Maths calculators
Every maths calculator here shows its result as you type, from a percentage or a GCD to a determinant, a derivative or a confidence interval. They are grouped below by branch, so you can go straight to geometry, statistics or algebra rather than hunting through a single long list.
3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.Annulus (ring) area calculatorCompute the area of a ring from its outer and inner radius.Aquarium volume calculatorCompute the water volume of a rectangular aquarium in litres and gallons.Area calculatorCompute the area of a rectangle, square, circle or triangle.Circle calculatorCompute the area, circumference and diameter of a circle from its radius.
ANOVA Calculator (One-Way)Full one-way ANOVA table — SS, df, MS, F and p — plus η², ω² and Cohen's f, because a significant F on its own tells you nothing about how large the difference is. The equal-variance assumption is stated, not buried.Average (mean) calculatorCompute the mean, sum and count of a list of numbers.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Bayes Theorem CalculatorCompute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.
Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Absolute Value Inequality SolverSolve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.Algebraic Expression SimplifierCombines like terms, expands or factors, with implicit multiplication understood (2x is 2·x). When a cancellation removes a factor, the excluded value is stated — (x²−4)/(x−2) is x+2 only for x ≠ 2, and that restriction is part of the answer.Beta Function CalculatorCompute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.Boolean Algebra SimplifierReduces a boolean expression to a minimal sum of products, accepting every common notation — AB, A·B, A&B for AND, A+B or A|B for OR, ~A, !A or A' for NOT, plus XOR, NAND and NOR. Shows the prime implicants, not just the final answer.Characteristic polynomial calculatorEnter a square matrix (2×2 to 5×5) and get its characteristic polynomial p(λ) = det(λI − A), whose roots are the eigenvalues. It uses the Faddeev–LeVerrier algorithm, which is exact at any size, and also reports the trace and determinant.
Antilog Calculator (inverse logarithm)The antilogarithm undoes the logarithm: antilog_b(y) = bʸ, so log_b(bʸ) = y. Pick base 10, e, 2 or your own, enter the exponent, and the result comes back with the inverse relationship spelled out and the round trip checked. Bases of zero or less, and base 1, are rejected with the reason.Arc length calculatorThe length of a circular arc from the radius and the central angle — arc = r·θ, with θ in radians. Work in either direction: find the arc from radius and angle, the radius from arc and angle, or the angle from arc and radius. It also returns the sector area and the chord length.Average rate of change calculatorCompute the average rate of change of a function on an interval: [f(b) − f(a)] / (b − a), the slope of the secant line between (a, f(a)) and (b, f(b)). Type any function of x, set the endpoints a and b, and see f(a), f(b) and the average rate instantly.Bernoulli ODE SolverSolves y′ + P(x)y = Q(x)yⁿ by showing the substitution v = y^(1−n) that turns it into a linear equation, then integrating. The two degenerate cases are handled explicitly: n = 0 is already linear, n = 1 is separable.Convolution CalculatorLinear and circular discrete convolution with the sliding-and-summing steps shown term by term, plus a symbolic continuous convolution solved exactly through the Laplace convolution theorem.Curl calculatorCompute the curl of a vector field: the scalar curl ∂Q/∂x − ∂P/∂y in 2D, or the full vector curl ∇×F = ⟨R_y − Q_z, P_z − R_x, Q_x − P_y⟩ in 3D. Enter each component in x, y, z and get every partial symbolically plus the curl evaluated at an optional point.
