Math

Percentage Calculator

Calculate any percentage in seconds. Find percentages, compare values, and see detailed steps for every calculation.

Fraction Calculator

Calculate fractions with step-by-step solutions. Add, subtract, multiply, divide fractions. Convert to decimals. Free, no signup required.

Ratio Calculator

Simplify ratios to lowest terms, convert to percentages, or solve proportions. Scale up or down, find equivalent forms, and see step-by-step solutions.

Average Calculator

Calculate mean, median, mode, and range for any set of numbers. Get step-by-step solutions and understand which average to use for your data.

Square Root Calculator

Calculate square roots, cube roots, nth roots, and simplified radicals with exact answers, decimals, and step-by-step solutions.

Exponent Calculator

Calculate powers and exponents with step-by-step explanations. Includes negative exponents, fractional powers, scientific notation, and exponential growth.

Scientific Calculator

Apply a scientific calculator with trig functions, logarithms, exponents, roots, factorials, percentages, memory functions, and degree or radian mode.

Area Calculator

Calculate area for squares, rectangles, circles, triangles, and more shapes with formulas, step-by-step solutions, and unit conversions.

Volume Calculator

Calculate volume for any 3D shape with step-by-step solutions. Works with cubes, spheres, cylinders, pyramids, and more. Includes formulas, surface area, and unit conversions.

Quadratic Solver

Free quadratic equation solver. Solve ax² + bx + c = 0 using quadratic formula, factoring, or completing the square. Get step-by-step solutions and graph with CalcZero.

Permutation & Combination

Calculate permutations, combinations, nPr, nCr, and factorials for arrangements and selections with step-by-step counting solutions.

Trigonometry Calculator

Calculate sin, cos, tan, inverse trig functions, right triangles, oblique triangles, Law of Sines, Law of Cosines, and unit circle values.

Absolute Value Calculator

Find a number's distance from zero and see why its sign disappears.

Greatest Common Factor Calculator

Identify the largest positive integer that divides two whole numbers evenly.

Least Common Multiple Calculator

Find the earliest positive multiple shared by two nonzero integers.

Prime Factorization Calculator

Break a whole number into the prime powers whose product reconstructs it.

Mixed Number to Improper Fraction Calculator

Convert a whole-number-and-fraction form into one reduced fraction.

Decimal to Fraction Calculator

Express a terminating or approximated decimal as a fraction in lowest terms.

Percent Error Calculator

Compare an observed value with an accepted value on a percentage scale.

Geometric Mean Calculator

Average positive multiplicative factors without letting one period dominate the scale.

Harmonic Mean Calculator

Combine rates or ratios when equal quantities are traveled, processed, or purchased.

Weighted Mean Calculator

Average values after assigning each observation its own influence.

Mean Absolute Deviation Calculator

Measure a dataset's typical absolute distance from its arithmetic mean.

Z-Score Calculator

Express a data value as a signed number of standard deviations from a mean.

Linear Equation Calculator

Solve an equation in the form ax + b = c and show the balancing steps.

Slope Calculator

Calculate rise over run between two coordinate points and detect vertical lines.

Distance Formula Calculator

Measure the straight-line separation between two points in a coordinate plane.

Midpoint Calculator

Average corresponding coordinates to locate the center of a line segment.

Pythagorean Theorem Calculator

Solve a right triangle for its hypotenuse or for one unknown leg.

Triangle Angle Calculator

Find a triangle's remaining interior angle from two known angles.

Polygon Interior Angle Calculator

Find an interior-angle sum or each angle of a regular polygon.

Regular Polygon Area Calculator

Compute area from a regular polygon's side count and common side length.

Arc Length Calculator

Measure part of a circle's circumference from radius and central angle.

Sector Area Calculator

Calculate the slice of a circle enclosed by two radii and their arc.

Cylinder Surface Area Calculator

Add two circular bases and the curved side of a closed right cylinder.

Cone Surface Area Calculator

Combine a cone's circular base with its slanted lateral surface.

Sphere Surface Area Calculator

Find the outside area of a sphere from its radius.

