Free Discrete Math Calculators

Combination Calculator | nCr & n Choose r

Calculate C(n,r) combinations without repetition, C̄(n,r) with repetition, P(n,r) permutations, and nʳ, all in one tool. Supports BigInt exact arithmetic for large n, step-by-step working, Pascal's triangle, combination listing, and session persistence.

Permutation Calculator | nPr

Calculate the number of permutations where order matters.

Boolean Algebra Calculator

Evaluate Boolean expressions with AND, OR, NOT, XOR, NAND, NOR, XNOR, implication, and biconditional. Generates truth tables for up to 4 variables with SOP, POS canonical forms, Σm/ΠM notation, and equivalence checking.

Combinations with Repetition | Stars & Bars

Calculate multiset combinations C̄(n,r) = C(n+r−1,r) where repetition is allowed. Features stars & bars visualization, step-by-step working, multiset listing, all four combinatorial variants, BigInt exact arithmetic, and session persistence.

Pascal's Triangle Calculator

Generate Pascal's triangle up to any row and expand (a + b)ⁿ using the binomial theorem. Shows all coefficients and the full polynomial expansion.

Set Theory Calculator | Union, Intersection, Complement & Venn Diagram

Define up to three sets A, B, C with any elements and compute all standard set operations: union, intersection, difference, symmetric difference, complement, Cartesian product, and power set. Displays a membership table, text Venn diagram, cardinality, and subset relationships.

Recurrence Relation Solver | Closed-Form Solution & Sequence Generator

Solve second-order linear homogeneous recurrence relations aₙ = p·aₙ₋₁ + q·aₙ₋₂ with initial conditions. Finds the characteristic equation, analyzes roots (distinct real, repeated, complex conjugate), builds the closed-form general solution, and generates the first N terms.

Sequence Analyzer | Detect Pattern, nth Term & Generate Terms

Enter any numerical sequence and automatically detect whether it is arithmetic, geometric, quadratic, cubic, Fibonacci-type, or power-based. Finds the closed-form nth term formula, builds a complete difference table at every order, generates the next N terms, and computes partial sums.

Advanced Combinatorics | Derangements, Bell, Catalan & Stirling Numbers

Compute advanced counting numbers in one place: derangements D(n), Bell numbers B(n), Catalan numbers C(n), Stirling numbers of the second kind S(n,k), multinomial coefficients, and stars-and-bars distributions. Each result includes the definition, step-by-step working, and a real-world application.

Truth Table Generator | Boolean Expression Evaluator

Generate complete truth tables for any Boolean expression with up to 4 variables. Supports AND, OR, NOT, XOR, NAND, NOR, and XNOR operators. Automatically identifies tautologies, contradictions, and contingencies, and derives the canonical DNF and CNF forms with minterm and maxterm listings.

Permutation Group Calculator | Cycle Notation, Composition & Order

Work with permutations in cycle notation. Compose two permutations, compute the inverse, raise a permutation to any power, and find its order. Displays each permutation in two-line notation, full cycle decomposition, sign (even or odd), and supports the symmetric group Sₙ for n up to 8.

Markov Chain Calculator | Steady State, n-Step & Absorbing States

Analyze discrete-time Markov chains with up to 4 states. Enter the transition probability matrix and compute: the n-step transition matrix (matrix multiplication), the steady-state (stationary) distribution by power iteration, absorption probabilities for absorbing states, and the expected return time for each state.

Game Theory Calculator | Nash Equilibria, Minimax & Dominant Strategies

Analyze 2×2 and 3×3 two-player strategic games. Finds all pure Nash equilibria by best-response check, computes mixed Nash equilibria for 2×2 games, identifies strictly and weakly dominant strategies, determines minimax and maximin values for zero-sum games, and classifies the game type.