Math Calculators

Algebra Calculator

Solve one-variable linear equations, quadratic equations, and small systems of linear equations. See simplification steps, the discriminant and roots, elimination steps, and exact fractions where possible.

2x + 3 = 7

x = 2

Linear solution

Arithmetic Sequence Calculator

Calculate any term or the sum of an arithmetic sequence from the first term and common difference, or from two known terms. Shows the formula, intermediate values, and the first terms of the sequence.

a₁ = 2 • d = 3

n = 5

a₅ = 14

S₅ = 40

Circle Area Calculator

Calculate a circle

Radius r = 3

Area = 28.27

Circumference = 18.85

Combination Calculator

Calculate the number of unordered ways to choose r items from n items (nCr), with or without repetition. Review the formula and copy or download the result.

n = 5 • r = 2

No repetition

C(5,2) = 10

Combinations

Cone Volume Calculator

Calculate a right circular cone

Radius 3

Height 4

Volume ≈37.70

Cubic units

Cylinder Volume Calculator

Calculate a cylinder

Radius 3

Height 5

Volume ≈141.37

Cubic units

Distance Formula Calculator

Calculate the straight-line distance between two coordinate points in 2D or 3D. Shows the governing distance formula, every intermediate value, supported units, and a copyable or downloadable result.

(0, 0) → (3, 4)

Distance = 5

Coordinate distance

Exponent Calculator

Calculate a base raised to a real exponent. Negative bases with non-integer exponents are not accepted by this real-number calculator. See the formula, assumptions, supported units, and copyable result.

Base 2

Exponent 8

2⁸ = 256

Power calculated

Factorial Calculator

Calculate the factorial (n!) or subfactorial / derangement number (!n) of nonnegative integers from 0 through 10,000. Shows the formula, exact result, and calculation steps.

n = 5

Factorial mode

5! = 120

Exact result

Fraction and Ratio Calculator

Add, subtract, multiply, and divide fractions and mixed numbers, simplify ratios to lowest terms, and solve direct or inverse proportions with step-by-step results.

1/2 + 1/3

Fraction operation

5/6

Reduced result

Fraction Calculator

Simplify a fraction or mixed number to lowest terms, or add, subtract, multiply, and divide a chain of fractions and mixed numbers. See every step, the exact simplified fraction, and a decimal equivalent.

3/4 × 2/3

Multiply fractions

1/2

Reduced result

Geometric Sequence Calculator

Calculate any term, the sum of the first n terms, or the infinite sum of a geometric sequence from the first term and common ratio, or from two known terms. Shows the formula and every intermediate value.

a₁ = 2 • r = 3

n = 4

a₄ = 54

Geometric term

Geometry Calculator

Calculate slope, distance, midpoint, triangle area, circle measurements, polygon area, and common solid volume or surface area. Choose units, see the formula used, and view a labeled diagram.

Rectangle

4 × 6

Area = 24

Perimeter = 20

Greatest Common Factor Calculator

Calculate the greatest common factor (GCF / GCD) of two or more integers. Shows the Euclidean algorithm steps, every intermediate value, and a copyable, downloadable result.

18 and 24

GCF = 6

Common factor

Least Common Multiple Calculator

Calculate the least common multiple (LCM) of two or more integers. Shows the governing formula, the Euclidean algorithm GCF steps, every intermediate value, and a copyable, downloadable result.

6 and 8

LCM = 24

Common multiple

Linear Equation Calculator

Solve a one-variable linear equation. Enter an equation like 2x + 3 = 7 and see the combined form, governing formula, result, and exact fraction when applicable.

2x + 4 = 10

x = 3

Linear solution

Logarithm Calculator

Calculate a logarithm for a supported positive value and base. Shows the governing formula, intermediate values, input validation, and a copyable or downloadable result.

log₁₀(1000)

Result = 3

Base-10 logarithm

Matrix Calculator

Add, subtract, multiply, and transpose matrices, compute determinant, inverse, and rank, or solve Ax = b. See calculation steps, including row-elimination steps where applicable, with exact fractions for matrices up to 6x6.

[1 2; 3 4] + [5 6; 7 8]

[6 8; 10 12]

Matrix result

Matrix Determinant Calculator

Calculate the determinant of a square matrix up to 8x8. See every row-elimination step with exact fraction arithmetic, clear singular-matrix reporting, and a copyable or downloadable result.

[1 2; 3 4]

det = −2

Determinant

Matrix Inverse Calculator

Calculate the inverse of a square matrix up to 8x8 using Gauss-Jordan elimination on [A | I]. See every row-operation step with exact fraction arithmetic and clear singular-matrix reporting.

[1 2; 3 4]

[−2 1; 1.5 −0.5]

Inverse matrix

Midpoint Calculator

Calculate the midpoint between two coordinate points in 2D or 3D. Shows the governing midpoint formula, every intermediate value, supported units, and a copyable or downloadable result.