Scientific Notation Converter

Normalize a large or small number as a coefficient times a power of ten.

Logarithm Calculator

Evaluate a positive argument at any valid logarithm base.

Modulo Calculator

Return the standard nonnegative remainder after integer division.

Arithmetic Sequence Calculator

Find any term in a sequence with a constant difference between neighbors.

Midrange Calculator

Average a dataset's smallest and largest values to locate the center of its range.

Rounding Calculator

Round a value to a chosen decimal place without hiding which digit controls the change.

Significant Figures Calculator

Round a number to a specified count of meaningful digits across very large or very small scales.

Order of Operations Calculator

Evaluate an arithmetic expression with parentheses, exponents, multiplication, division, addition, and subtraction in the correct order.

Long Addition Calculator

Add two whole numbers exactly and retain every digit beyond ordinary browser-number precision.

Long Subtraction Calculator

Subtract one whole number from another exactly, including results larger than the safe numeric range.

Long Multiplication Calculator

Multiply two whole numbers with exact integer arithmetic instead of a rounded floating-point result.

Long Division Calculator

Divide one whole number by another and report an exact integer quotient with its remainder.

Integer Calculator

Perform addition, subtraction, multiplication, quotient, or remainder operations on signed integers.

Negative Number Calculator

Work through addition, subtraction, multiplication, and division when one or both values are negative.

Reciprocal Calculator

Find the multiplicative inverse of a nonzero number in exact-looking fraction and decimal form.

Opposite Number Calculator

Reverse a number’s sign to find the value that pairs with it to make zero.

Sum of Consecutive Integers Calculator

Add a specified run of consecutive integers beginning from any whole-number starting point.

Product of Consecutive Integers Calculator

Multiply a run of consecutive integers exactly and expose whether zero controls the result.

Digital Root Calculator

Repeatedly sum the digits of a nonnegative integer until only one digit remains.

Casting Out Nines Checker

Check a claimed addition or multiplication using digit residues modulo nine.

Improper Fraction to Mixed Number Calculator

Convert an improper fraction into a whole-number part and a reduced proper fraction.

Fraction to Decimal Calculator

Divide a numerator by a nonzero denominator and identify whether the decimal terminates or repeats.

Repeating Decimal to Fraction Calculator

Convert a decimal with a stated repeating block into an exact reduced fraction.

Fraction Simplifier

Reduce a numerator and denominator to lowest terms while preserving the fraction’s exact value.

Equivalent Fractions Calculator

Scale a fraction’s numerator and denominator by the same nonzero integer.

Common Denominator Calculator

Rewrite two fractions over their least common positive denominator.

Complex Fraction Calculator

Simplify a fraction whose numerator, denominator, or both are themselves fractions.

Unit Fraction Calculator

Create the fraction representing one equal part out of a chosen positive number of parts.

Fraction of a Number Calculator

Multiply a number by a stated fraction and retain a reduced exact fraction when appropriate.

Ratio to Fraction Calculator

Interpret a two-part ratio a:b as the fraction a/b and reduce it to lowest terms.

Ratio to Decimal Calculator

Convert a two-term ratio into the decimal quotient of its first term divided by its second.

Ratio to Percentage Calculator

Express the first term of a two-part ratio as a percentage of the second term.

Proportion Solver

Solve a/b = c/x for the missing fourth term using cross multiplication.

Percentage Difference Calculator

Compare two values symmetrically by scaling their absolute difference to their average magnitude.

Basis Points Calculator

Convert between percentage points and basis points without confusing relative percent change.

Prime Number Checker

Determine whether an integer greater than one has exactly two positive divisors.

Next Prime Calculator

Find the smallest prime strictly greater than a supplied integer.

Previous Prime Calculator

Find the greatest prime strictly smaller than a supplied integer.

Prime Gap Calculator

Measure the distance between the nearest prime below and nearest prime above an integer.

Factor Calculator

List every positive integer that divides a nonzero whole number without remainder.

Divisor Count Calculator

Count the positive divisors of a nonzero integer from its prime exponents.