Adjacency matrix calculatorTurn any graph into its adjacency matrix. Paste an edge list (A-B), an adjacency list (A: B C D) or a binary matrix — the tool auto-detects the format, builds the labelled adjacency matrix, and reports the degree sequence, in/out-degrees for directed graphs, and the vertex and edge counts.Angle Between Two Vectors Calculatorθ = arccos(a·b / (|a||b|)) in 2D or 3D, in degrees and radians, with the dot product, both magnitudes, the projections and a parallel / perpendicular / acute / obtuse verdict.Cholesky decomposition calculatorFactor a symmetric positive-definite matrix A into L·Lᵀ, where L is lower triangular — the Cholesky decomposition. Enter A on an editable square grid and it returns L, Lᵀ and the product L·Lᵀ; if the matrix is not symmetric or not positive-definite, it tells you which condition failed. Twice as fast as LU, Cholesky is used in optimization, Kalman filters and Monte-Carlo simulation.Column Space Calculator (basis of Col(A), rank, pivot columns)A basis of the column space of any matrix up to 6×6, taken from the ORIGINAL pivot columns rather than the reduced ones — with the rank, the free columns, the full RREF and every row operation.Cramer's Rule CalculatorSolves a 2×2 or 3×3 system with exact fractions, shows every determinant expanded term by term, and when D = 0 separates the two cases most calculators merge: dependent with infinitely many solutions, or inconsistent with none.Cross Product Calculatora × b in 3D with the determinant expansion shown, the magnitude |a||b|sin θ, the parallelogram and triangle areas, the unit normal and the right-hand rule.
Golden Ratio CalculatorSplit a length in the golden ratio φ = (1+√5)/2: give the total, the larger or the smaller segment and get the other two, drawn to scale.Mass percent calculatorCompute the mass percent of a solute in a solution.Odds Ratio CalculatorCompute the odds ratio from a 2×2 table with its log-odds standard error, the Wald interval at 90/95/99 %, relative risk, risk difference — and the Haldane–Anscombe correction when a cell is zero.Percent off calculatorTake a percentage off a price: the amount you save and the final sale price. Enter the original price and the discount.Percent to Fraction CalculatorConvert a percentage into its reduced fraction and equivalent decimal (e.g. 12.5% → 1/8).Percentage calculatorFour percentage calculations in one: X% of Y, what percent X is of Y, and increasing or decreasing a value by a percentage.
Arithmetic sequence calculatorFind the nth term and the sum of an arithmetic sequence.Catalan number generatorGenerate the nth Catalan number exactly, with big-integer precision. The Catalan numbers Cₙ = (2n)! / ((n+1)! n!) count an astonishing range of structures: balanced parentheses, binary trees, polygon triangulations, Dyck paths and hundreds more. Also lists C₀ through Cₙ.Collatz conjecture calculatorTrace the Collatz sequence from any positive integer: halve it if even, triple-plus-one if odd, and repeat until you reach 1. The famous unproven conjecture says every number eventually does. See the full trajectory, the number of steps and the peak value it soars to.Cube numbers listGenerate a list of perfect cubes — n³ for consecutive integers from any starting point. Set how many you want and where to start, and it returns the cubes, their sum and the underlying roots, computed with exact big-integer arithmetic.Fibonacci calculatorFind the nth number in the Fibonacci sequence.Fibonacci Number CheckerTest any number up to 60 digits with the exact 5n^2 +/- 4 identity, with its index, its neighbours in the sequence and the ratio compared with the golden ratio.
Combination calculator (nCr)Compute the number of combinations nCr of r items from n.Derangement (subfactorial) calculator !nCompute the subfactorial !n — the number of derangements, permutations of n items in which nothing stays in its original place. It uses the exact recurrence !n = (n−1)·(!(n−1) + !(n−2)) with big integers, and shows the ratio !n / n!, which converges astonishingly fast to 1/e ≈ 0.3679. That ratio is the probability that a random shuffle leaves no element fixed — the classic 'hat-check' problem.Factorial calculatorCompute the factorial n! of a whole number.Inclusion–exclusion principle calculatorCompute the size of a union of 2 to 5 sets by inclusion–exclusion: add the individual sizes, subtract the pairwise overlaps, add back the triple overlaps, and so on, alternating signs. Work directly from your element lists — the tool sorts every element into its region and cross-checks the count — or from raw cardinalities like |A|, |A∩B|, |A∩B∩C| when you only know the counts. It shows each level's contribution and the final |A ∪ B ∪ …|.Permutation calculator (nPr)Compute the number of permutations nPr of r items from n.Permutations with repetition calculatorCount the ordered arrangements of length r drawn from n items when repetition is allowed — every position can be any of the n choices independently, giving exactly nʳ. This is the arrangement count for PIN codes, passwords, DNA strings and dice rolls, and it differs from ordinary permutations nPr, which forbid reuse. The result is computed exactly with big integers, however large it grows.
