Calculator with Steps | Free Online Math Solver

This calculator works out any math expression in the correct order of operations and shows the exact answer with every step.

Example: 2 + 3 × (4 − 1)² ÷ 6. Brackets give 3, the power gives 9, then 3 × 9 = 27, 27 ÷ 6 = 9/2, and 2 + 9/2 = 13/2, which is 6.5.

Rule of thumb: a power is done before a minus sign, so −3² = −9. Type (−3)^2 if you want 9.

A calculator with steps is a math calculator that shows how it reached the answer, one operation at a time, instead of only printing a number. A math solver calculator goes one step further and also solves equations such as 2x² − 4x − 6 = 0.

You use it to check homework, to learn the order of operations, to get exact fractions and surds that a basic calculator turns into long decimals, and to solve or graph equations quickly. On the headline problem, 2 + 3 × (4 − 1)² ÷ 6, a simple calculator that works strictly left to right gives 22.5. The correct answer is 6.5, because the power and the brackets come first.

Who uses it: school students from Grade 6 to Grade 12 (CBSE, ICSE, IGCSE, GCSE, A level, SAT, ACT), first-year university students in algebra and calculus, teachers building answer keys, engineers and programmers who need an exact result, and parents checking homework.

1.1 Basic calculator vs scientific calculator vs this math solver

4.1 What your answer means

___ Solve a problem above to fill this in.

4.2 The order the calculator followed

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4.3 Exact answer or decimal: which one to write

___ Solve a problem above to fill this in.

An exact answer such as 13/2, 2√2 or π/3 has no rounding at all. A decimal is a rounded copy. Write the exact form when a question says “exact”, “simplest form” or “in surd form”. Write a decimal when the question gives a number of decimal places or significant figures, or when the answer is a measurement.

4.4 How the answer was checked

___ Solve a problem above to fill this in.

4.5 Why 0.1 + 0.2 is exactly 0.3 here

Most computer calculators store numbers in binary floating point, where 0.1 cannot be stored exactly, so 0.1 + 0.2 comes out as 0.30000000000000004. This calculator reads 0.1 as the fraction 1/10 and 0.2 as 2/10 before adding, so the answer is exactly 3/10. Goldberg (1991) explains why binary floating point behaves this way.

4.6 What the angle mode changes

sin, cos and tan read the angle in the mode you choose. In DEG, sin(30) = 1/2 exactly. In RAD, sin(30) means 30 radians, which is about 1,719°, so the answer is −0.988. If a trig answer looks wrong, the angle mode is the first thing to check. In RAD mode, write π in the angle (sin(pi/6) = 1/2) to get exact values.

4.7 When there is no real answer

Some inputs have no real value: √(−4), ln(0), log of a negative number, tan(90°) and anything divided by 0. The calculator stops and says why, instead of printing NaN or Infinity. For √(−4) it also tells you the complex answer, 2i. In the equation solver, a negative discriminant gives a pair of complex roots such as −1 ± 2i.

4.8 How this links to the next topic

Order of operations is the base of algebra. Once it is solid, the next steps are simplifying expressions, solving linear equations, then quadratics. For a full quadratic working with the discriminant and vertex, use the quadratic formula calculator. For comparing two values, the greater than sign calculator shows which is bigger and why.

▶ Solve a problem above to fill all five cards with your own answer.

This flowchart shows how the calculator works out an expression step by step, from what you type to the checked answer. Every box uses the same worked example as the Excel, R, Python and by-hand sections: 2 + 3 × (4 − 1)² ÷ 6.

Sections 9, 10 and 11 do the same calculation in Excel, R and Python, and Section 14 shows it by hand and on Casio and TI calculators.

1. Choose a tab. Calculator for sums and expressions, Solve Equation for anything with x and “=”, Graph for y = f(x), Batch for many problems at once.
2. Type your problem or pick a sample. The Sample problem list has ten worked problems, from simple order of operations to a trap question.
3. Use the keypad if you are on a phone. Keys insert sin(, sqrt(, ^, π and the other symbols at the cursor.
4. Set the angle mode. DEG for degrees, RAD for radians. Only sin, cos, tan and their inverses use it.
5. Choose decimal places. 2, 4, 6 or 10 places. The exact answer is never rounded.
6. Press Calculate (or Enter). Nothing is worked out until you press it.
7. Read the answer box. Exact answer first, decimal under it, and badges for the answer type and the Verified check.
8. Follow the steps. Each step is one operation, with the rule it used and the expression after it.
9. Look at the four charts. They show the value after each step, the operations used, the function or number line, and your history tape.
10. Download the working. Download Doc saves every step as a text file. Download PDF prints a clean copy.