Divisor Sum Calculator

Add all positive divisors of a nonzero integer using its prime-power structure.

Coprime Checker

Check whether two integers share no positive factor greater than one.

Euclidean Algorithm Calculator

Trace repeated quotient-and-remainder divisions that produce the greatest common divisor.

Extended Euclidean Algorithm Calculator

Find the GCF together with coefficients x and y satisfying ax + by = gcd(a,b).

Modular Inverse Calculator

Find x such that ax leaves remainder one modulo a positive modulus.

Congruence Calculator

Solve ax ≡ b (mod n) and list every distinct solution modulo n.

Chinese Remainder Theorem Calculator

Combine two compatible congruences into one residue class modulo their least common multiple.

Euler Totient Calculator

Count integers from one through n that are coprime to a positive integer n.

Perfect Number Checker

Check whether a positive integer equals the sum of its proper positive divisors.

Fibonacci Membership Checker

Determine whether a nonnegative integer appears in the Fibonacci sequence.

Two-Equation System Solver

Solve two linear equations in x and y and identify unique, parallel, or coincident cases.

Three-Equation System Solver

Solve three linear equations in x, y, and z using elimination with singular-system detection.

Slope-Intercept Form Calculator

Create y = mx + b from a slope and vertical intercept.

Point-Slope Form Calculator

Write y − y₁ = m(x − x₁) from one point and a finite slope.

Standard Form Line Calculator

Convert two points into an integer-normalized line equation Ax + By = C.

Parallel Line Calculator

Find the equation of a line through a point with the same slope as a given nonvertical line.

Perpendicular Line Calculator

Construct a line through a point using the negative reciprocal of a nonzero finite slope.

Linear Interpolation Calculator

Estimate y between two known points by following their straight-line slope.

Absolute Value Equation Solver

Solve equations of the form |ax + b| = c and report both, one, or no real solutions.

Absolute Value Inequality Solver

Solve |ax + b| <, ≤, >, or ≥ c as an interval or pair of exterior intervals.

Compound Inequality Calculator

Solve a chained inequality lower < or ≤ ax + b < or ≤ upper.

Polynomial Evaluator

Evaluate a polynomial from descending-order coefficients at a chosen x value.

Polynomial Addition Calculator

Add two polynomials by aligning equal powers and combining their coefficients.

Polynomial Multiplication Calculator

Multiply two polynomials by convolving their descending-order coefficient lists.

Synthetic Division Calculator

Divide a polynomial by x − c using a compact coefficient recurrence.

Polynomial Long Division Calculator

Divide one polynomial by another and report quotient and remainder coefficient lists.

Rational Root Theorem Calculator

List every reduced rational candidate ±p/q allowed by integer polynomial coefficients.

Cubic Equation Solver

Find all real or complex roots of ax³ + bx² + cx + d = 0 numerically.

Quartic Equation Solver

Find all four real or complex roots of ax⁴ + bx³ + cx² + dx + e = 0 numerically.

Completing the Square Calculator

Rewrite ax² + bx + c as a(x − h)² + k and expose the vertex.

Vertex Form Converter

Convert between expanded quadratic coefficients and a(x − h)² + k parameters.

Direct Variation Calculator

Find a direct-variation constant or missing proportional value from the relationship y = kx.

Inverse Variation Calculator

Find an inverse-variation constant or missing value from the relationship y = k/x.

Triangle Perimeter Calculator

Add three valid side lengths and check the triangle inequality.

Heron’s Formula Calculator

Find triangle area from three side lengths using the semiperimeter.

Isosceles Triangle Calculator

Find altitude, area, perimeter, and base angles from equal sides and a base.

Equilateral Triangle Calculator

Calculate altitude, area, perimeter, inradius, and circumradius from one side.

Right Triangle Altitude Calculator

Find the altitude to the hypotenuse and its two projection segments from the legs.

Triangle Centroid Calculator

Average three vertices to locate the intersection of a triangle’s medians.

Triangle Inradius Calculator

Find the radius of the inscribed circle from three triangle sides.