Bitwise CalculatorAND, OR, XOR, NOT and shifts in binary, decimal or hex, at 8, 16, 32 or 64 bits, with the bit-by-bit diagram and the result in all three bases. Computed with BigInt, so the 64-bit answers are right where JavaScript's own 32-bit operators would silently truncate.Delaunay triangulation generatorPaste a set of 2D points and it triangulates them the Delaunay way — the triangulation that avoids thin sliver triangles, where no point lies inside another triangle's circumcircle. It runs the Bowyer-Watson algorithm in your browser and draws the mesh, with point, triangle and edge counts.Dijkstra shortest path calculatorEnter a weighted graph as edges ("A, B, 4" per line) and a source node: Dijkstra's algorithm returns the shortest distance and the exact path from the source to every reachable vertex. Works for directed or undirected graphs, accepts many edge formats, and flags unreachable vertices — ideal for routing, networks and pathfinding.Graph coloring calculatorColor a graph so that no two adjacent vertices share a color. Enter an edge list and the DSATUR (or greedy) heuristic assigns a color to every vertex, shows the color classes, and reports an upper bound on the chromatic number χ. K4 needs 4 colors, an even cycle 2, an odd cycle 3 — see it instantly.Group theory order calculatorAnalyse the classic finite groups — cyclic Zₙ, direct products Zₘ×Zₙ, dihedral Dₙ and symmetric Sₙ. It gives the group order, whether it is abelian, its structure, the number of generators for cyclic groups, and the order of any element you enter, including a permutation in cycle notation for Sₙ.Hamiltonian path & cycle checkerCheck whether a graph has a Hamiltonian path (visits every vertex once) or a Hamiltonian cycle (also returns to the start). Enter an edge list, pick directed or undirected, and an exhaustive backtracking search either returns a concrete path and cycle or proves that none exists. Capped at 12 vertices for speed.
CalculatorEvaluate math expressions with parentheses, powers and modulo, live.Amicable Number CheckerCheck whether two numbers are amicable — or give just one and get its candidate partner plus the verified loop, with perfect and sociable numbers identified.Arctan2 Calculator (atan2 of y and x)atan2(y, x) is not atan(y/x): it reads the signs of both arguments to place the angle in the right quadrant over the full −180°…180° turn, and it stays defined when x = 0. Enter x and y, read the angle in degrees or radians, see the quadrant and the point plotted. For a single ratio with no quadrant information, use the arctan calculator instead.Carry and borrow visualizerAdds or subtracts two whole numbers the way it is taught in school — set up in columns, digit by digit — and highlights every carry (addition) or borrow (subtraction) as it happens. A clear way to see the mechanic behind column arithmetic.Ceiling and floor function calculatorThe ceiling ⌈x⌉ rounds up to the next integer, the floor ⌊x⌋ rounds down. Enter any number to get both, plus the ordinary round, the truncation toward zero and the fractional part left over.Common Factor CalculatorFind every common factor of 2 to 10 numbers, with the greatest common factor highlighted and coprime pairs flagged.
Arccos CalculatorFind the inverse cosine (arccos) of a value between −1 and 1, in degrees and radians.Arcsin CalculatorFind the inverse sine (arcsin) of a value between −1 and 1, in degrees and radians.Arctan CalculatorFind the inverse tangent (arctan) of any real value, in degrees and radians.Cosine calculator (cos)Enter an angle in degrees or radians and get its cosine, along with the secant (1/cos) and the same angle in the other unit. Exact for the common angles.Cosecant, Secant & Cotangent CalculatorGet csc, sec and cot for any angle at once, with undefined values flagged.Graphical degree sequence validatorCan a list of vertex degrees actually be realised by a simple graph? Enter the degrees and the Erdős–Gallai / Havel–Hakimi test decides whether the sequence is graphical — a real network with those connection counts exists — and explains the verdict.