, mass percents add to 100%\n")

# ---- 4. Optional: grams to moles -----------------------------------
if (!is.na(mass_g)) cat(sprintf("n = m / M = %.1f g / %.3f g/mol = %s mol\n", mass_g, M, signif(mass_g / M, 3)))

# ---- 5. One 300 dpi figure: each element's share of M --------------
png("molar_mass.png", width = 2100, height = 1350, res = 300)
par(mar = c(4.5, 5, 3, 1))
barplot(sub_mass, names.arg = names(counts), las = 1, border = NA,
        col = c("#94a3b8", "#ea580c", "#2563eb", "#16a34a", "#9333ea")[seq_along(counts)],
        xlab = "Element", ylab = "Contribution to M (g/mol)",
        main = sprintf("M(%s) = %.3f g/mol", formula, M))
invisible(dev.off())
cat("Saved molar_mass.png\n")

Output: Molar mass M(H2O) = 18.015 g/mol (18.02 to 2 d.p.), Verdict: Verified, mass percents add to 100%, n = m / M = 25.0 g / 18.015 g/mol = 1.39 mol. With formula <- "Ca(NO3)2" it prints 164.086 g/mol.

10.2 R traps

• round(M, 2) rounds to decimal places; signif() rounds to significant figures.
• Named vectors must match: W[names(counts)] picks the right weight for each element.
• Element symbols are case sensitive in the lookup, just as in chemistry: "Co" and "CO" differ.

10.3 What each part does

10.4 Using a package

The PeriodicTable package gives mass("O") for any element, and the CHNOSZ package has mass("H2O") for whole formulas. Check that their atomic weights match the edition your course uses.

10.5 The figure

The script saves molar_mass.png at 2100 × 1350 pixels and 300 dpi: one bar per element, its height the element’s contribution to M (2.016 and 15.999 g/mol for water).

This script does the same job in plain Python: it parses the formula, prints the element table with mass percents, checks the total, converts grams to moles and saves a 300 dpi chart. It uses the same method the molar mass calculator runs in your browser.

Install once: pip install matplotlib

11.1 The complete script

Python, saves molar_mass.png

# ============================================================
# Molar mass calculator in Python: M = sum(atoms x atomic weight)
# StatsUnlock - https://statsunlock.com/molar-mass-calculator/
# pip install matplotlib
# ============================================================
import re
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

# ---- 1. Your formula ---------------------------------------------
formula = "H2O"        # brackets and hydrates work: Ca(OH)2, Ca(NO3)2, CuSO4.5H2O
mass_g = 25.0          # optional: a mass to convert to moles (or None)

# CIAAW 2024 standard atomic weights (g/mol); add any element you need
W = {"H": 1.008, "Li": 6.94, "C": 12.011, "N": 14.007, "O": 15.999, "F": 18.998,
     "Na": 22.990, "Mg": 24.305, "Al": 26.982, "Si": 28.085, "P": 30.974,
     "S": 32.06, "Cl": 35.45, "K": 39.098, "Ca": 40.078, "Mn": 54.938,
     "Fe": 55.845, "Cu": 63.546, "Zn": 65.38, "Br": 79.904, "Ag": 107.87,
     "I": 126.90, "Ba": 137.33, "Au": 196.97, "Pb": 207.2}

def parse_formula(f):
    """Count atoms in a formula such as Ca(OH)2, Al2(SO4)3 or CuSO4.5H2O."""
    total = {}
    for i, part in enumerate(re.split(r"[.*·]", f)):
        mult = 1
        m = re.match(r"^(\d+)(.*)$", part)
        if m and i > 0:                        # the 5 in CuSO4.5H2O
            mult, part = int(m.group(1)), m.group(2)
        tokens = re.findall(r"[A-Z][a-z]?|\d+|[()\[\]]", part)
        stack, j = [{}], 0
        while j < len(tokens):
            t = tokens[j]; j += 1
            if t in "([":
                stack.append({}); continue
            n = 1
            if j < len(tokens) and tokens[j].isdigit():
                n = int(tokens[j]); j += 1
            if t in ")]":                      # close a bracket, multiply what is inside
                for k, v in stack.pop().items():
                    stack[-1][k] = stack[-1].get(k, 0) + v * n
            else:                              # an element symbol
                stack[-1][t] = stack[-1].get(t, 0) + n
        for k, v in stack[0].items():
            total[k] = total.get(k, 0) + v * mult
    return total

