Math Calculators

Percentages, geometry, algebra and trigonometry made effortless, with the formulas explained.

410 calculators available.

Percentages

Arithmetic

Average (Mean) Calculator Find the arithmetic mean of up to five numbers. GCF Calculator Find the greatest common factor of two numbers. LCM Calculator Find the least common multiple of two numbers. Factorial Calculator Compute n! (the product 1 × 2 × … × n). Square Root Calculator Find the square root of a number. Cube Root Calculator Find the cube root of a number. Exponent Calculator Raise a base to a power. Logarithm Calculator Find the logarithm of a number in any base. Rounding Calculator Round a number to a chosen number of decimals. Scientific Notation Calculator Convert a number to scientific notation. Ratio Calculator Simplify a ratio to its lowest terms. Adding Fractions Calculator Add two fractions and simplify the result. Simplify Fractions Calculator Reduce a fraction to its lowest terms. Decimal to Fraction Calculator Convert a decimal into a simplified fraction. Proportion Calculator Solve a/b = c/x for the missing value. Prime Number Calculator Check whether a number is prime. Digit Sum Calculator Add up the digits of a number. Modulo Calculator Find the remainder and quotient of a division. Prime Factorization Calculator Break a number into its prime factors. Reciprocal Calculator Find the reciprocal (multiplicative inverse) of a number. Absolute Value Calculator Find the absolute value (distance from zero). Harmonic Mean Calculator Find the harmonic mean of up to three numbers. Significant Figures Calculator Round a number to a number of significant figures. Triangular Number Calculator Find the nth triangular number. Unit Rate Calculator Find a rate per single unit. Addition Calculator Sum of numbers. Subtraction Calculator Difference between two numbers. Multiplication Calculator Product of two numbers. Division Calculator Quotient of two numbers. Ceiling and Floor Calculator Round up or down to integer. Perfect Square Checker Is a number a perfect square? Standard Form Calculator Write a number in A × 10ⁿ form. Absolute Change Calculator |a − b|. Cross Multiplication Calculator Check if a/b = c/d. Consecutive Integers Calculator Sum of n consecutive integers. Divisibility Test Calculator Check if a divides b. Inverse Modulo Calculator Find x where a·x ≡ 1 (mod m). Order of Magnitude Calculator Power of 10 of a number. Root Mean Square Calculator RMS of values. Multiplicative Inverse Calculator 1/x. Power Mod Calculator (a^b) mod m. Simplify Radicals Calculator Simplify √(a²·b) = a√b. Round to the Nearest Ten Calculator Round to nearest 10. Round to the Nearest Hundred Calculator Round to nearest 100. Round to Thousandth Calculator Round to 3 decimal places. Rationalize Denominator Calculator 1/√a → √a/a. Even or Odd Checker Is a number even or odd? Mean Calculator Find the arithmetic mean (average) of a list of numbers. Chinese Remainder Theorem Calculator Solve x ≡ a (mod m) and x ≡ b (mod n) for coprime moduli. Fundamental Counting Principle Calculator Multiply the number of choices at each stage to count total outcomes. Relatively Prime Calculator Check whether two numbers are coprime (share no common factor). Perfect Cube Calculator Check if a number is a perfect cube and find its cube root. Powers of i Calculator Find iⁿ, which cycles through i, −1, −i and 1. Quotient Calculator Find the quotient and remainder of integer division. Remainder Calculator Find the remainder when one number is divided by another. Place Value Calculator Find the place value of a chosen digit in a whole number. Greater Than or Less Than Calculator Compare two numbers and get the correct inequality symbol. Distributive Property Calculator Apply a(b + c) = ab + ac and verify both sides match. Associative Property Calculator Show that (a + b) + c = a + (b + c). Ceiling Function Calculator Round a number up to the nearest integer. Floor Function Calculator Round a number down to the nearest integer. Floor Division Calculator Divide and round the result down to a whole number. Compatible Numbers Calculator Round numbers to compatible values for quick mental estimates. Egyptian Fractions Calculator Express a fraction as a sum of distinct unit fractions. Fermat's Little Theorem Calculator Compute aᵖ⁻¹ mod p, which is 1 when p is prime and a is not a multiple of p. GCF and LCM Calculator Find both the greatest common factor and least common multiple of two numbers. Magic Square Calculator Find the magic constant of an n×n magic square. Partial Products Calculator Multiply two numbers and see the product (partial-products method). Sum of Products Calculator Compute Σ(aᵢ × bᵢ) for paired values. Terminating Decimals Calculator Check whether a fraction gives a terminating decimal. Simplify Cube Root Calculator Simplify ∛n into a·∛b form. Long Addition Calculator Add two numbers, column by column. Long Subtraction Calculator Subtract two numbers, column by column. Long Multiplication Calculator Multiply two multi-digit numbers. Fourth Root Calculator Find the fourth root of a number. Fifth Root Calculator Find the fifth root of a number. Engineering Notation Calculator Convert a number to engineering notation (powers of 1000). Divisor Calculator List the divisors of a number, with their count and sum. Euclidean Algorithm Calculator Find the GCD of two numbers using the Euclidean algorithm. Permutation and Combination Calculator Find nPr (permutations) and nCr (combinations).