Excel is a powerful calculator once you know its rules. Every formula starts with =, and Excel follows the order of operations with one famous exception, explained in 9.4. Here is the headline problem, 2 + 3 × (4 − 1)² ÷ 6, worked in a sheet.

9.1 The functions you need

9.2 Step by step

9.3 The awkward cases

• Square root of a negative number: =SQRT(-4) gives #NUM!. Use =IMSQRT(-4), which returns the text 2i.
• Big numbers lose digits: Excel keeps 15 significant digits, so =FACT(25) shows 1.55112E+25 and the exact 15511210043330985984000000 is lost. This calculator gives every digit.
• Trig in degrees: =SIN(30) is −0.988 because Excel reads 30 as radians. Wrap the angle in RADIANS().
• Fractions typed into a cell: typing 3/4 into a cell often turns it into a date (3 April). Type 0 3/4 or =3/4 instead.

9.4 Why Excel might disagree with R, Python or your textbook

9.5 Charting it in Excel

To graph a function, put x values in column A (for example −5 to 5 in steps of 0.1) and =A2^2-4 in column B, then Insert → Scatter with Smooth Lines. Never use a Line chart for a function, because it spaces the x values evenly whatever they are. Then set both axes to cross at 0 (Format Axis → Vertical axis crosses at 0) so the roots are easy to read.

9.6 Excel errors you will probably hit

R is a full scientific calculator at its prompt. It follows the textbook order of operations, including −3^2 = −9 and 2^3^2 = 512. The script below works the headline example step by step, prints the exact fraction, checks it, and saves a 300 dpi chart of the value after each step.

10.1 The complete script

# StatsUnlock calculator: order of operations in R
library(MASS)                       # fractions() shows exact fractions

expr_txt <- "2 + 3*(4 - 1)^2 / 6"   # change this line

# 1. Evaluate the whole expression
value <- eval(parse(text = expr_txt))

# 2. The same thing, one operation at a time
s1 <- 4 - 1            # brackets     -> 3
s2 <- s1^2             # powers       -> 9
s3 <- 3 * s2           # multiply     -> 27
s4 <- s3 / 6           # divide       -> 4.5
s5 <- 2 + s4           # add          -> 6.5
step_values <- c(s1, s2, s3, s4, s5)

# 3. Report
cat("Expression :", expr_txt, "\n")
cat("Decimal    :", format(value, digits = 15), "\n")
cat("Exact      :", as.character(fractions(value)), "\n")
cat("Steps      :", step_values, "\n")

# 4. Check: the step-by-step result must equal the one-line result
residual <- abs(value - s5)
cat("Check      : residual =", residual,
    if (residual < 1e-9) "(Verified)\n" else "(CHECK FAILED)\n")

# 5. Traps worth seeing once
cat("-3^2 =", -3^2, "  (-3)^2 =", (-3)^2, "  2^3^2 =", 2^3^2, "\n")
cat("sin(30 deg) =", sinpi(30 / 180), "  log10(1000) =", log10(1000), "\n")

# 6. Figure: value after each step, saved at 300 dpi
png("calculator_steps.png", width = 1800, height = 1200, res = 300)
barplot(step_values, names.arg = c("( )", "^2", "x 3", "/ 6", "+ 2"),
        col = c(rep("#2563eb", 4), "#16a34a"),
        main = "2 + 3(4 - 1)^2 / 6, step by step", ylab = "Value")
abline(h = 0, col = "#475569")
dev.off()

10.2 What each part does

R traps: log() is the natural log (use log10()); round(2.5) is 2 (half to even); doubles lose exact integers above 2^53, so factorial(25) is not exact (use the gmp package and factorialZ(25)); %% is the remainder and %/% is integer division.

10.3 What the figure shows

Five bars: 3, 9, 27, 4.5 and 6.5. The value jumps to 27 after the multiply and drops to 4.5 after the divide, then the final add gives 6.5 (green). It is a picture of the expression being simplified one rule at a time.

10.4 Common R problems and fixes

10.5 Useful one-liners

• choose(10, 3) gives 120; factorial(5) gives 120.
• polyroot(c(-6, -4, 2)) solves 2x² − 4x − 6 = 0 (coefficients in ascending order): 3 and −1.
• uniroot(function(x) 2^x - 10, c(0, 10))$root gives 3.3219.
• curve(x^2 - 4, -5, 5); abline(h = 0) draws a quick graph.
• signif(pi, 3) gives 3.14; format(1e6, big.mark = ",") gives 1,000,000.