# ---- 2. Molar mass, element by element ----------------------------
counts = parse_formula(formula)
missing = [e for e in counts if e not in W]
if missing:
    raise SystemExit(f"Add the atomic weight of {missing} to W")
sub = {e: n * W[e] for e, n in counts.items()}
M = sum(sub.values())
print(f"{'Element':8}{'Atoms':>6}{'Ar':>9}{'Subtotal':>11}{'% mass':>9}")
for e, n in counts.items():
    print(f"{e:8}{n:>6}{W[e]:>9}{sub[e]:>11.3f}{100 * sub[e] / M:>8.2f}%")
print(f"Molar mass M({formula}) = {M:.3f} g/mol  ({M:.2f} to 2 d.p.)")

# ---- 3. Check: subtotals and percents ------------------------------
pct_total = sum(100 * s / M for s in sub.values())
assert abs(pct_total - 100) < 1e-9, "mass percents do not add to 100"
print(f"Verdict: Verified, mass percents add to {pct_total:.6f}%")

# ---- 4. Optional: grams to moles -----------------------------------
if mass_g:
    print(f"n = m / M = {mass_g} g / {M:.3f} g/mol = {mass_g / M:.3g} mol")

# ---- 5. One 300 dpi figure: each element's share of M --------------
fig, ax = plt.subplots(figsize=(7, 4.5))
ax.bar(list(sub), list(sub.values()), color=["#94a3b8", "#ea580c", "#2563eb", "#16a34a", "#9333ea"][:len(sub)])
ax.set_xlabel("Element")
ax.set_ylabel("Contribution to M (g/mol)")
ax.set_title(f"M({formula}) = {M:.3f} g/mol")
fig.tight_layout()
fig.savefig("molar_mass.png", dpi=300)
print("Saved molar_mass.png")

Output: Molar mass M(H2O) = 18.015 g/mol (18.02 to 2 d.p.), Verdict: Verified, mass percents add to 100.000000%, n = m / M = 25.0 g / 18.015 g/mol = 1.39 mol. With formula = "CuSO4.5H2O" it prints 249.677 g/mol.

11.2 Python traps

• f"{M:.2f}" rounds to 2 decimal places; f"{x:.3g}" rounds to 3 significant figures.
• round() rounds half to even, so round(55.845, 2) can give 55.84. Use the decimal module for exam-style rounding.
• Dictionary keys are case sensitive: W["Co"] is cobalt.

11.3 Using a package

With pip install periodictable, periodictable.formula("Ca(OH)2").mass returns the molar mass directly, and .mass_fraction gives each element’s share. Package atomic weights may differ from CIAAW 2024 in the last digit for a few elements.

11.4 What each part does

11.5 The figure

The script saves molar_mass.png at 300 dpi with each element’s contribution to the molar mass.

12.1 Atomic weights of common elements

Source: CIAAW, abridged standard atomic weights. The molar mass of an element in g/mol is the same number; for diatomic gases double it: O₂ is 31.998 g/mol, not 15.999.

12.2 Molar mass of common compounds

Each row was computed by the same engine as the molar mass calculator, from CIAAW 2024 atomic weights.

12.3 Molar mass of common gases, and their density at STP

ρ = PM ÷ RT with P = 100 kPa and T = 273.15 K. Air’s average molar mass is about 28.97 g/mol; a gas with a larger M sinks, a smaller one rises.

12.4 Amino acid molar masses (for protein calculations)

A residue is the amino acid minus one water (18.015 g/mol). Protein M = sum of residues + 18.015 for the water at the two ends. The quick rule of 110 Da per residue is an average estimate only.

12.5 Molar mass worksheet: calculate the molar mass for each of the following

Twenty molar mass calculations followed by ten mass and mole calculations, with answers checked by the calculator engine. Cover the last two columns and try them first.

