Math calculators

146 free math tools, each with the formula and step-by-step working.

• 2D Vector Addition CalculatorAdd two vectors and find the resultant magnitude and angle.
• 2x2 Eigenvalue CalculatorEigenvalues of a 2x2 matrix from the characteristic equation.
• 2x2 Matrix Addition & Subtraction CalculatorAdd or subtract two 2x2 matrices.
• 2x2 Matrix Multiplication CalculatorMultiply two 2x2 matrices.
• 3D Distance CalculatorStraight-line distance between two points in space.
• 3x3 Matrix Determinant CalculatorDeterminant of a 3x3 matrix by cofactor expansion.
• Absolute Value CalculatorDistance from zero, and |ax+b| equations.
• Antilog CalculatorInverse logarithm for any base.
• Arc Length CalculatorLength of a circular arc.
• Area Between Two Curves CalculatorArea enclosed between two polynomial curves.
• Arithmetic Sequence Calculatornth term and sum of an arithmetic series.
• Arithmetic Series Sum CalculatorSum of the first n terms of an arithmetic sequence.
• Asymptote Finder (Rational Function)Vertical and horizontal asymptotes of P(x)/Q(x).
• Binary ConverterBinary, decimal, hex and octal in one step.
• Bisection Method CalculatorBracket a root and halve the interval, safely every time.
• Change of Base CalculatorRewrite any logarithm in the base your calculator supports.
• Circle CalculatorArea, circumference and diameter from any one value.
• Circle Equation CalculatorCentre, radius, standard and general form of any circle.
• Circular Permutation CalculatorSeating people round a table, with and without reflections.
• Circular Sector Area CalculatorArea and arc length of a circle sector.
• Circumference CalculatorCircle circumference from radius or diameter.
• Coin Flip Probability CalculatorOdds of getting a number of heads in N flips.
• Combination and Permutation CalculatornCr, nPr and factorials for counting problems.
• Combinations With Repetition CalculatorMultiset counting — donuts, dice and stars and bars.
• Completing the Square CalculatorTurn ax² + bx + c into a(x − h)² + k with every step.
• Complex Number Operations CalculatorAdd, subtract, multiply and divide two complex numbers.
• Complex Number Polar Form CalculatorConvert a complex number between rectangular and polar form.
• Composite Function CalculatorEvaluate f(g(x)) for two linear functions.
• Cone Volume CalculatorVolume and surface area of a cone.
• Conic Eccentricity CalculatorClassify any conic and find its eccentricity.
• Critical Points Calculator (Cubic)Find critical points of a cubic and classify them.
• Cross Product CalculatorVector cross product in 3D.
• Cube Root CalculatorCube root of any number.
• Cylinder Surface Area CalculatorTotal and lateral area, volume and paint coverage.
• Definite Integral Calculator (Polynomial)Exact definite integral of a cubic polynomial.
• Degrees to Radians CalculatorConvert an angle from degrees to radians.
• Derivative Power Rule CalculatorDifferentiate a polynomial term by term.
• Determinant Calculator2×2 and 3×3 matrix determinants.
• Difference of Cubes CalculatorFactor a³ − b³ and a³ + b³ step by step.
• Discriminant Calculatorb² − 4ac tells you how many roots a quadratic has.
• Distance Formula CalculatorDistance and midpoint between two coordinates.
• Domain & Range Calculator (Square Root / Rational)Domain restrictions for sqrt and rational expressions.
• Dot Product CalculatorScalar product and angle between vectors.
• Ellipse CalculatorArea, perimeter and foci of an ellipse.
• Ellipse Eccentricity CalculatorEccentricity, foci and axes of an ellipse.
• Equilateral Triangle CalculatorArea, height, perimeter and radii from one side.
• Euler's Method CalculatorStep a differential equation forward one interval at a time.
• Exponent CalculatorPowers, roots, scientific notation and logs in one place.
• Extrapolation CalculatorLinear extrapolation beyond two known points.
• Factorial Calculatorn! and related combinatorics.
