Free Math Calculators with Steps
Calculators for school and college math that show the working, not just the answer — the method a teacher would write on the board, with exact fractions and radicals kept exact. They run from percentages and fractions through algebra, matrices and geometry to calculus. Use them to check homework, follow a method you have forgotten, or see where your own working went wrong. Free, no sign-up.
Math Calculators
65 tools · free, no sign-up
Percentage Calculator
Calculate percentages three ways: X% of Y, what percent X is of Y, and percent change between two numbers — with the working shown.
Weighted Average Calculator
Calculate a weighted average from values and weights — with the working shown step by step. For grades, statistics, and finance.
Ratio Calculator
Simplify ratios, find equivalent ratios, and solve proportions (A:B = C:x) — with the working shown step by step.
Fraction Calculator
Add, subtract, multiply, and divide fractions with the steps shown — plus simplify fractions and convert between fractions and decimals.
Significant Figures Calculator
Count significant figures with the reason for every digit, round to any number of sig figs without float errors, and add, subtract, multiply or divide by the rules.
GCF & LCM Calculator
Find the greatest common factor and least common multiple of two or more whole numbers — Euclid's algorithm step by step beside the prime factorization method.
Prime Factorization Calculator
Factor any whole number up to 10^20 into primes — exponent form, a factor tree, the division ladder, a prime check and the full list of divisors.
Quadratic Equation Solver
Solve ax² + bx + c = 0 exactly — discriminant, rational, radical or complex roots, vertex, factored form and a graph, worked by the formula and by completing the square.
Slope Calculator
Find the slope between two points as an exact fraction and a decimal, with the angle, distance, midpoint, three forms of the line's equation and a graph.
Long Division Calculator
Long division with every step shown: remainder or decimal answers, repeating decimals detected, bracket or inline layout, and a check of the result.
Long Multiplication Calculator
Column multiplication with every carry and partial product shown, decimals and negatives handled, placeholder zeros or shifted rows, and an estimate to check.
Exponent Calculator
Exact powers with whole, negative, decimal and fractional exponents — any size of whole-number result, the working shown, and the exponent laws checked on your numbers.
Square Root Calculator
Square roots and nth roots to any precision with exact digits, simplest radical form, a perfect-power check, bounds between perfect squares and Heron's method.
Logarithm Calculator
Logarithms to any base, natural log, antilogarithms and solving b^x = y — exact fractions where they exist and change-of-base working for every other answer.
Factorial Calculator
Exact n! up to 10,000 with every digit, plus double factorial, digit count, trailing zeros and Stirling's approximation with its error. Decimals via the gamma function.
Modulo Calculator
a mod n under the truncated, floored and Euclidean conventions for negatives, modular addition, multiplication and powers, and mod n tables — exact for decimals too.
Rounding Calculator
Round to any decimal place or multiple with ten rules — half up, banker's half even, floor, ceiling, truncate — on exact decimal digits, with every rule compared.
Expanded Form Calculator
Write whole numbers and decimals in expanded form, expanded notation, powers of ten and words, with a place-value chart — or type an expanded form to find the number.
Order of Operations Calculator
Evaluate any expression step by step with PEMDAS or BODMAS — each reduction shown, exact fractions throughout, and the ambiguous cases like 8 ÷ 2(2 + 2) explained.
Scientific Calculator
Full scientific calculator in your browser: trig in degrees, radians or gradians, logs, powers, roots, factorials, memory, history and keyboard input.
Prime Number Checker
Test any number up to 200 digits for primality with Miller–Rabin, see the working, find the previous and next prime, and list every prime in a range.
Modular Inverse Calculator
Find the inverse of a number modulo n with the extended Euclidean algorithm table, or solve a system of congruences with the Chinese remainder theorem.
Number Properties Calculator
Enter a whole number to see if it is even, prime, square, triangular, Fibonacci or a palindrome, and whether it is perfect, abundant or deficient.
