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Free Math Calculators

50+ free math calculators covering percentages, fractions, algebra, geometry, statistics, and more. From basic arithmetic to scientific notation — solve any math problem instantly with step-by-step explanations.

50+ Math Calculators Step-by-Step Solutions All Grade Levels No Sign-Up Required
Quick Percentage Calculator
What is X% of Y?
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Result

The tools millions of students and professionals use every month

Basic Math & Arithmetic
🔥 #1 Most Searched~22M/mo

Percentage Calculator

The most-searched math calculator in the US. Calculate what percent X is of Y, find X% of any number, compute percentage increase or decrease, and work out original values from percentages. Covers all percentage scenarios with instant results and formulas shown.

X% of Y% increase/decreaseWhat % is X of YReverse %Tip %
% = (X ÷ Y) × 100  |  X% of Y = Y × (X ÷ 100)
what is 20% of 150percentage increase calculatorhow to calculate percentage
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~9.5M/mo

Scientific Calculator

Full-featured online scientific calculator with sin, cos, tan, log, ln, √, π, e, and exponents. Works like a TI-84 in your browser.

Trig functionsLogarithmsExponents
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~7.2M/mo

Fraction Calculator

Add, subtract, multiply, and divide fractions and mixed numbers. Automatically simplifies results to lowest terms and converts to decimals. Shows step-by-step LCD method so students can learn while they calculate.

Add fractionsSubtract fractionsMultiply fractionsDivide fractionsMixed numbers
1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12
how to add fractions with different denominatorssimplify fractions calculator
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~5.8M/mo

Square Root Calculator

Calculate the square root, cube root, or nth root of any number. Also calculates x² and xⁿ. Shows exact and decimal forms.

√ Square root∛ Cube rootxⁿ Power
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Popular

Exponent Calculator

Calculate any base raised to any power. Handles negative exponents, fractional exponents, and scientific notation output for very large numbers.

bⁿ powerNegative exponentsFractional exponents
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Algebra
~4.1M/mo

Algebra Calculator

Solve linear equations, inequalities, and systems of equations. Enter any equation and get the solution with step-by-step work. Covers one-variable and two-variable linear equations, simplification, and factoring.

Solve for xLinear equationsInequalitiesSystems (2×2)Simplify expressions
solve for x calculatoralgebra equation solversolve 2x + 5 = 15
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~1.7M/mo

Quadratic Formula Calculator

Solve any quadratic equation ax²+bx+c=0 using the quadratic formula. Shows discriminant, both roots (real and complex), and factored form.

x = (−b ± √(b²−4ac)) / 2a
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~2.9M/mo

Long Division Calculator

Shows step-by-step long division work including remainder. Essential for students learning division. Also calculates as a decimal.

Step-by-stepRemainderDecimal result
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~1.9M/mo

Ratio Calculator

Simplify ratios, find missing values in proportions, scale ratios up or down, and convert ratios to fractions, percentages, or decimals.

Simplify ratioProportion solverRatio scaling
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Number Theory
~2.1M/mo

GCF Calculator – Greatest Common Factor

Find the Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), of two or more numbers. Uses prime factorization and Euclidean algorithm methods. Also shows all common factors and the step-by-step solution — essential for simplifying fractions.

GCF of 2 numbersGCF of 3+ numbersPrime factorizationEuclidean algorithmSimplify fractions
greatest common factor of 12 and 18GCF calculator with steps
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~2.4M/mo

LCM Calculator

Find the Least Common Multiple of two or more numbers using prime factorization or listing multiples. Essential for adding fractions.

LCM of 2+ numbersLCD for fractionsPrime factorization
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Popular

Prime Factorization Calculator

Break any number into its prime factors using a factor tree. Shows the prime factorization in standard form and exponential notation.

Factor treePrime factors listIs it prime?
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Geometry
~2.7M/mo

Area Calculator

Calculate the area of any 2D shape — circle, rectangle, triangle, trapezoid, parallelogram, ellipse, and more. Enter dimensions in any unit (inches, feet, cm, meters). Also calculates perimeter and circumference for each shape. Includes formulas for all shapes.

Circle areaRectangleTriangleTrapezoidPerimeter
Circle: A = πr²  |  Rectangle: A = l×w  |  Triangle: A = ½bh
area of a circle calculatortriangle area calculatorarea calculator with units
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~1.3M/mo

Pythagorean Theorem Calculator

Find the hypotenuse or any missing side of a right triangle. Enter any two sides to find the third. Shows the full Pythagorean formula.

a² + b² = c²
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~2.6M/mo

Volume Calculator

Calculate the volume and surface area of 3D shapes — sphere, cube, cylinder, cone, rectangular prism, and pyramid.