Fractions

Algebra

Quadratic Formula Calculator Solve ax² + bx + c = 0 for its real roots. Arithmetic Sequence Calculator Find the nth term and sum of an arithmetic sequence. Geometric Sequence Calculator Find the nth term and sum of a geometric sequence. Binomial Coefficient Calculator n choose k = C(n,k). Discriminant Calculator Δ = b² − 4ac for ax²+bx+c. Complex Number Magnitude |a+bi| = √(a²+b²). Complex Conjugate Calculator a+bi → a−bi. Complex Number to Polar Form a+bi → r∠θ. Absolute Value Equation Calculator Solve |ax + b| = c for both solutions. System of Equations Calculator Solve two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂. Substitution Method Calculator Solve a 2×2 linear system by substitution. Elimination Method Calculator Solve a 2×2 linear system by elimination (addition). Direct Variation Calculator Find the constant k in y = kx and predict a new y. Inverse Variation Calculator Find the constant k in y = k/x and predict a new y. FOIL Calculator Expand (ax + b)(cx + d) into a quadratic using FOIL. Multiplying Binomials Calculator Multiply two binomials (ax + b)(cx + d) and get the expanded form. Square of a Binomial Calculator Expand (ax + b)² into a perfect-square trinomial. Perfect Square Trinomial Calculator Check whether ax² + bx + c is a perfect square and factor it. Cubic Equation Calculator Find a real root of ax³ + bx² + cx + d = 0. Gamma Function Calculator Evaluate the gamma function Γ(x), the continuous extension of factorial. Error Function Calculator Evaluate the error function erf(x) and its complement erfc(x). Complex Number Calculator Add, subtract, multiply or divide two complex numbers. Quaternion Calculator Multiply two quaternions (Hamilton product). Power Set Calculator Count the subsets (power set size) of a set with n elements. Subset Calculator Count how many subsets and k-element subsets a set has. Union and Intersection Calculator Find |A ∪ B| from the sizes of two sets and their intersection. Completing the Square Calculator Rewrite ax² + bx + c in vertex form a(x − h)² + k. Factoring Trinomials Calculator Factor ax² + bx + c by finding its roots. Diamond Problem Calculator Find two numbers given their product and sum. Synthetic Division Calculator Divide a cubic ax³ + bx² + cx + d by (x − r). Polynomial Division Calculator Divide ax² + bx + c by a linear divisor dx + e. Complex Root Calculator Find the principal square root of a complex number a + bi. Descartes' Rule of Signs Calculator Estimate the possible number of positive and negative real roots of a cubic. Adding and Subtracting Polynomials Calculator Add or subtract two quadratics by combining like terms. Multiplying Polynomials Calculator Multiply two quadratics to get a degree-4 polynomial. Bessel Function Calculator Evaluate the Bessel functions J₀(x) and J₁(x). Box Method Calculator Multiply (ax + b)(cx + d) using the box (area) method. Generic Rectangle Calculator Use a generic rectangle to expand or factor a quadratic. Interval Notation Calculator Build interval notation from endpoints and inclusivity. Inequality to Interval Notation Calculator Solve a linear inequality ax + b ≷ c and write the interval. Absolute Value Inequalities Calculator Solve |ax + b| < c or |ax + b| > c. Partial Fraction Decomposition Calculator Decompose (px + q) ÷ ((x − r₁)(x − r₂)) into A/(x − r₁) + B/(x − r₂). Rational Zeros Calculator List possible rational zeros from the leading and constant coefficients. Imaginary Number Calculator Find the modulus, conjugate and argument of a + bi. Complex Number to Polar Form Calculator Convert a + bi into polar form r∠θ. Complex Number to Rectangular Form Calculator Convert polar form r∠θ into a + bi. Multiply Complex Numbers Calculator Multiply two complex numbers (a + bi)(c + di). Divide Complex Numbers Calculator Divide two complex numbers (a + bi) ÷ (c + di).