Fibonacci Calculator
Find any Fibonacci number exactly up to F(100000), list a run of terms, check Binet's formula and watch the ratio of terms converge to the golden ratio.
Number Sequence Solver
Find a rule for a list of numbers and the next terms: arithmetic, geometric, polynomial (with a difference table) or Fibonacci-style, with exact fractions.
Arithmetic Sequence Calculator
Find the nth term and the sum of the first n terms of an arithmetic sequence, work out a₁ and d from two known terms, or find which term equals a value.
Geometric Sequence Calculator
Find the nth term, the sum of the first n terms and the infinite sum (when |r| < 1) of a geometric sequence, or recover a₁ and r from two known terms.
Summation Calculator
Evaluate a sum in sigma notation over any range: exact closed forms for polynomial and geometric terms, infinite geometric series, and a term table.
Pascal's Triangle Generator
Generate Pascal's triangle up to 100 rows with exact big integers, highlight odd numbers, multiples or diagonals, and print or copy the result.
Binomial Expansion Calculator
Expand (a + b)ⁿ with exact coefficients, see the general term, find the kth term or the coefficient of a given power, and check it term by term.
Linear Equation Solver
Solve one-variable linear equations with brackets, fractions and decimals — exact answers, every algebra step shown, a check, and a graph.
System of Equations Solver
Solve 2×2 and 3×3 linear systems by elimination or Cramer's rule, with exact fractions, a check, and no-solution and infinite cases explained.
Inequality Solver
Solve linear, double and compound inequalities with every step, the sign flip highlighted, interval notation, and a number-line graph.
Polynomial Calculator
Add, subtract, multiply and long-divide polynomials, evaluate at a value, and find roots — exact coefficients and every step shown.
Factoring Calculator
Factor polynomials with steps: GCF, trinomials by the AC method, difference of squares, sum and difference of cubes, grouping and rational roots.
Exponential Growth Calculator
Solve discrete and continuous exponential growth or decay for amount, rate or time, with doubling time, half-life and the rule of 72 and 70 compared.
Complex Number Calculator
Add, subtract, multiply and divide complex numbers exactly, with modulus, argument, polar and exponential form, De Moivre powers and nth roots.
Set Calculator
Union, intersection, difference, symmetric difference, complement, Cartesian product, power set and cardinality of two sets, with a Venn diagram.
Truth Table Generator
Truth table for any propositional formula with sub-formula columns, tautology or contradiction check, minterms, canonical CNF and DNF.
Karnaugh Map Solver
Minimal SOP and POS for 2 to 4 variables from minterms, a truth table or a formula, with K-maps, drawn groups and Quine–McCluskey with Petrick's method.
Matrix Calculator
Add, subtract, multiply, transpose, invert and row-reduce matrices with exact fractions — determinant, rank, trace and powers, with every row operation shown.
Eigenvalue Calculator
Find the eigenvalues and eigenvectors of a 2×2 to 6×6 matrix: exact radicals and complex values when the polynomial allows, numeric QR beyond, with the characteristic polynomial.
Vector Calculator
Magnitude, unit vector, sum, dot and cross product, angle between vectors and projection in 2D or 3D, exact in radicals — plus magnitude-and-direction to components.
Pythagorean Theorem Calculator
Find the missing side of a right triangle from a² + b² = c² in exact simplest radical form, check Pythagorean triples and test whether three sides make a right triangle.
Triangle Solver
Solve any triangle from SSS, SAS, ASA, AAS or SSA — including the ambiguous case with both triangles — with the laws of sines and cosines, area, perimeter and a to-scale diagram.
Distance and Midpoint Calculator
Find the distance and midpoint between two points in 2D or 3D in exact radical form, the section formula for any ratio, and the missing endpoint from a midpoint.
Polar Coordinates Converter
Convert between rectangular and polar coordinates with correct quadrant handling, and between rectangular, cylindrical and spherical coordinates in 3D, exact where possible, with a plot.