(1, 2) • (5, 6)

Midpoint = (3, 4)

Coordinate midpoint

Mixed Number Calculator

Add, subtract, multiply, or divide two mixed numbers, fractions, or whole numbers. See conversion steps and exact fraction and mixed-number results alongside a displayed decimal.

1 1/2 + 2 1/4

3 3/4

Mixed-number result

Modulo Calculator

Calculate a mod n for integer dividends and nonzero divisors up to 100 digits. Shows the governing formula, quotient, remainder, and every intermediate value for both truncated and floored (divisor-sign) modulo conventions.

17 mod 5

Remainder = 2

Modulo result

Number Theory Calculator

Calculate GCF, LCM, prime factorization, modular arithmetic, factorials, permutations, and combinations with exact integer results and calculation details.

18 and 24

GCF mode

GCF = 6

Number-property result

Percentage Calculator

Calculate a percentage of a number, find what percent one number is of another, measure percentage change, or increase or decrease a number by a percentage. See the formula and steps for each mode.

20% of 150

Result = 30

Percentage calculation

Permutation Calculator

Calculate the number of ordered arrangements of r items from n items (nPr), with or without repetition. Review the formula and calculation steps, then copy or download the result.

n = 5 • r = 2

No repetition

P(5,2) = 20

Ordered selections

Polygon Area Calculator

Calculate the area of a regular polygon from its side count and length, or a simple polygon from ordered vertex coordinates using the shoelace formula. Review the main calculation steps, supported units, and copy or download the result.

Regular hexagon

Side = 2

Area ≈10.39

Square units

Prime Factorization Calculator

Break whole numbers from 2 through 999,999,999,999,999 down into their prime factors. Shows the trial-division formula, successful division steps, and a copyable, downloadable result.

n = 84

2² × 3 × 7

Prime factors

Proportion Calculator

Solve the missing value in a direct proportion (a/b = c/d) or inverse proportion (a x b = c x d). See the governing formula, assumptions, and every intermediate step, with exact fraction and decimal results.

2/3 = x/12

x = 8

Direct proportion

Pythagorean Theorem Calculator

Calculate the missing side of a right triangle from two known sides using the Pythagorean theorem. Shows the formula, every intermediate value, supported units, and a copyable or downloadable result.

a = 3 • b = 4

c = 5

Right-triangle side

Quadratic Equation Calculator

Solve a supported single-variable quadratic equation by entering coefficients or a full equation. See the discriminant, calculation steps, and real or complex roots.

x² − 5x + 6 = 0

x₁ = 2

x₂ = 3

Ratio Calculator

Simplify a ratio to lowest terms, solve a missing term in an equivalent ratio (a:b = c:?), or divide a total quantity by a ratio. See the formula, assumptions, and every step, with exact fraction results.

12 : 18

Simplify mode

2 : 3

Reduced ratio

Scientific Calculator

Evaluate scientific expressions with arithmetic, powers, roots, logarithms, trigonometry, constants, percentages and scientific notation. Choose degrees, radians or gradians, set significant figures, and see the parsed expression, precision settings and calculation history.

sin(30°)

Degree mode

0.5

Evaluated expression

Sequence Calculator

Calculate arithmetic and geometric sequence terms, the common difference or ratio, sums of a finite number of terms, and missing values from the terms you supply. Shows the formula, indexing convention, and validation.

Arithmetic: a₁=2 • d=3

n = 5

a₅ = 14

S₅ = 40

Slope Calculator

Calculate the slope of a line from two points or from rise and run values. Review the formula, intermediate values, and mode-dependent results, then copy or download the plain-text result.

(1, 2) → (3, 6)

Slope = 2

Rise/run

Sphere Volume Calculator

Calculate a sphere

Radius r = 3

Volume ≈113.10

Cubic units

Square Root Calculator

Calculate real square roots and nth roots of a number. Even-index roots of negative numbers are rejected. See the formula, intermediate values, input validation, and a copyable result.

√144

Result = 12

Principal root

Systems of Equations Calculator

Solve two or more simultaneous linear equations at once. Enter equations like 2x + y = 5 and x - y = 1 and see the governing formula, Gaussian elimination steps, and an exact fraction result you can copy or download.

x + y = 5

x − y = 1

x = 3

y = 2

Triangle Area Calculator

Calculate a triangle

Base 6 • height 4

Area = 12

Square units

Vector Calculator

Calculate vector magnitude, unit vector, addition, subtraction, scalar multiplication, dot product, cross product, angle between vectors, and vector projection. Works in 2D and 3D with exact fractions, formulas, and step-by-step results.

(1, 2) + (3, 4)

(4, 6)

Vector sum

Vector Magnitude Calculator

Calculate the magnitude (length) of a vector from its components. Supports 2D, 3D, and higher-dimensional vectors, shows the formula and every intermediate value, and lets you attach common units for context.

Vector (3, 4)

Magnitude = 5

Euclidean length