Triangle Circumradius Calculator

Find the radius of the circle through all three triangle vertices.

Polygon Exterior Angle Calculator

Find a regular polygon’s exterior angle or infer its side count from that angle.

Regular Polygon Apothem Calculator

Find the center-to-side distance of a regular polygon from side count and side length.

Regular Polygon Diagonal Calculator

Count all diagonals and find lengths for a chosen vertex step in a regular polygon.

Circle Circumference Calculator

Calculate the distance around a circle from radius or diameter.

Circle Segment Area Calculator

Find the minor circular segment cut off by a chord and central angle.

Circle Chord Length Calculator

Find a chord from circle radius and its central angle.

Annulus Area Calculator

Calculate the area between two concentric circles. Review the entered quantities alongside the resulting annulus area value.

Ellipse Area Calculator

Find ellipse area from its semimajor and semiminor axes.

Ellipse Circumference Approximation Calculator

Estimate ellipse perimeter with Ramanujan’s high-accuracy second approximation.

Parallelogram Diagonal Calculator

Find both diagonals from adjacent sides and their included angle.

Trapezoid Midsegment Calculator

Average the two parallel bases to find the segment joining leg midpoints.

Section Formula Calculator

Find the point dividing a segment internally in a specified ratio.

Endpoint Calculator

Recover one endpoint from a midpoint and the other endpoint.

Factorial Calculator

Multiply every positive integer through n and return the exact whole-number result.

Double Factorial Calculator

Multiply integers of the same parity as n while stepping downward by two.

Binomial Coefficient Calculator

Calculate the exact number of ways to choose k objects from n without order.

Multinomial Coefficient Calculator

Count arrangements of a multiset from the multiplicities of its repeated groups.

Permutations with Repetition Calculator

Count length-n sequences when each position may reuse any available symbol.

Combinations with Repetition Calculator

Count unordered selections of k items from n types when repeats are allowed.

Circular Permutation Calculator

Count rotations of n distinct objects as the same circular arrangement.

Derangement Calculator

Count permutations in which no object remains in its original position.

Pascal’s Triangle Calculator

Generate an exact row of Pascal’s triangle from its zero-based row number.

Binomial Expansion Calculator

Expand (ax+b)ⁿ into descending powers of x for a nonnegative integer exponent.

Fundamental Counting Principle Calculator

Multiply the available choice counts across consecutive independent stages.

Inclusion-Exclusion Calculator

Find the size of a three-set union while correcting pairwise and triple overlaps.

Basic Probability Calculator

Divide favorable outcomes by total equally likely outcomes.

Complement Probability Calculator

Subtract an event probability from one to find the chance it does not occur.

Independent Events Calculator

Find the chance all or at least one of several independent events occurs.

Mutually Exclusive Events Calculator

Add probabilities of events that cannot occur in the same outcome.

Conditional Probability Calculator

Calculate P(A|B) from P(A∩B) and P(B). A worked result shows how the entered values determine the conditional probability answer.

Bayes’ Theorem Calculator

Update a prior using a likelihood and total evidence probability.

Probability of At Least One Calculator

Find one or more successes across identical independent trials.

Odds to Probability Calculator

Convert favorable-to-unfavorable ratio odds into probability. Review the entered quantities alongside the resulting odds to probability value.

Probability to Odds Calculator

Convert probability into reduced favorable-to-unfavorable odds. Review the entered quantities alongside the resulting probability to odds value.

Expected Value Calculator

Calculate the probability-weighted average of a discrete variable.

Discrete Variance Calculator

Measure probability-weighted squared spread around a discrete mean.

Binomial Distribution Calculator

Find exact or cumulative success probability for independent Bernoulli trials.

Geometric Distribution Calculator

Find the chance the first success occurs on trial k.

Negative Binomial Distribution Calculator

Find the chance the rth success occurs on trial k.

Hypergeometric Distribution Calculator

Calculate successes in a sample drawn without replacement.

Poisson Distribution Calculator

Find exact or cumulative event-count probability from an interval rate.