Eight molar mass examples run through the calculator, from water to an adrenaline molecule and a hydrated borate. Each figure is drawn from the computed numbers: bar length is each element’s contribution to the molar mass.

This is the written method examiners expect, on the same example as Sections 7, 9, 10 and 11: what is the molar mass of water, H₂O?

14.1 How to calculate molar mass step by step

1. Write the formula correctly. H₂O, with a capital H and a capital O.
2. Count the atoms of each element. H: 2, O: 1. A symbol with no number has 1 atom.
3. Look up each atomic weight. H = 1.008, O = 15.999 (or H = 1, O = 16 with exam values).
4. Multiply each count by its atomic weight. 2 × 1.008 = 2.016; 1 × 15.999 = 15.999.
5. Add the products. M = 2.016 + 15.999 = 18.015 g/mol.
6. Give the unit. g/mol for molar mass; no unit for M_r.
7. Check. The answer should be a little more than the heaviest atom times its count: 18.015 is just above 16. Mass percents 11.19% + 88.81% = 100%.

14.2 How to calculate the molar mass of an element

For a single element, the molar mass is its atomic weight in g/mol: carbon is 12.011 g/mol and iron 55.845 g/mol. For elements that exist as molecules, multiply by the atoms in the molecule: oxygen gas O₂ is 2 × 15.999 = 31.998 g/mol, chlorine gas Cl₂ is 70.90 g/mol. Read the question carefully: “0.5 mol of oxygen atoms” weighs 0.5 × 15.999 = 8.0 g, but 0.5 mol of O₂ weighs 16.0 g.

14.3 How to calculate molar mass with brackets and hydrates

Multiply every atom inside a bracket by the number after it. Ca(OH)₂ = 40.078 + 2 × (15.999 + 1.008) = 74.092 g/mol. Ca(NO₃)₂ = 40.078 + 2 × 14.007 + 6 × 15.999 = 164.086 g/mol. For a hydrate, add the water after the dot: CuSO₄·5H₂O = 159.602 + 5 × 18.015 = 249.677 g/mol.

14.4 Mass and mole calculations: how to calculate mass from moles and moles from mass

Once you have M, mass = moles × molar mass and moles = mass ÷ molar mass. The mass in grams of 0.800 mol of H₂CO₃ is 0.800 × 62.024 = 49.6 g; the mass of 0.35 mol of CH₄ is 0.35 × 16.043 = 5.6 g; 25.0 g of water is 25.0 ÷ 18.015 = 1.39 mol.

14.5 How to calculate the molecular formula from molar mass

Find the empirical formula mass, divide the molar mass by it, and multiply every subscript by the whole number you get. CH₂O has an empirical mass of 30.026 g/mol; a substance with M = 180.16 g/mol gives 180.16 ÷ 30.026 = 6.00, so its molecular formula is C₆H₁₂O₆.

14.6 How to calculate the molar mass of a gas

Measure the gas density, or a mass and volume, at a known temperature and pressure, then use the ideal gas law: M = ρRT ÷ P, or M = mRT ÷ PV. A gas with density 1.25 g/L at 0 °C and 1 atm has M = 1.25 × 8.314 × 273.15 ÷ 101.325 = 28.0 g/mol, which fits nitrogen or carbon monoxide. Use kelvin and the same pressure unit as R.

14.7 How to calculate molar mass from a titration

Moles of base = c × V; moles of acid = moles of base ÷ the number of acidic hydrogens; M = mass of acid ÷ moles of acid. For 0.250 g of an unknown diprotic acid needing 27.8 mL of 0.100 M NaOH: 0.00278 mol OH⁻ ÷ 2 = 0.00139 mol acid, so M = 0.250 ÷ 0.00139 = 1.80 × 10² g/mol.

14.8 How to calculate average molar mass

Multiply each component’s molar mass by its mole fraction and add. For dry air, 0.7808 × 28.014 + 0.2095 × 31.998 + 0.0093 × 39.95 + 0.0004 × 44.009 = 28.97 g/mol. For isotopes the same sum gives the atomic weight: 0.7576 × 34.969 + 0.2424 × 36.966 = 35.453 for chlorine.