Geometric Transformation Calculator
Translate, reflect, rotate and dilate points or polygons, chain several steps, and see each 3×3 matrix and a before-and-after plot — exact for standard angles.
Area Calculator
Area of a square, rectangle, triangle (incl. Heron's formula), parallelogram, trapezoid, rhombus, polygon, ellipse, ring or sector — exact, with a figure and unit conversion.
Volume Calculator
Volume of a cube, box, prism, cylinder, cone, sphere, pyramid, frustum or ellipsoid — exact in terms of π, with the working, a labeled figure and liter and gallon conversion.
Surface Area Calculator
Lateral and total surface area of a cube, box, prism, cylinder, cone, sphere, hemisphere, pyramid or frustum — exact in terms of π, with the net, the working and a labeled figure.
Circle Calculator
Find a circle's radius, diameter, circumference and area from any one of them — exact in terms of π — plus arc length, sector, chord and segment area for any central angle.
Polygon Angle Calculator
Interior and exterior angle sums, each angle of a regular polygon in degrees and radians, the number of sides from an angle, and a missing angle of any polygon, with a figure.
Unit Circle Chart
Interactive, printable unit circle: degrees, radians and exact sine, cosine and tangent for every standard angle, with all six trig values at any angle you click.
Trigonometry Calculator
Sine, cosine, tangent, cosecant, secant and cotangent of any angle in degrees or radians — exact for special angles — with reference angle, quadrant and the inverse functions.
Angle Converter
Convert angles between degrees, radians, gradians, turns, arcminutes, arcseconds and degrees-minutes-seconds — radians as exact π fractions — with a labeled circle figure.
Derivative Calculator
Differentiate any function symbolically, with the rule named at every step — power, product, quotient, chain — plus higher orders, the value at a point and a graph.
Tangent Line Calculator
Find the tangent and normal line to y = f(x) at a point, exactly where the algebra allows, in point-slope, slope-intercept and standard form, with a graph and a linear approximation.
Taylor Series Calculator
Build the Taylor or Maclaurin polynomial of any function to degree 12 about any point, with exact coefficients, the Lagrange error bound and graphs of the approximation and its error.
Definite Integral Calculator
Evaluate a definite integral numerically with an error estimate, the total and net area, a shaded graph, and clear warnings for singularities, divergence and infinite limits.
Riemann Sum Calculator
Approximate an integral with left, right, midpoint, trapezoid or Simpson's rule, with the sample table, the error against the exact value and the rectangles drawn on a graph.
Newton's Method Calculator
Find roots of f(x) = 0 with Newton's method, the secant method or bisection, with the full iteration table, convergence order, failure diagnosis and a graph of every step.
Euler's Method Calculator
Approximate dy/dx = f(x, y) with Euler's method, improved Euler (Heun) or Runge–Kutta 4: a step table with slopes, error against the exact solution, step halving and a slope-field plot.
Average Rate of Change Calculator
Find the average rate of change of a function or a table of data over an interval, with the secant line, units interpretation, the limit toward the derivative and the Mean Value Theorem point.
Linear Interpolation Calculator
Interpolate or extrapolate between two points, within a table of values, or bilinearly on a grid, with the working shown, the inverse (x for a given y) and a graph.
Arithmetic, Number Work and Algebra
- Percentages, ratios and averages. The Percentage Calculator handles X% of Y, what percent X is of Y, and percent change; the Ratio Calculator simplifies ratios and solves proportions; the Weighted Average Calculator weights values the way a grade or an index does.
- Fractions and whole numbers. The Fraction Calculator, GCF & LCM Calculator, Prime Factorization Calculator, Long Division and Long Multiplication calculators write out the paper method. The Order of Operations Calculator shows which step comes first.
- Powers, roots and rounding. Exponent, Square Root, Logarithm, Factorial and Modulo calculators, plus Rounding and Significant Figures for science classes.