Exponents and logarithms

Natural Log Calculator Find the natural logarithm (ln) of a number. Log Base 2 Calculator Find the base-2 logarithm of a number. e^x Calculator Raise Euler's number e to a power. Nth Root Calculator Find the nth root of a number. Exponential Growth Calculator Project exponential growth or decay over time. Power of a Power Calculator Simplify (base^a)^b. Antilog Calculator 10^x from a log value. Change of Base Calculator log_b(x) using any base. Condense Logarithms Calculator Combine a·log(x) + b·log(y) into a single logarithm value. Expanding Logarithms Calculator Expand log(xᵃ · yᵇ) into separate logarithm terms. Multiplying Exponents Calculator Multiply powers with the same base by adding exponents. Dividing Exponents Calculator Divide powers with the same base by subtracting exponents. Multiplying Radicals Calculator Multiply two square roots: √a × √b = √(ab). Dividing Radicals Calculator Divide two square roots: √a ÷ √b = √(a/b). Exponential Function Calculator Evaluate y = a · bˣ for given values. Negative Log Calculator Compute −log₁₀(x), as used for pH and pKa. Power of 2 Calculator Compute 2 raised to any exponent. Power of 10 Calculator Compute 10 raised to any exponent. Math Power Calculator Raise any base to any exponent. Power Function Calculator Evaluate a power function f(x) = a·xⁿ. Rational Exponents Calculator Evaluate x^(p/q), a power with a fractional exponent. Exponential Form Calculator Convert a radical ᵑ√x into exponential form x^(1/n).