Python is an exact calculator if you use the right tools. fractions.Fraction keeps answers as exact fractions, and SymPy gives surds and π in exact form. The script works the headline example, prints the exact and decimal answers, checks them, and saves a 300 dpi figure.

Install once with pip install sympy matplotlib. It runs in a terminal (python calc.py), in Jupyter, or in Google Colab.

11.1 The complete script

# StatsUnlock calculator: order of operations in Python
from fractions import Fraction as F
import sympy as sp
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

expr_txt = "2 + 3*(4 - 1)**2 / 6"   # change this line (use ** for powers)

# 1. Exact, one operation at a time
s1 = F(4) - 1          # brackets  -> 3
s2 = s1 ** 2           # powers    -> 9
s3 = 3 * s2            # multiply  -> 27
s4 = s3 / 6            # divide    -> 9/2 (exact, not 4.5)
s5 = 2 + s4            # add       -> 13/2
steps = [s1, s2, s3, s4, s5]

# 2. Whole expression: exact with SymPy, decimal with floats
exact = sp.nsimplify(sp.sympify(expr_txt, rational=True))
decimal = eval(expr_txt)

print("Expression :", expr_txt)
print("Steps      :", [str(s) for s in steps])
print("Exact      :", exact)
print("Decimal    :", decimal)

# 3. Check: exact steps, SymPy and floats must all agree
residual = abs(float(s5) - decimal) + abs(float(exact) - decimal)
print("Check      : residual =", residual, "(Verified)" if residual < 1e-9 else "(CHECK FAILED)")

# 4. Traps worth seeing once
print("-3**2 =", -3**2, " (-3)**2 =", (-3)**2, " 2**3**2 =", 2**3**2, " 3^2 =", 3 ^ 2, "(XOR, not a power)")
print("0.1 + 0.2 =", 0.1 + 0.2, " but F('0.1') + F('0.2') =", F("0.1") + F("0.2"))
print("sqrt(48) =", sp.sqrt(48), " sin(30 deg) =", sp.sin(sp.pi / 6))

# 5. Figure: value after each step, saved at 300 dpi
fig, ax = plt.subplots(figsize=(6, 4))
ax.bar(["( )", "^2", "x 3", "/ 6", "+ 2"], [float(s) for s in steps],
       color=["#2563eb"] * 4 + ["#16a34a"])
ax.set_title("2 + 3(4 - 1)^2 / 6, step by step")
ax.set_ylabel("Value")
fig.savefig("calculator_steps.png", dpi=300, bbox_inches="tight")
print("Saved calculator_steps.png")

11.2 What each part does

Python traps: 1/3 is a float (use F(1, 3)); round(2.5) is 2 (half to even); math.sqrt(-1) raises an error while cmath.sqrt(-1) gives 1j; math.sin wants radians, so use math.sin(math.radians(30)).

11.3 What the figure shows

The same five bars as the R figure: 3, 9, 27, 4.5 and 6.5, with the final answer in green. Both scripts print Exact 13/2 and Decimal 6.5, matching the calculator above.

11.4 Common Python problems and fixes

11.5 Useful one-liners

• import math; math.comb(10, 3) gives 120 and math.factorial(25) gives every digit.
• sp.solve(2*x**2 - 4*x - 6, x) (after x = sp.symbols("x")) gives [−1, 3].
• sp.sqrt(48) + sp.sqrt(27) gives 7*sqrt(3).
• math.gcd(84, 36) gives 12; pow(2, 100, 7) gives 2^100 mod 7.
• f"{12345.678:,.2f}" gives 12,345.68.

12.1 Order of operations names around the world

How to use this table: all five give the same answer. M and D have equal rank, and so do A and S; the letter order does not mean multiply comes before divide.

12.2 Exact trig values

How to use this table: these are the values the calculator returns exactly. Other angles return a 15-digit decimal.

12.3 Fraction, decimal and percent equivalents

How to use this table: a fraction ends as a decimal only if its denominator has no prime factors other than 2 and 5.

12.4 Perfect squares and the square roots they simplify

How to use this table: look for the largest of 4, 9, 16, 25, 36, 49, 64, 81, 100 that divides the number.

12.5 Powers of 2 and 10

How to use this table: log(10^n) = n and log2(2^n) = n exactly, which the calculator uses for exact log answers.

12.6 Operator symbols this calculator accepts

How to use this table: functions need brackets, and functions with two inputs use a comma.

Eight worked problems, each different from the headline example, covering the cases students meet most and the traps that cost marks.

This is the pen and paper method a teacher expects to see, worked on the same example as Sections 7, 9, 10 and 11: 2 + 3 × (4 − 1)² ÷ 6.