- Equations. The Linear Equation Solver, Quadratic Equation Solver, System of Equations Solver and Inequality Solver, then the Polynomial Calculator and Factoring Calculator. The Slope Calculator and Exponential Growth Calculator cover lines and curves, and the Complex Number Calculator handles i.
Discrete Math, Matrices and Geometry
| Topic | Calculators |
|---|---|
| Sequences and series | Arithmetic Sequence, Geometric Sequence, Fibonacci, Number Sequence Solver, Summation |
| Counting and algebra patterns | Pascal's Triangle, Binomial Expansion |
| Number theory | Prime Number Checker, Modular Inverse, Number Properties |
| Logic and sets | Set Calculator, Truth Table Generator, Karnaugh Map Solver |
| Linear algebra | Matrix Calculator, Eigenvalue Calculator, Vector Calculator |
| Triangles and coordinates | Pythagorean Theorem, Triangle Solver, Distance and Midpoint, Polar Coordinates, Geometric Transformations |
| Shapes | Area, Volume, Surface Area, Circle, Polygon Angles |
| Trigonometry | Trigonometry Calculator, Unit Circle Chart, Angle Converter |
Calculus and Numerical Methods
The Derivative Calculator differentiates step by step and names the rule at each line, and the Tangent Line Calculator and Average Rate of Change Calculator apply it. For integrals, the Definite Integral Calculator evaluates the area under a curve and the Riemann Sum Calculator shows the left, right and midpoint approximations that lead up to it. The Taylor Series Calculator builds a polynomial approximation, while Newton's Method, Euler's Method and Linear Interpolation are the numerical tools: they approximate roots, differential equations and in-between values when no tidy formula exists. The Scientific Calculator covers anything that is a plain evaluation.
Using a Calculator to Learn, Not Just to Finish
The calculators write out the method in the order you would on paper — Euclid's algorithm for a greatest common factor, the quadratic formula with the discriminant evaluated first, a common denominator before fractions are added. Where the math is exact, so is the answer: the fraction and equation solvers keep ⅓ as ⅓ and √2 as √2, with a decimal approximation beside them rather than instead of them.
A worked solution is most useful after you have tried the problem yourself. Solve it on paper, then compare your steps with the calculator's line by line: the first line where they differ is where to look. Most teachers want the method as well as the answer, so copy the reasoning into your own work rather than the result alone. For data rather than equations, see Statistics Calculators; for physics and chemistry formulas, Science & Lab Calculators.
Frequently Asked Questions
- How do I calculate percent change?
- Subtract the old value from the new one, divide by the old value, and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase. The Percentage Calculator shows each step.
- How do I solve a quadratic equation?
- Write it as ax² + bx + c = 0, compute the discriminant b² − 4ac, then use x = (−b ± √discriminant) ÷ 2a. For x² − 5x + 6 = 0 the discriminant is 25 − 24 = 1, so x = (5 ± 1) ÷ 2, giving 3 and 2. A negative discriminant means there are no real roots. The Quadratic Equation Solver shows the roots in simplest radical form with every step.
- How do I find the GCF and LCM of two numbers?
- The greatest common factor is the largest number that divides both; the least common multiple is the smallest number both divide. For 12 and 18 the GCF is 6 and the LCM is 36, and GCF × LCM = 12 × 18. The GCF & LCM Calculator shows both by prime factorization and by Euclid's algorithm.
- Why does the calculator give a fraction or a square root instead of a decimal?
- Because that is the exact answer. A decimal like 0.333… or 1.414… is an approximation. The fraction and equation calculators keep fractions, radicals and complex numbers exact and show a rounded decimal next to them for convenience.
- How do I find a missing side of a right triangle?
- With two sides known, use the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. With one side and one acute angle, use sine, cosine or tangent. The Pythagorean Theorem Calculator handles the first case and the Triangle Solver both, including triangles without a right angle.
- Can I use these calculators on a test?
- Only if your teacher allows online tools. They are built for homework, revision and checking work, and they run in any browser on a phone or laptop.