Normal Distribution Calculator

Estimate area below, above, or between values in a normal distribution.

Empirical Probability Calculator

Estimate probability from observed frequency. The displayed steps make the empirical probability result independently reproducible.

Limit Calculator

Estimate a two-sided finite limit from values approaching the target.

One-Sided Limit Calculator

Approach a finite target from only the left or right.

Limit at Infinity Calculator

Inspect function values at increasingly large positive or negative inputs.

Continuity Checker

Compare a function value with nearby left and right evaluations.

Derivative Calculator

Differentiate a polynomial supplied as descending coefficients. A worked result shows how the entered values determine the derivative answer.

Derivative at a Point Calculator

Estimate f′(x) at a selected point using symmetric samples.

Second Derivative Calculator

Estimate f″(x) to measure curvature and changing slope.

Higher-Order Derivative Calculator

Estimate derivatives through order five at a point.

Partial Derivative Calculator

Differentiate a two-variable function with respect to x or y while holding the other fixed.

Implicit Differentiation Calculator

Estimate dy/dx on a level curve F(x,y)=0 from its partial derivatives.

Tangent Line Calculator

Build the point-slope tangent line to y=f(x) at x₀.

Normal Line Calculator

Construct the line perpendicular to a curve’s tangent at x₀.

Critical Point Calculator

Search an interval for points where the numerical derivative is zero.

Local Extrema Calculator

Classify stationary points by derivative sign changes. A worked result shows how the entered values determine the local extrema answer.

Increasing and Decreasing Intervals Calculator

Divide a finite interval into increasing and decreasing portions by examining derivative signs.

Concavity Calculator

Identify concave-up and concave-down regions from the sign of the second derivative.

Inflection Point Calculator

Search for second-derivative sign changes and report curve coordinates.

Newton’s Method Calculator

Iterate tangent-line intersections from an initial guess. The page keeps the newton’s method operation and input roles visible.

Linear Approximation Calculator

Approximate f(x) near a base point with its tangent line.

Differential Approximation Calculator

Estimate dy from a small dx and the derivative at a base point.

Definite Integral Calculator

Numerically integrate f(x) between finite bounds. Its fields preserve the quantities needed to check the definite integral method.

Polynomial Antiderivative Calculator

Integrate a polynomial coefficient list exactly and append the constant term.

Area Under a Curve Calculator

Integrate the absolute function height over a finite interval.

Area Between Curves Calculator

Integrate the absolute vertical separation of two functions.

Average Value of a Function Calculator

Divide a definite integral by interval length. Review the entered quantities alongside the resulting average value of a function value.

Riemann Sum Calculator

Approximate an integral with left, right, or midpoint rectangles.

Trapezoidal Rule Calculator

Approximate a definite integral with straight-line panels. The displayed steps make the trapezoidal rule result independently reproducible.

Simpson’s Rule Calculator

Approximate a definite integral with weighted quadratic panels.

Disk and Washer Method Calculator

Integrate π(R²−r²) around the x-axis. A worked result shows how the entered values determine the disk and washer method answer.

Euler’s Method Calculator

Step through y′=f(x,y) from an initial condition to a target x.

Degree to Radian Converter

Convert an angle between degrees and radians without changing its rotation.

Angle Normalization Calculator

Reduce any signed angle to a standard positive or signed interval.

Reference Angle Calculator

Find the acute angle between a terminal side and the x-axis.

Unit Circle Calculator

Return cosine, sine, and tangent from an angle on the unit circle.

Sine Calculator

Evaluate the sine of an angle entered in degrees or radians.

Cosine Calculator

Evaluate the cosine of an angle with an explicit angle unit.

Tangent Calculator

Evaluate tangent as the signed sine-to-cosine ratio. The displayed steps make the tangent result independently reproducible.

Secant Calculator

Compute secant as the reciprocal of cosine. The displayed steps make the secant result independently reproducible.

Cosecant Calculator

Compute cosecant as the reciprocal of sine. A worked result shows how the entered values determine the cosecant answer.