• Fibonacci CalculatorFibonacci terms and the golden ratio.
• Fraction CalculatorAdd, subtract, multiply and divide fractions with full working.
• Fraction to Decimal CalculatorConvert fractions to decimals and percentages, both ways.
• GCF and LCM CalculatorGreatest common factor and least common multiple, with prime factors.
• Geometric Mean CalculatorAverage growth rate across multiple periods.
• Geometric Sequence Calculatornth term and sum of a geometric series.
• Geometric Series Sum CalculatorSum of a finite or infinite geometric series.
• Graphing CalculatorPlot any function instantly, with roots, extrema and a value table.
• Harmonic Mean CalculatorThe right average for rates, speeds and ratios.
• Harvard Graphing CalculatorThe Harvard-style online function plotter: graph f(x) with roots, extrema and a value table.
• Hexagon Area CalculatorRegular hexagon area and perimeter.
• Hyperbola Asymptote CalculatorVertices, foci and asymptotes of a hyperbola.
• Hyperbola CalculatorCenter, vertices, foci, eccentricity and asymptotes from a, b and the center.
• Inverse Function Calculator (Linear)Find the inverse of y = mx+b.
• Isosceles Trapezoid CalculatorArea, perimeter, legs, diagonals and base angles.
• Law of Cosines CalculatorSolve triangles with two sides and an angle.
• Law of Sines CalculatorSolve triangles from angles and a side.
• Limit Calculator (Rational Function at a Point)Numerically estimate the limit of a rational function.
• Logarithm Calculatorlog base 10, natural log and any custom base.
• Logarithm Calculatorlog base 10, natural log and any custom base at once.
• Logarithm Change of Base CalculatorCompute log base b of x using the change-of-base formula.
• Matrix Determinant Calculator2×2 and 3×3 determinants with cofactor working.
• Matrix Inverse Calculator (2×2)Invert a 2×2 matrix and solve the linear system.
• Mean Value Theorem CalculatorFind every c in (a, b) where the instantaneous rate equals the average rate of change.
• Midpoint CalculatorMidpoint between two coordinates.
• Midpoint of a Line Segment CalculatorMidpoint and length of a line segment between two points.
• Mixed Number CalculatorConvert and add mixed numbers.
• Modular Inverse CalculatorFind x where a·x ≡ 1 (mod m), with the GCD check.
• Modulo CalculatorRemainder after division.
• Natural Log (ln) CalculatorCompute ln(x) and its inverse e^x.
• Newton Raphson CalculatorOne Newton step at a time, with convergence check.
• Normal Line CalculatorEquation of the normal line to a curve at a point.
• Numerical Integration Calculator (Simpson's Rule)Approximate a definite integral of a list of function values.
• Oblique Triangle CalculatorSolve any non-right triangle from three known parts.
• Parabola CalculatorFocus, directrix, vertex and latus rectum of a parabola.
• Parabola Vertex & Focus CalculatorVertex, focus and directrix from a quadratic.
• Partial Derivative CalculatorNumeric partial derivatives of multivariable functions at a point, including gradients.
• Partial Fraction Decomposition CalculatorSplit a fraction over (x-p)(x-q) into two simple fractions.
• Pascal's Triangle CalculatorAny row of Pascal's triangle and the binomial expansion.
• Percent Error CalculatorExperimental accuracy against a true value.
• Percentage CalculatorPercent of a number, percent change and 'X is what % of Y'.
• Percentage Change CalculatorIncrease, decrease and percentage-point difference.
• Percentage Increase CalculatorGrowth or decline between two values, in percent.
• Permutation CalculatorOrdered arrangements nPr.
• Perpendicular Bisector CalculatorMidpoint, slope and equation of the bisector.
• Piecewise Function CalculatorEvaluate and graph piecewise-defined functions, and test continuity at a point.
• Piecewise Function EvaluatorEvaluate a two-piece function at a point.
• Point Slope Form Calculatory − y₁ = m(x − x₁), converted to every other form.
• Polynomial Long Division Calculator (Cubic ÷ Linear)Divide a cubic by (x - r) with quotient and remainder.