2D geometry

Circle Calculator Find a circle's area, circumference and diameter from its radius. Rectangle Area Calculator Find the area and perimeter of a rectangle. Triangle Area Calculator Find a triangle's area from its base and height. Square Calculator Find a square's area, perimeter and diagonal. Cube Calculator Find a cube's volume, surface area and diagonal. Sphere Calculator Find a sphere's volume and surface area. Cylinder Calculator Find a cylinder's volume and surface area. Cone Calculator Find a cone's volume, slant height and surface area. Trapezoid Area Calculator Find the area of a trapezoid. Golden Ratio Calculator Find golden-ratio segments from a length. Pentagon Calculator Area and perimeter of a regular pentagon. Hexagon Calculator Area and perimeter of a regular hexagon. Octagon Calculator Area and perimeter of a regular octagon. Ellipse Calculator Area and approximate perimeter of an ellipse. Parallelogram Area Calculator Find the area of a parallelogram. Rhombus Area Calculator Find the area of a rhombus from its diagonals. Sector Area Calculator Find the area and arc length of a circle sector. Arc Length Calculator Find the arc length of a circle. Circumference Calculator Find a circle's circumference and diameter from the radius. Slope Calculator Find the slope between two points. Midpoint Calculator Find the midpoint between two points. Distance Calculator (2D) Find the distance between two 2D points. 3D Distance Calculator Find the distance between two 3D points. Semicircle Area Calculator Area and perimeter of a semicircle. Kite Area Calculator Area = (d1 × d2) ÷ 2. Regular Polygon Calculator Area and perimeter from side count and length. Perimeter Calculator Rectangle perimeter. Diagonal of a Rectangle Calculator d = √(L²+W²). Area of a Circle Calculator A = π r². Perimeter of a Square Calculator P = 4a. Perimeter of a Rectangle Calculator P = 2(L+W). Parallelogram Area Calculator (Alias) A = b × h. Area of a Trapezoid Calculator A = (a+b)·h/2. Circumference of a Circle Calculator C = 2πr. Diameter to Radius Calculator r = d ÷ 2. Radius of a Circle Calculator r from circumference or area. Polygon Angle Calculator Interior angle of n-gon. Area of a Square Calculator A = side². Diagonal of a Square Calculator d = a√2. Quarter Circle Area Calculator A = πr²/4. Foci of an Ellipse c = √(a²−b²). Circumference to Radius Calculator Find a circle's radius and diameter from its circumference. Equation of a Circle Calculator Get circle properties from centre (h, k) and radius r. Square in a Circle Calculator Find the largest square that fits inside a circle of given radius. Tangent of a Circle Calculator Find the tangent length from an external point to a circle. Irregular Polygon Area Calculator Find the area of a polygon from up to five vertex coordinates (shoelace formula). Center of Mass Calculator Find the 1D center of mass of up to three point masses. Centroid Calculator Find the centroid of a triangle from its three vertices. Chord Length Calculator Find a circle's chord length from its radius and central angle. Cycloid Calculator Find the arc length and area of one cycloid arch. Ellipse Calculator Find an ellipse's area, circumference and eccentricity. Golden Rectangle Calculator Find the dimensions of a golden rectangle from one side. Moment of Inertia Calculator Find the moment of inertia for common rigid shapes. Orthocenter Calculator Find the orthocenter of a triangle from its three vertices. Segment Addition Postulate Calculator Use AB + BC = AC to find a missing segment length. Segment Area Calculator Find the area of a circular segment from radius and central angle. Spiral Length Calculator Estimate the length of an Archimedean spiral. Heptagon Calculator Find the area and perimeter of a regular heptagon (7 sides). Decagon Calculator Find the area and perimeter of a regular decagon (10 sides). Dodecagon Calculator Find the area and perimeter of a regular dodecagon (12 sides). Parallelogram Perimeter Calculator Find the perimeter of a parallelogram from its two side lengths. Rhombus Area Calculator Find a rhombus's area from its two diagonals. Quarter Circle Calculator Find the area and perimeter of a quarter circle. Quarter Circle Perimeter Calculator Find just the perimeter of a quarter circle.

Triangles

Heron's Formula Calculator Find a triangle's area from its three sides. Equilateral Triangle Calculator Area, height and perimeter of an equilateral triangle. Isosceles Triangle Calculator Area, height and perimeter of an isosceles triangle. Right Triangle Calculator Solve a right triangle from its two legs. Triangle Angle Calculator Find the third angle of a triangle. 45 45 90 Triangle Calculator Solve a 45-45-90 right triangle from a leg. 30 60 90 Triangle Calculator Solve a 30-60-90 triangle from the short leg. Pythagorean Triples Checker Check if (a,b,c) is a Pythagorean triple. Triangle Inequality Checker Can three sides form a triangle? Perimeter of a Triangle Calculator P = a + b + c. Area of a Triangle SAS Calculator Area = ½ a b sin(C). Area of a Triangle SSS Calculator Heron's formula alias. Sum of Angles in a Triangle Third angle from two. Isosceles Right Triangle Hypotenuse c = a√2. Triangle Height Calculator h = 2A ÷ b. Midsegment of a Triangle Calculator Midsegment = base/2. Scalene Triangle Calculator Area via Heron for scalene. Area of a Right Triangle Calculator Find the area of a right triangle from its two legs. Hypotenuse Calculator Find the hypotenuse of a right triangle from its two legs. Classifying Triangles Calculator Classify a triangle by its sides and angles. Similar Triangles Calculator Find a missing side using the scale factor between similar triangles. Circumscribed Circle Calculator Find the circumradius of a triangle from its three sides. Inscribed Circle Calculator Find the inradius of a triangle from its three sides. Right Triangle Side and Angle Calculator Find the remaining sides and angle from one leg and its opposite angle. Special Right Triangles Calculator Find all sides of a 45-45-90 or 30-60-90 triangle from the short side.