Sphere, cylinderCone, cubeSurface area
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Statistics & Probability
~1.5M/mo

Mean, Median, Mode & Range Calculator

Enter any dataset and instantly calculate the mean (average), median (middle value), mode (most frequent), and range. Also computes sum, count, minimum, maximum, and shows the data sorted in ascending order. Handles datasets of any size.

Mean (average)MedianModeRangeAny dataset size
mean median mode calculator with stepsfind the mean of a data set
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~1.2M/mo

Standard Deviation Calculator

Calculate population and sample standard deviation, variance, and mean for any dataset. Shows the complete formula and each step.

Population σSample sVariance
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Popular

Permutation & Combination Calculator

Calculate nPr (permutations) and nCr (combinations). Shows factorials, step-by-step formula, and the key difference between ordered and unordered selection.

nCr = n! / (r! × (n−r)!)
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All Math Calculators

Complete list — from basic arithmetic to advanced calculus

%
Percentage Calculator
X% of Y, % change, what % is X of Y
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🔬
Scientific Calculator
Sin, cos, tan, log, ln, √, π, exponents
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½
Fraction Calculator
Add, subtract, multiply, divide fractions
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√
Square Root Calculator
√x, ∛x, nth root, x²
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x
Algebra Calculator
Solve linear equations, systems, inequalities
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xⁿ
Exponent Calculator
bⁿ powers, negative & fractional exponents
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÷
Long Division Calculator
Step-by-step long division with remainder
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ax²
Quadratic Formula Calculator
ax²+bx+c=0 — both roots, discriminant
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GCF
GCF / GCD Calculator
Greatest common factor of 2+ numbers
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LCM
LCM Calculator
Least common multiple of 2+ numbers
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∶
Ratio Calculator
Simplify ratios, proportion solver, scaling
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📐
Area Calculator
Circle, rectangle, triangle, trapezoid area
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📦
Volume Calculator
Sphere, cylinder, cone, cube volume
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△
Pythagorean Theorem Calculator
a²+b²=c², find any side of a right triangle
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x̄
Mean, Median, Mode Calculator
Average, middle value, mode, range of a dataset
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σ
Standard Deviation Calculator
Population & sample σ, variance
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p
Prime Factorization Calculator
Factor tree, prime factors, is it prime?
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nCr
Permutation & Combination
nPr and nCr with factorial steps
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log
Logarithm Calculator
Log base 10, natural log (ln), any base
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|x|
Absolute Value Calculator
|x|, absolute value equations
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≈
Rounding Calculator
Round to decimal places or significant figures
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M
Matrix Calculator
Add, multiply matrices, determinant, inverse
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▲
Triangle Calculator
All sides & angles — SAS, SSS, ASA, AAS
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10ⁿ
Scientific Notation Calculator
Convert to/from scientific notation, multiply
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Math Formula Reference

Quick-reference formulas for the most commonly needed topics

ShapeAreaPerimeter / CircumferenceVolume (3D)Calculator
Circle (r = radius)A = πr²C = 2πr—Circle Area →
Rectangle (l × w)A = l × wP = 2(l+w)—Rectangle →
Triangle (base, height)A = ½bhP = a+b+c—Triangle →
Trapezoid (b₁, b₂, h)A = ½(b₁+b₂)hP = a+b₁+c+b₂—Trapezoid →
Sphere (r = radius)SA = 4πr²—V = (4/3)πr³Sphere →
Cylinder (r, h)SA = 2πr(r+h)—V = πr²hCylinder →
Cone (r, h)SA = πr(r+l)—V = (1/3)πr²hCone →
Formula / RuleExpressionExampleCalculator
Quadratic Formulax = (−b ± √(b²−4ac)) / 2aFor ax²+bx+c=0Quadratic →
Slope-Intercept Formy = mx + bm = slope, b = y-interceptAlgebra →
Distance Formulad = √((x₂−x₁)² + (y₂−y₁)²)Distance between 2 pointsDistance →
Exponent Rulesaᵐ × aⁿ = aᵐ⁺ⁿ2³ × 2⁴ = 2⁷ = 128Exponent →
Pythagorean Theorema² + b² = c²3² + 4² = 5²Pythagorean →
FOIL Method(a+b)(c+d) = ac+ad+bc+bd(x+2)(x+3) = x²+5x+6Algebra →
MeasureFormulaDataset Example {2, 4, 4, 7, 8}Calculator
Mean (Average)x̄ = Σx / n(2+4+4+7+8)/5 = 5.0Mean →
MedianMiddle value when sortedSorted: {2,4,4,7,8} → 4Median →
ModeMost frequent value4 (appears twice)Mode →
Rangemax − min8 − 2 = 6Range →
Variance (sample)s² = Σ(x−x̄)² / (n−1)5.5Variance →
Std Deviation (sample)s = √[Σ(x−x̄)²/(n−1)]2.345Std Dev →
Combination nCrC(n,r) = n! / (r!(n−r)!)C(5,2) = 10nCr →
ConceptDefinitionExampleCalculator
GCF / GCDLargest number dividing both evenlyGCF(12, 18) = 6GCF →
LCMSmallest number divisible by bothLCM(4, 6) = 12LCM →
Prime FactorizationExpress as product of primes60 = 2² × 3 × 5Primes →
RatioComparison of two quantities12:8 simplified = 3:2Ratio →
ProportionTwo ratios equal each other3/4 = x/12 → x = 9Proportion →
Absolute ValueDistance from zero on number line|−7| = 7, |5| = 5|x| →

