Maths & numbers
tools and calculators.
99 practical tools with clear inputs and explanations. Choose a tool below, or explore a role-based toolbox for a collection that fits your day.
Percentage calculator
Discounts, increases and everyday percentage puzzles.
Convex hull builder
Find and plot the outer boundary of a point cloud.
Closest pair in a point cloud
Find the nearest two points and show their distance on a plot.
Polygon centroid calculator
Locate the uniform-area centre of a simple polygon and plot it.
Point-in-polygon checker
Test whether a point lies inside, outside or on the edge of a polygon.
Line segment intersection
Find a crossing point or collinear overlap between two finite segments.
Circle intersection points
Find the intersection coordinates of two circles and view their geometry.
Infinite line & circle intersections
Find where the line through two points crosses a circle.
Triangle centres from coordinates
Plot the centroid, incentre, circumcentre, orthocentre and nine-point centre.
Complex number arithmetic
Add, subtract, multiply or divide complex numbers and inspect polar form.
Nth roots of a complex number
List and plot all distinct nth roots of a complex value.
Triangle barycentric coordinates
Express a point as weights of three triangle vertices and check containment.
Point-to-plane distance
Find signed distance and the closest point on a 3D plane.
Plane through three 3D points
Find a unit-normal plane equation from three non-collinear coordinates.
3D line & plane intersection
Intersect an infinite directed line with a plane or identify parallel cases.
Intersection of two planes
Find a point and unit direction for the line where two 3D planes meet.
3D Euler rotation workspace
Apply an explicit X–Y–Z rotation order and inspect the resulting matrix.
Quaternion vector rotation
Normalise a Hamilton quaternion and use it to rotate a 3D vector.
Polynomial evaluator
Evaluate a coefficient list and its derivative using Horner arithmetic.
Polynomial arithmetic
Add, subtract or multiply polynomial coefficient lists and export the resulting coefficients.
Polynomial long division
Divide two polynomial coefficient lists and inspect quotient and remainder.
Adaptive numerical integration
Estimate a definite integral with an evaluation count and error estimate.
Numerical derivative workspace
Estimate first and second derivatives and compare sensitivity to the chosen step.
Bracketed root finder
Find one root in a sign-changing interval and inspect the final residual.
Function value table
Sample an expression at evenly spaced X positions and export the full table.
Finite difference table
Build successive forward differences from equally spaced observations.
Polynomial interpolation workspace
Interpolate up to 20 points and export a sampled polynomial curve.
Natural cubic spline workspace
Interpolate an ordered point set with natural endpoint conditions and export samples.
Row reduction, rank & nullspace
Reduce a small matrix and inspect pivot columns, numerical rank and nullspace basis.
2 × 2 eigenvalue calculator
Find real or complex-conjugate eigenvalues of a real 2 × 2 matrix.
Cholesky decomposition
Factor a small symmetric positive-definite matrix as L times its transpose.
Pivoted LU decomposition
Inspect lower and upper triangular factors and the row permutation.
QR decomposition
Factor a small matrix into an orthonormal basis and upper-triangular coefficients.
Polynomial least-squares fit
Fit a low-degree curve to point data and inspect fitted values and residuals.
Iterative linear-system solver
Trace Jacobi or Gauss–Seidel iterations and inspect residual convergence.
Chinese remainder solver
Solve compatible integer congruences, including non-coprime moduli.
Modular multiplicative inverse
Find an exact integer inverse and verify the modular product.
Continued fractions & convergents
Inspect rational convergents of a supplied decimal number.
Venn diagram builder
Compare two or three lists, see exact overlaps and export the diagram and memberships.
Interactive function plotter
Graph up to three expressions, zoom the viewport and inspect values along the X axis.
3D vector calculator
Calculate lengths, dot and cross products, angle and vector projection.
Small matrix calculator
Add, multiply, transpose, invert or find a determinant for matrices up to 6 × 6.
Triangle from sides & angles
Solve a plane triangle from two sides and their included angle, or one side and two angles.
Circle through three points
Find the circumcentre, radius and equation of the circle through three plane points.