Cotangent Calculator

Evaluate cotangent as cosine divided by sine. The displayed steps make the cotangent result independently reproducible.

Inverse Sine Calculator

Recover the principal angle whose sine equals a supplied ratio.

Inverse Cosine Calculator

Recover the principal angle whose cosine equals a supplied ratio.

Inverse Tangent Calculator

Turn any finite tangent ratio or slope into its principal angle.

Right Triangle Solver

Solve all sides and acute angles from a supported pair of known quantities.

SOHCAHTOA Calculator

Recover right-triangle side lengths with the appropriate sine, cosine, or tangent relationship.

Law of Sines Calculator

Solve the remaining sides and angle from one opposite pair and another angle.

Law of Cosines Calculator

Solve a triangle from two sides and their included angle.

SSA Ambiguous Case Calculator

Determine whether side-side-angle data produce zero, one, or two triangles.

Triangle Area with Sine Calculator

Find triangle area from two sides and their included angle.

Height and Distance Calculator

Estimate vertical height from an elevation angle and a measured horizontal distance.

Trigonometric Identity Checker

Compare two trigonometric expressions at several ordinary sample points.

Sum and Difference Angle Calculator

Evaluate sine, cosine, or tangent of a sum or difference and show the expanded value.

Double Angle Calculator

Evaluate a selected trigonometric function at twice the entered angle.

Half Angle Calculator

Evaluate sine, cosine, or tangent at half of a supplied directed angle.

Trigonometric Equation Solver

List degree solutions to sin x, cos x, or tan x equal to a target over a finite interval.

Sinusoid Amplitude and Period Calculator

Read amplitude, period, phase shift, and midline from A sin(Bx+C)+D.

Sine Wave Calculator

Evaluate a sine wave from amplitude coefficient, period, phase, midline, and x.

Cosine Wave Calculator

Evaluate a cosine wave using explicit period and horizontal phase shift.

Angular and Linear Speed Calculator

Convert angular rate to radians per second and compute tangential linear speed.

Bearing Turn Calculator

Apply a signed clockwise or counterclockwise turn to a compass bearing.

Matrix Addition Calculator

Add two matrices entry by entry. The displayed steps make the matrix addition result independently reproducible.

Matrix Subtraction Calculator

Subtract matrix B from matrix A entry by entry.

Matrix Multiplication Calculator

Multiply compatible matrices using row-by-column dot products. Review the entered quantities alongside the resulting matrix multiplication value.

Matrix Scalar Multiplication Calculator

Multiply every matrix entry by one scalar. The page keeps the matrix scalar multiplication operation and input roles visible.

Matrix Transpose Calculator

Exchange matrix rows and columns. Its fields preserve the quantities needed to check the matrix transpose method.

Matrix Determinant Calculator

Compute the determinant of a square matrix up to 8×8.

Matrix Inverse Calculator

Find A⁻¹ by Gauss–Jordan elimination when it exists.

Matrix Rank Calculator

Count pivot columns after row reduction. A worked result shows how the entered values determine the matrix rank answer.

Matrix Row Echelon Form Calculator

Reduce a matrix to forward row echelon form.

Matrix RREF Calculator

Compute the unique reduced row echelon form of a matrix.

Linear System Gaussian Elimination Calculator

Solve or classify a linear system from its augmented matrix.

Matrix LU Decomposition Calculator

Factor a square matrix into lower and upper triangular matrices.

Matrix Trace Calculator

Add the main diagonal entries of a square matrix.

Matrix Power Calculator

Raise a square matrix to a nonnegative integer power.

2x2 Characteristic Polynomial Calculator

Form λ²−tr(A)λ+det(A) for a 2×2 matrix. The page keeps the 2x2 characteristic polynomial operation and input roles visible.

2x2 Matrix Eigenvalues Calculator

Find real or complex eigenvalues of a 2×2 matrix.

2x2 Matrix Eigenvectors Calculator

Return normalized real eigenvector directions for a 2×2 matrix.

Matrix Vector Multiplication Calculator

Multiply a matrix by a compatible column vector.