Find the Right Math Calculator for Your Problem

Whether you're a student doing homework, a teacher building a lesson, or just need to check a calculation — our math calculators cover every topic from basic arithmetic to college-level statistics.

Percentages & Basics

What is 15% of 80? How to calculate percentage increase Percentage decrease calculator How to add fractions with different denominators Long division calculator with remainder How to round to nearest hundredth Absolute value of a negative number

Algebra & Equations

Solve for x calculator Quadratic formula solver with steps Negative exponent calculator Log base 2 calculator Greatest common factor of 24 and 36 Least common multiple of 4 and 6 Simplify ratio 12 to 8

Geometry & Statistics

Area of a circle with radius 5 Find hypotenuse with sides 3 and 4 Volume of a cylinder calculator How to find mean median mode Sample standard deviation with steps Combinations calculator nCr Convert 0.00045 to scientific notation

Math Calculator FAQs

Step-by-step answers to the most common math questions

How do you calculate a percentage?
X% of Y: multiply Y × X/100. E.g., 15% of 80 = 80 × 0.15 = 12. What % is X of Y: (X ÷ Y) × 100. E.g., 12 is what % of 80? = (12÷80) × 100 = 15%. % change: ((New−Old)÷Old) × 100. Use our percentage calculator for any scenario.
How do you add fractions with different denominators?
Find the LCD, convert both fractions, then add numerators. 1/3 + 1/4: LCD = 12 → 4/12 + 3/12 = 7/12. To find LCD, use the LCM of the denominators. Our fraction calculator shows every step automatically.
What is the Pythagorean theorem?
In any right triangle: a² + b² = c², where c is the hypotenuse. To find the hypotenuse: c = √(a² + b²). Example: a=3, b=4 → c = √(9+16) = √25 = 5. The 3-4-5 triangle. Use our Pythagorean theorem calculator.
How do you calculate mean, median, and mode?
Mean: sum ÷ count. {4,7,13,2,8} → 34÷5 = 6.8. Median: middle value sorted. {2,4,7,8,13} → 7. Mode: most frequent. {2,4,4,7,8} → 4. Range: max−min = 13−2 = 11. Use our mean median mode calculator for any dataset.
How do you find the area of a circle?
Area = A = πr². If diameter is given, r = d/2. Example: r = 5 inches → A = π × 25 ≈ 78.54 sq inches. Circumference = 2πr ≈ 31.42 in. Use our area calculator which supports all shapes.
How do you find the GCF (greatest common factor)?
List factors of each number and find the largest common one. GCF(12, 18): factors of 12 = {1,2,3,4,6,12}; factors of 18 = {1,2,3,6,9,18}; GCF = 6. Or use prime factorization: 12=2²×3, 18=2×3² → common = 2¹×3¹=6. Use our GCF calculator.
What is standard deviation and how is it calculated?
Standard deviation measures how spread out data values are from the mean. Steps: 1) Find the mean. 2) Subtract mean from each value, square the result. 3) Find the average of those squares (variance). 4) Take the square root. For samples, divide by n−1 instead of n. Use our standard deviation calculator.
What is the difference between permutation and combination?
Permutation (nPr): order matters. Arranging 3 of 5 people in a line = 5×4×3 = 60. Combination (nCr): order doesn't matter. Choosing 3 from 5 people for a committee = 10. Formula: nCr = n! ÷ (r! × (n−r)!). Use our permutation & combination calculator.

About Our Math Calculators

Our math calculators are built to serve students from middle school through college, as well as professionals who need quick, reliable calculations. Every calculator shows the formula used and, where applicable, a step-by-step solution — so you learn the method, not just get an answer.

The percentage calculator is the most-searched math tool in the US (over 22 million monthly searches), and our version handles all three core percentage problems: finding X% of a number, finding what percentage X is of Y, and calculating the percentage change between two values.

Our fraction calculator uses the standard LCD (Least Common Denominator) method taught in US schools, showing each step so students can verify their work. The GCF calculator and LCM calculator use both the listing-factors method and prime factorization, matching the two approaches taught in US curricula.

For geometry, our area calculator covers all shapes on the Common Core State Standards curriculum. The statistics calculator handles unlimited dataset sizes and shows sorted data, making it useful for both classroom homework and data analysis.