Cartesian & spherical coordinates
Translate 3D Cartesian coordinates and radius/azimuth/polar-angle coordinates.
Annulus calculator
Find the area, ring width and boundary lengths of a circular ring.
Spherical cap calculator
Calculate the volume, base radius and surface areas of a sphere cut by a plane.
Conical frustum calculator
Find the volume and surface areas of a truncated right circular cone.
Rectangular pyramid calculator
Calculate a centred right pyramid’s volume, side areas and edge length.
Capsule volume & area
Measure a cylinder with two hemispherical ends.
Ellipsoid volume calculator
Calculate volume and axis lengths from three semi-axes.
Descriptive statistics
Mean, median, mode, spread and standard deviation for your numbers.
Fraction calculator
Add, subtract, multiply or divide exact fractions.
Ratio simplifier
Reduce a ratio of whole numbers to its simplest form.
Percentage change
Find the increase or decrease from one value to another.
Random number generator
Generate unbiased whole numbers within your chosen range.
Prime number checker
Check whether a whole number is prime.
GCD & LCM calculator
Find the greatest common divisor and least common multiple.
Quadratic equation solver
Solve ax² + bx + c = 0, including complex roots.
Circle calculator
Find a circle’s area, diameter and circumference from its radius.
Rectangle calculator
Calculate area, perimeter and diagonal from two side lengths.
Triangle calculator
Find area and perimeter from three side lengths.
Pythagorean calculator
Find the hypotenuse of a right-angled triangle.
Factorial calculator
Calculate exact factorials from 0! to 1000!.
Combinations & permutations
Count ordered or unordered selections without replacement.
Prime factorisation
Break a whole number into its prime factors.
Roman numeral converter
Convert whole numbers and canonical Roman numerals.
Number to words
Write whole numbers in British English.
Scientific notation converter
Express a number in standard and scientific notation.
Proportion calculator
Solve a / b = c / x for the missing fourth value.
Percentage difference
Compare two non-negative values symmetrically.
Weighted average
Calculate an average with a different weight for each value.
Sphere calculator
Calculate a sphere’s volume and surface area from its radius.
Cylinder calculator
Find a right cylinder’s volume, curved area and total surface.
Cone calculator
Calculate volume, slant height and surface area of a right cone.
Cube calculator
Find a cube’s volume, surface area and space diagonal.
Cuboid calculator
Calculate a rectangular box’s volume, surface and space diagonal.
Trapezoid area calculator
Find area from parallel sides and perpendicular height.
Parallelogram area calculator
Use a base and its perpendicular height to calculate area.
Ellipse calculator
Calculate area and an approximate ellipse perimeter.
Regular polygon calculator
Find the area, perimeter and radii of a regular polygon.
Arc length calculator
Translate a circle’s central angle into an arc length.
Circular sector calculator
Calculate a sector’s area, arc and perimeter.
Polygon coordinate area
Calculate a simple polygon’s area from ordered coordinates.
Distance between two points
Find straight-line distance in a two-dimensional coordinate plane.
Midpoint calculator
Find the point halfway between two coordinate pairs.
Line slope calculator
Find a line’s gradient and intercept from two points.
Line equation evaluator
Evaluate y = mx + b and find its axis intercepts.
Linear equation solver
Solve a single equation of the form ax + b = c.
Two linear equations solver
Solve two equations in x and y using their coefficients.
Arithmetic sequence calculator
Find a term and partial sum of a constant-step sequence.
Geometric sequence calculator
Find a term and finite sum of a constant-ratio sequence.
Logarithm calculator
Calculate a logarithm in a chosen positive base.
Exponent calculator
Raise a number to a power with real-number validation.
Nth root calculator
Find a real positive- or odd-negative-number root.
Standard error of the mean
Summarise sample variability and the standard error of its mean.
Z-score calculator
Express a value in standard deviations from a supplied mean.
Percentile calculator
Find an interpolated percentile in a set of numbers.
Linear interpolation calculator
Estimate a y value on the line through two known points.