14.9 On a scientific calculator

On a Casio fx-991EX or fx-82MS: 2 × 1.008 + 15.999 = gives 18.015. For Ca(OH)₂, use brackets on the calculator too: 40.078 + 2 × ( 15.999 + 1.008 ) = gives 74.092.

The calculator does multiplication before addition, so 2 × 1.008 + 15.999 works without brackets; a bracket group from the formula needs brackets on the calculator. Key names differ between models; check your manual.

14.10 Do it in the lab: the molar mass of butane from a lighter

Example data. A result 3.8% high is typical: a little water left on the lighter adds to the mass lost. The mass (0.150 g) has three significant figures, so the answer is good to about ±1 g/mol.

14.11 Molar mass practice problems with answers

Ten practice problems, easy to hard. Open each one to see the answer.

14.12 Mistakes that lose marks

Research on the mole concept finds that students often confuse molar mass with mass, and subscripts with coefficients (Krishnan & Howe, 1994; Furió et al., 2002).

• Counting only the first atom in a bracket: Ca(OH)₂ is 74.092 g/mol, not 57.085.
• Forgetting the water of a hydrate: CuSO₄·5H₂O is 249.677 g/mol, not 159.602.
• Using 16 g/mol for oxygen gas instead of 32 g/mol for O₂.
• Including a coefficient: the molar mass of 2H₂O is still 18.015 g/mol.
• Typing Co (cobalt, 58.933) for CO (carbon monoxide, 28.010).
• Rounding the atomic weights too early, then quoting four significant figures.
• Writing “g” instead of “g/mol” for a molar mass.

Four real examples

Decision tree

1. Do you know the formula or the name? Yes: molar mass from a formula. No: go on.
2. Do you know a mass and the moles? Yes: M = m ÷ n. No: go on.
3. Is it a gas with a measured density, or mass and volume? Yes: the gas mode.
4. Is it an acid you titrated? Yes: the titration mode. Have percentages? The percent composition mode.

Limitations. A molar mass calculator gives the mass of one mole of the formula you type; it cannot tell you whether that formula is the real substance. Molar masses of ions ignore the electron mass (under 0.003% for most ions). For elements with no standard atomic weight, such as Tc, the mass number of the longest-lived isotope is used and a note appears.

What the answer is

Molar mass is the sum of the atomic weights in a formula, in g/mol. Water is 2 × 1.008 + 15.999 = 18.015 g/mol.

What it means chemically

It is the mass of one mole, 6.022 × 10²³ formula units, so it converts grams into moles and moles into grams. Every reacting mass, concentration and gas volume calculation passes through it.

Watch out for

Read the formula carefully: brackets, hydrate water, diatomic gases and capital letters cause most wrong answers. Keep the full value for later steps and round only the final answer.

Next steps

Use the molar mass to convert grams to moles, then the mole ratio from a balanced equation for stoichiometry. Practise with the worksheet in Section 12.5 and the ten problems in Section 14.11, or calculate a whole list on the Batch tab.

Rearranging M = m ÷ n is algebra, and judging whether a measured molar mass really differs from the expected one is statistics; these tools cover both.

Peer-reviewed sources for the methods and data used in this molar mass calculator: standard atomic weights, the definition of the mole and the Avogadro constant, and research on how students learn molar mass and the mole concept.