14.1 The written method

1. Copy the expression exactly. 2 + 3 × (4 − 1)² ÷ 6. Underline anything inside brackets.
2. Work out the brackets. 4 − 1 = 3. Rewrite: 2 + 3 × 3² ÷ 6.
3. Work out the powers. 3² = 9. Rewrite: 2 + 3 × 9 ÷ 6.
4. Multiply and divide from left to right. 3 × 9 = 27 first, then 27 ÷ 6. Rewrite: 2 + 27/6.
5. Simplify the fraction. gcd(27, 6) = 3, so 27/6 = 9/2.
6. Add and subtract from left to right. 2 = 4/2, so 4/2 + 9/2 = 13/2.
7. Convert if asked. 13/2 = 6 1/2 = 6.5.
8. Check. Work backwards: 6.5 − 2 = 4.5, and 4.5 × 6 = 27 = 3 × 9. It checks.

14.2 On a scientific calculator

All three follow the order of operations, so you can type the whole line at once. The mistake to avoid is the minus key: use the subtraction key between numbers and the (−) negative key for a negative number, especially on the TI-84. Key labels and menus can differ between versions, so check your model’s manual if a key is missing.

14.3 Practice problems with answers

14.4 Mistakes that lose marks

• Working strictly left to right and adding before multiplying: 2 + 3 × 4 is 14, not 20.
• Thinking M comes before D because of the letter order in PEMDAS. They are equal; go left to right.
• Squaring a negative without brackets: −3² = −9.
• Typing 5/6 ÷ 2/3 on one line. It means ((5/6) ÷ 2) ÷ 3 = 5/36, not 5/4.
• Rounding in the middle: 1/3 written as 0.33 and multiplied by 3 gives 0.99, not 1.
• Forgetting the calculator is in RAD when the question uses degrees.

15.1 Four real examples

• Homework check: a Grade 7 student gets 22.5 for 2 + 3 × (4 − 1)² ÷ 6. The steps show the power was skipped, and the right answer is 6.5.
• Exact surds for an exam: √48 + √27 must be written as 7√3, not 12.124. The calculator gives both.
• Interest: 1000 × 1.05³ = 9261/8 = 1157.625 exactly, so you know the amount to the cent before rounding.
• Physics: −4.9t² + 20t + 1.5 = 0 (type it with x) gives the time a ball lands, t ≈ 4.1553 s.

15.2 Which tab to use

17.1 Assumptions

1. Real numbers. Answers are real unless the solver finds complex roots, which are shown as a ± bi. Check: the badge says “No real solution” when only complex roots exist.
2. Typed decimals are exact. 0.333 means 333/1000, not 1/3. If you mean one third, type 1/3.
3. Implicit multiplication has the same rank as ×. 1/2x means (1/2) × x. Some handheld calculators give implied multiplication a higher rank, so type 1/(2x) when that is what you mean.
4. Angles follow the mode you pick. Only trig functions use it.
5. x is the only variable. The equation solver and the graph use x.

17.2 Limitations

1. Exact forms cover fractions, single surds and multiples of π. Mixtures such as π + √2, and anything with e, are given as 15-digit decimals with an amber badge.
2. Factorials up to 5000! and powers up to a few hundred thousand digits stay exact; beyond that the page stops with a message.
3. Polynomials up to degree 30. Rational roots are exact; the rest are found numerically to about 12 significant figures.
4. Non-polynomial equations are solved numerically between x = −100 and 100. Roots outside that range, or roots where the curve touches 0 without crossing, can be missed. Use the Graph tab to look.
5. No calculus, matrices or two-variable systems. Use a dedicated tool for those.

This calculator is built for the moment a number alone is not enough. It works in the correct order of operations, keeps every answer exact for as long as possible, shows each step, and checks itself with a second, independent calculation.

On the headline problem, 2 + 3 × (4 − 1)² ÷ 6, the order of operations gives 13/2 = 6.5, and a strict left-to-right calculator gives 22.5. That gap is the reason the steps matter. The same discipline explains −3² = −9, why 5/6 ÷ 2/3 needs brackets, and why sin(30) depends on the angle mode.

For exams, practise the same problems on your own handheld calculator with the keystrokes in Section 14, and use the exact form whenever a question asks for it. When you are ready for more, the Solve Equation and Graph tabs take the same skills into algebra. Bookmark this free online calculator and come back whenever you need the working, not just the answer.

Peer-reviewed sources for the methods in this calculator: exact and floating-point arithmetic, elementary function evaluation, polynomial root finding, and research on how students learn the order of operations.

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