• Prime Factorization CalculatorBreak any number into its prime building blocks.
• Prism Volume CalculatorVolume and surface area for rectangular and triangular prisms.
• Pyramid Volume CalculatorVolume and surface area of a pyramid.
• Pythagorean Theorem CalculatorSolve for any missing side of a right triangle.
• Quadratic Discriminant CalculatorDiscriminant and root type for ax²+bx+c.
• Quadratic Formula CalculatorRoots, vertex and discriminant for ax² + bx + c.
• Quadratic Vertex CalculatorVertex, axis, intercepts and vertex form from a, b, c.
• Radians to Degrees CalculatorConvert an angle from radians to degrees.
• Radical Form CalculatorSimplify square and nth roots to exact radical form, with the decimal value.
• Random Number GeneratorRandom integers in any range, with or without repeats.
• Ratio CalculatorSimplify ratios, scale them and solve for a missing term.
• Rectangle Area CalculatorArea, perimeter and diagonal.
• Recursive Sequence CalculatorGenerate terms from aₙ = r·aₙ₋₁ + d, including Fibonacci-style rules.
• Reference Angle CalculatorReference angle, quadrant and exact trig signs.
• Regular Polygon Area CalculatorArea, perimeter, apothem and angles for any n-gon.
• Relative Extrema CalculatorLocate local maxima, local minima and inflection points on any interval.
• Remainder Theorem CalculatorEvaluate a cubic at x = a to get the remainder instantly.
• Rhombus Area CalculatorArea from diagonals, side and angle, or base and height.
• Riemann Sum CalculatorLeft, right, midpoint and trapezoid sums from your own function values.
• Right Triangle Side CalculatorMissing leg or hypotenuse, plus both acute angles.
• Rolle's Theorem CalculatorCheck the hypotheses and find every c in (a, b) with f′(c) = 0.
• Roman Numeral ConverterNumbers to Roman numerals and back.
• Root Mean Square CalculatorRMS value of any dataset, waveform or error list.
• Rounding CalculatorRound to decimals, whole numbers or any nearest multiple.
• Scientific Notation ConverterConvert between standard form and decimal notation.
• Sector Area CalculatorArea of a pie slice of a circle.
• Segment Addition Postulate CalculatorSolve AB + BC = AC for the missing segment.
• Sig Fig Counter & Rounding CalculatorCount sig figs and round correctly.
• Simplify Fraction CalculatorReduce any fraction to lowest terms.
• Simpson's Rule CalculatorApproximate definite integrals with Simpson's 1/3 rule and compare with the trapezoid rule.
• Slope CalculatorGradient, angle, distance and the line equation.
• Slope Intercept Form CalculatorTwo points in, y = mx + b out, with every related form.
• Sphere Volume CalculatorSphere volume and surface area.
• Square Root CalculatorExact simplified radical plus the decimal value.
• Sum of Series CalculatorArithmetic, geometric and infinite series sums in one place.
• Surface Area CalculatorSurface area of common 3D shapes.
• Synthetic Division CalculatorDivide a polynomial by (x − a) with the full working shown.
• Tangent Line CalculatorFind the tangent line to a curve at any point, in slope-intercept form.
• Taylor Series Expansion Calculator (e^x, sin x, cos x)Taylor polynomial approximation for common functions.
• Trapezoid Area CalculatorArea and perimeter of a trapezoid.
• Trapezoidal Rule CalculatorNumeric integration from a table of function values.
• Triangle Area CalculatorArea from base and height, or all three sides.
• Unit Circle CalculatorSine, cosine and tangent of any angle.
• Unit Circle Reference Angle CalculatorReference angle, quadrant and sine/cosine on the unit circle.
• Vector Magnitude CalculatorLength, unit vector and direction angles in 2D or 3D.
• Vector Projection CalculatorProject vector A onto vector B.
• Volume CalculatorVolume of cylinders, boxes, spheres and cones.

Looking for something else? Browse all categories or start from the home page. Category path: /category/math