1. Andreas, B., Azuma, Y., Bartl, G., Becker, P., Bettin, H., Borys, M., ... Zakel, S. (2011). Determination of the Avogadro constant by counting the atoms in a ²⁸Si crystal. Physical Review Letters, 106(3), 030801. https://doi.org/10.1103/PhysRevLett.106.030801
2. Azuma, Y., Barat, P., Bartl, G., Bettin, H., Borys, M., Busch, I., ... Zakel, S. (2015). Improved measurement results for the Avogadro constant using a ²⁸Si-enriched crystal. Metrologia, 52(2), 360–375. https://doi.org/10.1088/0026-1394/52/2/360
3. Dori, Y. J., & Hameiri, M. (2003). Multidimensional analysis system for quantitative chemistry problems: Symbol, macro, micro, and process aspects. Journal of Research in Science Teaching, 40(3), 278–302. https://doi.org/10.1002/tea.10077
4. Furió, C., Azcona, R., & Guisasola, J. (2002). The learning and teaching of the concepts ‘amount of substance’ and ‘mole’: A review of the literature. Chemistry Education Research and Practice, 3(3), 277–292. https://doi.org/10.1039/B2RP90023H
5. Gabel, D. L., & Sherwood, R. D. (1984). Analyzing difficulties with mole-concept tasks by using familiar analog tasks. Journal of Research in Science Teaching, 21(8), 843–851. https://doi.org/10.1002/tea.3660210806
6. Güttler, B., Bettin, H., Brown, R. J. C., Davis, R. S., Mester, Z., Milton, M. J. T., ... Stock, M. (2019). Amount of substance – the Avogadro constant and the SI unit “mole”. Metrologia, 56(4), 044002. https://doi.org/10.1088/1681-7575/ab1fae
7. Krishnan, S. R., & Howe, A. C. (1994). The mole concept: Developing an instrument to assess conceptual understanding. Journal of Chemical Education, 71(8), 653–655. https://doi.org/10.1021/ed071p653
8. Marquardt, R., Meija, J., Mester, Z., Towns, M., Weir, R., Davis, R., & Stohner, J. (2018). Definition of the mole (IUPAC Recommendation 2017). Pure and Applied Chemistry, 90(1), 175–180. https://doi.org/10.1515/pac-2017-0106
9. Meija, J., Coplen, T. B., Berglund, M., Brand, W. A., De Bièvre, P., Gröning, M., ... 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
10. Mills, I. M., Mohr, P. J., Quinn, T. J., Taylor, B. N., & Williams, E. R. (2006). Redefinition of the kilogram, ampere, kelvin and mole: A proposed approach to implementing CIPM recommendation 1 (CI-2005). Metrologia, 43(3), 227–246. https://doi.org/10.1088/0026-1394/43/3/006
11. Nakhleh, M. B. (1992). Why some students don’t learn chemistry: Chemical misconceptions. Journal of Chemical Education, 69(3), 191–196. https://doi.org/10.1021/ed069p191
12. Newell, D. B., Cabiati, F., Fischer, J., Fujii, K., Karshenboim, S. G., Margolis, H. S., ... Ullrich, J. N. (2018). The CODATA 2017 values of h, e, k, and N_A for the revision of the SI. Metrologia, 55(1), L13–L16. https://doi.org/10.1088/1681-7575/aa950a
13. Nurrenbern, S. C., & Pickering, M. (1987). Concept learning versus problem solving: Is there a difference? Journal of Chemical Education, 64(6), 508–510. https://doi.org/10.1021/ed064p508
14. Pekdağ, B., & Azizoğlu, N. (2013). Semantic mistakes and didactic difficulties in teaching the “amount of substance” concept: A useful model. Chemistry Education Research and Practice, 14(1), 117–129. https://doi.org/10.1039/C2RP20132A
15. Prohaska, T., Irrgeher, J., Benefield, J., Böhlke, J. K., Chesson, L. A., Coplen, T. B., ... Zhu, X. (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
16. Sanger, M. J. (2005). Evaluating students’ conceptual understanding of balanced equations and stoichiometric ratios using a particulate drawing. Journal of Chemical Education, 82(1), 131–134. https://doi.org/10.1021/ed082p131
17. Schmidt, H.-J., & Jignéus, C. (2003). Students’ strategies in solving algorithmic stoichiometry problems. Chemistry Education Research and Practice, 4(3), 305–317. https://doi.org/10.1039/B3RP90018E
18. Staver, J. R., & Lumpe, A. T. (1995). Two investigations of students’ understanding of the mole concept and its use in problem solving. Journal of Research in Science Teaching, 32(2), 177–193. https://doi.org/10.1002/tea.3660320206
19. Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Reviews of Modern Physics, 93(2), 025010. https://doi.org/10.1103/RevModPhys.93.025010
20. Yarroch, W. L. (1985). Student understanding of chemical equation balancing. Journal of Research in Science Teaching, 22(5), 449–459. https://doi.org/10.1002/tea.3660220507