Quadratic Form Calculator

Evaluate xᵀAx for a square matrix and matching vector.

Vector Addition Calculator

Add vectors of the same dimension component by component.

Vector Subtraction Calculator

Subtract vector b from vector a component by component.

Vector Scalar Multiplication Calculator

Multiply every vector component by one scalar. Review the entered quantities alongside the resulting vector scalar multiplication value.

Vector Magnitude Calculator

Compute Euclidean vector length from its components. Its fields preserve the quantities needed to check the vector magnitude method.

Unit Vector Calculator

Normalize a nonzero vector to magnitude one. A worked result shows how the entered values determine the unit vector answer.

Dot Product Calculator

Multiply matching vector components and add the products.

Cross Product Calculator

Compute the oriented vector perpendicular to two 3D vectors.

Angle Between Vectors Calculator

Find the principal angle between two nonzero vectors.

Vector Projection Calculator

Project vector a onto the direction of nonzero vector b.

Vector Distance Calculator

Compute Euclidean distance between equal-dimensional vectors. The page keeps the vector distance operation and input roles visible.

Scalar Triple Product Calculator

Compute a·(b×c) and its associated 3D volume. Review the entered quantities alongside the resulting scalar triple product value.

Set Union Calculator

Combine the distinct elements appearing in either of two finite sets.

Set Intersection Calculator

Keep only the distinct elements shared by two finite sets.

Set Difference Calculator

Return elements in set A that do not belong to set B.

Symmetric Difference Calculator

Find elements belonging to exactly one of two finite sets.

Cartesian Product Calculator

List every ordered pair in A×B for two finite sets.

Power Set Calculator

List every subset of a finite set, including the empty set.

Subset and Proper Subset Checker

Determine whether every element of A belongs to B and whether containment is proper.

Set Equality Calculator

Compare two finite sets without treating order or repeated entries as differences.

Set Cardinality Calculator

Count the distinct elements in a finite set.

Three-Set Inclusion–Exclusion Calculator

Find the size of a three-set union from individual and overlapping cardinalities.

Truth Table Calculator

Generate every truth assignment for a propositional expression.

Logical Equivalence Checker

Compare two propositional expressions across every truth assignment.

Tautology and Contradiction Checker

Classify a proposition as a tautology, contradiction, or contingency.

Boolean Expression Calculator

Evaluate one logical expression under a supplied assignment of truth values.

Relation Properties Calculator

Test reflexivity, symmetry, antisymmetry, and transitivity on a finite universe.

Equivalence Relation Checker

Check whether a finite relation is reflexive, symmetric, and transitive.

Partial Order Checker

Check whether a finite relation is reflexive, antisymmetric, and transitive.

Transitive Closure Calculator

Add the smallest collection of ordered pairs needed to make a finite relation transitive.

Finite Function Properties Calculator

Classify a finite mapping as injective, surjective, and bijective.

Adjacency Matrix Calculator

Convert a finite simple undirected graph into a zero-one matrix.

Graph Degree Sequence Calculator

Compute and sort the vertex degrees of a finite simple undirected graph.

Graph Density Calculator

Compare present edges with all possible edges in a finite simple undirected graph.

Complete Graph Edge Calculator

Count edges in the complete simple graph Kₙ.

Complete Bipartite Graph Calculator

Count edges in Kₘ,ₙ between two disjoint vertex parts.

Tree Vertices and Edges Calculator

Find the required edge count for a finite tree from its number of vertices.

Dijkstra Shortest Path Calculator

Find a minimum-weight path between two vertices in a nonnegative weighted graph.

Minimum Spanning Tree Calculator

Choose a minimum-total-weight tree connecting every vertex of a finite graph.

Graph Chromatic Number Calculator

Find the exact minimum vertex-color count for a small simple graph.

Catalan Number Calculator

Compute Cₙ for balanced, nested, and noncrossing combinatorial structures.

Stirling Number of the Second Kind Calculator

Count partitions of n labeled objects into k nonempty unlabeled groups.