Angles

3D geometry

Rectangular Prism Calculator Volume, surface area and diagonal of a box. Pyramid Volume Calculator Find the volume of a rectangular-base pyramid. Triangular Prism Calculator Find the volume of a triangular prism. Hemisphere Calculator Volume and surface area of a hemisphere. Torus Calculator Find torus volume and surface area. Tetrahedron Volume Calculator Volume of a regular tetrahedron. Truncated Cone (Frustum) Calculator Find frustum volume. Sphere Volume Calculator V = 4/3 π r³. Volume of a Cube Calculator V = a³. Cylinder Volume Calculator V = π r² h. Cone Volume Calculator V = π r² h / 3. Volume of a Pyramid Calculator V = base-area × h / 3. Volume of a Rectangular Prism V = l × w × h. Ellipsoid Volume Calculator V = 4/3 π a b c. Great Circle Distance Calculator Haversine distance on a sphere. Surface Area of a Sphere Calculator SA = 4πr². Surface Area of a Cube Calculator SA = 6a². Surface Area of a Cylinder Calculator SA = 2πr(r+h). Surface Area of a Cone Calculator SA = πr(r + l). Lateral Area of a Cone Calculator πrl. Slant Height of a Cone Calculator l = √(r² + h²). Radius of a Sphere Calculator r from volume. Radius of a Cone Calculator r from V and h. Radius of a Cylinder Calculator r from V and h. Height of a Cone Calculator h from V and r. Height of a Cylinder Calculator h from V and r. Cuboid Surface Area SA = 2(lw+lh+wh). Cuboid Volume Calculator V = lwh. Sphere Area Calculator SA = 4πr². Slant Height of a Cone l = √(r²+h²). Square Pyramid Volume V = a²h/3. Triangular Pyramid Volume V = Bh/3. Truncated Cone Volume V = πh/3(R²+Rr+r²). Volume of a Hemisphere Calculator Find the volume of a hemisphere from its radius. Surface Area of a Hemisphere Calculator Find the total surface area of a solid hemisphere. Euler's Formula for Polyhedron Calculator Use V − E + F = 2 to find the missing count for a convex polyhedron. Surface Area of a Triangular Prism Calculator Find the surface area of a triangular prism. Surface Area to Volume Ratio Calculator Find the surface-area-to-volume ratio of a sphere or cube. Volume of a Trapezoidal Prism Calculator Find the volume of a prism with a trapezoidal cross-section. Cuboid Calculator Find a cuboid's volume, surface area and space diagonal. Hollow Cylinder Volume Calculator Find the volume of a pipe / hollow cylinder. Square Pyramid Calculator Find a square pyramid's volume, surface area and slant height. Square Pyramid Volume Calculator Find the volume of a square pyramid. Rectangular Pyramid Volume Calculator Find the volume of a rectangular-based pyramid. Hexagonal Pyramid Calculator Find the volume and surface area of a regular hexagonal pyramid. Truncated Cone Calculator Find the volume, slant height and lateral area of a frustum (truncated cone). Area of a Frustum of a Cone Calculator Find the lateral and total surface area of a cone frustum. Lateral Area of a Trapezoidal Prism Calculator Find the lateral surface area of a trapezoidal prism. Pyramid Angle Calculator Find the face and edge angles of a square pyramid.

