Math & Tools

Math Calculators

Algebra, geometry, number theory and everyday maths. Free calculators with formulas and worked examples.

Geometry

Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values.Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle.Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles.Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c².Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal.Trapezoid Area CalculatorEnter the two parallel sides and the height to find the area of a trapezoid.Sphere Volume and Surface Area CalculatorEnter the radius to find the volume and surface area of a sphere.Cylinder Volume CalculatorEnter the radius and height to find a cylinder's volume and surface area.Cone Volume CalculatorEnter the radius and height of a cone to find its volume, slant height and surface area.Rectangular Prism (Box) Volume CalculatorEnter the three dimensions of a box to find its volume and surface area.Regular Polygon CalculatorEnter the number of sides and the side length of a regular polygon.Ellipse CalculatorEnter the semi-major and semi-minor axes of an ellipse.Arc Length and Sector Area CalculatorEnter the radius and central angle in degrees to find arc length, sector area and chord length.Right Triangle Calculator (Sides, Angles, Area)Choose what you know and enter the values.Law of Sines Calculator (Solve a Triangle from Two Angles and a Side)Enter side a, its opposite angle A, and angle B.Clock Angle Calculator (Angle Between the Hands)Enter the hour and minutes.Triangle Calculator (Three Sides)Enter three sides and get everything else.Pyramid CalculatorBase, height, volume and surface in one view.Torus CalculatorVolume and surface of a ring or donut.

Vectors and matrices

Matrix Multiplication Calculator (3×3)Enter matrices A and B row by row.Vector Calculator (3D Magnitude, Dot and Cross Product, Angle)Enter the components of two vectors (use z = 0 for 2D).Matrix Determinant and Inverse Calculator (3×3)Enter the nine entries of the matrix row by row (use 0 and 1 to embed a 2×2 matrix).Eigenvalue Calculator (2×2 Matrix)Enter the four entries of a 2×2 matrix.

Algebra

Linear Equation SolverSolve a one-variable linear equation of the form ax + b = c.System of Equations Calculator (2×2)Solve a system of two linear equations, a₁x + b₁y = c₁ and a₂x + b₂y = c₂.Cubic Equation Calculator (Solve ax³ + bx² + cx + d = 0)Enter the four coefficients to find every root.Complex Number Calculator (Add, Multiply, Divide, Polar Form)Enter two complex numbers a + bi and c + di and choose the operation.Exponential Growth and Decay CalculatorEnter the starting value, rate and time.Parabola Calculator (Vertex, Focus, Directrix, Vertex Form)Enter the coefficients a, b and c.Quadratic Equation SolverSolve any quadratic equation ax² + bx + c = 0 and see the discriminant, both roots and the vertex.

Coordinate geometry

Slope CalculatorEnter two points to get the slope of the line through them, its angle and its equation.Distance Between Two Points CalculatorFind the straight-line (Euclidean) distance between two points in three-dimensional space. Leave z at 0 for 2D.Midpoint CalculatorEnter the two endpoints to find the point exactly halfway between them.Polar to Cartesian Converter (and Back)Choose the direction and enter the coordinates.Polygon Area Calculator (Shoelace Formula from Coordinates)List the corner coordinates in order around the shape (clockwise or anticlockwise).

Powers and roots

Exponent CalculatorRaise any number to any power, and see the reciprocal and the equivalent root.Logarithm CalculatorFind log base b of x, along with ln(x), log₁₀(x) and log₂(x).Nth Root CalculatorFind the nth root of a number, such as a square root or cube root.

Number theory

GCD and LCM CalculatorEnter two whole numbers to find their greatest common divisor and least common multiple.Factorial CalculatorCalculate the factorial n! of a whole number.Fibonacci Number CalculatorFind the nth Fibonacci number, where each number is the sum of the two before it.Prime Factorization CalculatorEnter a whole number to break it into prime factors.Prime Number Calculator (Is It Prime? Next and Previous Prime)Enter a whole number to test whether it is prime.Factors Calculator (All Divisors of a Number)Enter a whole number to list all of its factors.

Trigonometry

Law of Cosines CalculatorEnter two sides and the included angle (SAS) to solve the rest of the triangle.Degrees to Radians ConverterConvert an angle between degrees and radians and see its sine, cosine and tangent.Trigonometry Calculator (sin, cos, tan, sec, csc, cot)Enter an angle and choose degrees or radians.

Arithmetic

Percentage Change CalculatorFind the percentage change from an old value to a new value.Ratio Simplifier CalculatorSimplify a ratio A : B to its lowest terms.Fraction CalculatorDo arithmetic with two fractions and see the answer in lowest terms.Scientific Notation ConverterWrite any number in scientific notation, a × 10ⁿ.Long Division Calculator (Quotient and Remainder)Enter the dividend and divisor.Modulo Calculator (a mod n)Enter a number and the modulus.Rounding Calculator (Decimals, Half Even, Up, Down)Enter a number, the decimal places and the rounding rule.Significant Figures Calculator (Count and Round)Type the number exactly as written (keep trailing zeros) and choose how many significant figures to round to.Number to Words Converter (Cheque Writing, Lakh and Crore)Enter a number to see it written out in words.Square Root CalculatorRoots and squares, with perfect-square neighbours.

Sequences and series

Arithmetic Sequence CalculatorEnter the first term, common difference and n to get the nth term and the sum.Geometric Sequence CalculatorEnter the first term, common ratio and n to get the nth term, the partial sum and the infinite sum.

Fractions

Simplify Fraction Calculator (Reduce to Lowest Terms)Enter the numerator and denominator to simplify the fraction.Decimal to Fraction CalculatorEnter a decimal number and, optionally, the largest denominator you want.Fraction to Decimal Calculator (Repeating Decimals)Enter a numerator and denominator to see the exact decimal.

Ratios

Proportion Calculator (Solve for x)Enter three known values to find the fourth.Golden Ratio Calculator (φ = 1.618…)Enter a length and say which part it is.

Percentages

Percent Error CalculatorEnter the measured value and the accepted value.Reverse Percentage Calculator (Find the Original Value)Enter the final amount and the percentage that was added or taken off.Percentage Difference CalculatorCompare two values when neither is the 'original'.

Special functions

Gamma Function Calculator (Γ(x))Enter a positive number.

3D shapes

Triangular Prism Calculator (Volume and Surface Area)Enter the three sides of the triangular end and the prism's length.Hemisphere Calculator (Volume and Surface Area)Enter the radius of the hemisphere.

About these calculators

From solving equations to finding the area of a shape, these calculators show the answer and the working. Each page explains the formula behind the result so you can learn the method, not just copy the number.

Each calculator explains its formula, includes a worked example and lists its sources. Read how we check them on our editorial policy page, or browse all calculators.

More in Math & Tools

Statistics & Probability Calculators & Generators

Please note: TheCalcTools gives general estimates for information and education. It is not financial, medical, legal or tax advice, and results should be checked before you make a decision. See our disclaimer and about page.