Coordinate geometry

Endpoint Calculator Find an endpoint from a start point and the midpoint. Line Equation from Two Points Find the slope-intercept equation through two points. Dot Product Calculator Find the dot product of two 2D vectors. Polar to Cartesian Converter (r,θ) → (x,y). Manhattan Distance Calculator |X₁−X₂| + |Y₁−Y₂|. Linear Interpolation Calculator Find y at x on a line. Rectangular to Polar Coordinates (x,y) → (r,θ). Area of Triangle with Coordinates Shoelace formula. Cross Product Calculator A × B for 3D. Vector Magnitude Calculator |v| = √(x²+y²+z²). Unit Vector Calculator Normalize vector. Average Rate of Change Calculator Find the average rate of change of a function between two points. Cosine Similarity Calculator Measure the cosine of the angle between two 3D vectors. Cylindrical Coordinates Calculator Convert Cartesian (x, y, z) to cylindrical (r, θ, z). Spherical Coordinates Calculator Convert Cartesian (x, y, z) to spherical (ρ, θ, φ). Direction of the Vector Calculator Find the direction angle of a 2D vector. Distance from Point to Plane Calculator Find the distance from a point to the plane ax + by + cz + d = 0. Intersection of Two Lines Calculator Find where two lines y = m₁x + b₁ and y = m₂x + b₂ cross. Parallel Line Calculator Find the line parallel to y = mx + b that passes through a given point. Perpendicular Line Calculator Find the line perpendicular to y = mx + b through a given point. Point Slope Form Calculator Build a line from a point and slope, and convert to slope-intercept form. Slope Intercept Form Calculator Evaluate y = mx + b and find roots and intercepts. Standard Form to Slope Intercept Form Calculator Convert Ax + By = C into y = mx + b. y-Intercept Calculator Find the y-intercept of the line through two points. Rise Over Run Calculator Find slope as rise divided by run, plus the angle. Rotation Calculator Rotate a point about the origin by a given angle. Ratios of Directed Line Segments Calculator Find the point dividing a segment in a given ratio (section formula). Vector Addition Calculator Add two 2D vectors and find the resultant magnitude and direction. Vector Projection Calculator Project vector a onto vector b (2D). Vertex Form Calculator Convert vertex form a(x − h)² + k into standard form. Parabola Calculator Find the vertex, axis and direction of y = ax² + bx + c. Latus Rectum Calculator Find the latus rectum length of the parabola y = ax². Volume of a Parallelepiped Calculator Find the volume from three edge vectors via the scalar triple product. Bilinear Interpolation Calculator Interpolate a value inside a grid from its four corner values. Catenary Curve Calculator Find the height and arc length of a hanging catenary y = a·cosh(x/a). Coordinate Grid Calculator Find the distance and midpoint between two grid points. Equation of a Sphere Calculator Get a sphere's volume, surface area and general-form constant from centre and radius. Gradient Calculator Find the gradient (slope) of the line through two points. Least Squares Regression Line Calculator Fit a best-fit line y = mx + b through up to five points. Line of Intersection of Two Planes Calculator Find the direction vector of the line where two planes meet. Triangulation Calculator Locate a point's distance using a baseline and two angles. Euclidean Distance Calculator Find the straight-line distance between two points in 3D.

Trigonometry

Pythagorean Theorem Calculator Find the hypotenuse of a right triangle from the two legs. Trigonometry Calculator Find sine, cosine and tangent of an angle. Law of Cosines Calculator Find the third side of a triangle from two sides and the included angle. Law of Sines Calculator Find a missing side using the law of sines. Double Angle Calculator sin(2θ), cos(2θ), tan(2θ). Half Angle Calculator sin(θ/2), cos(θ/2), tan(θ/2). Unit Circle Calculator Coordinates on the unit circle. Inverse Trig Calculator arcsin/arccos/arctan of a value. Secant and Cosecant Calculator sec θ = 1/cos θ ; csc θ = 1/sin θ. Hyperbolic Functions Calculator sinh x, cosh x, tanh x. Sine Calculator sin of an angle. Cosine Calculator cos of an angle. Tangent Calculator tan of an angle. Hyperbolic Sine/Cosine Calculator sinh/cosh of x. Arcsin Calculator (Inverse Sine) Find the angle whose sine is a given value. Arccos Calculator (Inverse Cosine) Find the angle whose cosine is a given value. Arctan Calculator (Inverse Tangent) Find the angle whose tangent is a given value. Cotangent Calculator Find the cotangent of an angle. Cofunction Calculator Apply cofunction identities like sin θ = cos(90° − θ). Phase Shift Calculator Find amplitude, period, phase and vertical shift of A·sin(Bx − C) + D. Power Reducing Calculator Evaluate power-reducing identities like sin²θ = (1 − cos 2θ)/2. Sum and Difference Identities Calculator Evaluate sin/cos/tan of a sum or difference of two angles. Decimal Degrees to DMS Converter Convert decimal degrees to degrees, minutes and seconds. DMS to Decimal Degrees Converter Convert degrees, minutes and seconds to decimal degrees.

Sequences

Binary