Free Discrete Mathematics Calculators with Step-by-Step Solutions

Enter a problem in logic, sets, graphs, number theory or automata and see it solved one step at a time. Every topic also has a written study guide with worked examples, so you learn the method and not just the answer.

Browse the topics Where should I start?

Topic pages with calculators

Glossary terms

Quiz questions

Practice problems

Topics

Module 01

Propositional Logic

Truth tables, tautologies, equivalence and simplification.

Module 02

Predicate Logic

Quantifiers, variable binding, and translation.

Module 03

Set Theory

Union, intersection, power sets, Venn diagrams.

Module 04

Functions

Injections, surjections, bijections, composition.

Module 05

Relations

Properties, closures, equivalence classes.

Module 06

Counting

Permutations, combinations, pigeonhole principle.

Module 07

Number Theory

Primes, GCD/LCM, modular arithmetic, CRT.

Module 08

Proofs

Direct, contrapositive, contradiction, induction.

Module 09

Graph Theory

Degree, handshaking, bipartite, Euler & Hamiltonian paths.

Module 10

Graph Algorithms

BFS, DFS, Dijkstra, Prim's & Kruskal's MST.

Module 11

Trees

Tree property checks and binary tree traversals.

Module 12

Matrices

Add, multiply, transpose, determinant, inverse.

Module 13

Boolean Algebra

Truth tables, SOP/POS, Quine-McCluskey minimization.

Module 14

Logic Circuits

Half/full adders & subtractors, mux/demux.

Module 15

Recurrence Relations

Closed forms via characteristic equations.

Module 16

Probability

Conditional probability, Bayes' theorem, expectation.

Module 17

Algebraic Structures

Groups, monoids, semigroups from a Cayley table.

Module 18

Algorithms & Complexity

Big-O growth comparison, sorting & searching traces.

Module 19

Automata

DFA / NFA simulation over an input string.

Module 20

Coding Theory

Hamming distance, parity, Hamming(7,4) codes.

Module 21

Quiz

Timed quizzes with scoring and leaderboard. Free account required.

Module 22

Practice

Random problems with hints and solutions. Free account required.

Popular tools and guides

Tool

Transitive Closure Calculator

Free transitive closure calculator: enter a set and a relation to get the transitive, reflexive or symmetric closure with every step explained. Try it now.

Tool

Predicate Logic Translator

Free predicate logic translator: type an English sentence and get its ∀ and ∃ formula, the predicates, a plain-English reading and the steps. Try it now.

Guide

How to Make a Truth Table

Learn how to make a truth table in five steps, with worked examples for AND, OR, implication and three-variable formulas, then check it with our calculator.

Guide

Simplify Boolean Expressions

Learn how to simplify Boolean expressions with the algebra laws, Karnaugh maps and Quine–McCluskey, with worked examples you can check in our free calculator.

Guide

Find a Recurrence Relation

Learn how to find a recurrence relation from a counting problem, algorithm or rule. Five methods with worked examples, plus how to check and solve the result.

Guide

Mathematical Induction

Learn how mathematical induction works in three steps, with worked examples for sums, inequalities and divisibility, a write-up template and common mistakes.

Guide

Euclidean Algorithm

Learn the Euclidean algorithm with worked examples: find a GCD in a few divisions, get the LCM, and use the extended version to write gcd(a, b) = ax + by.

Guide

Permutations vs Combinations

Know when to use permutations and when to use combinations. Clear formulas, a one-question test, repetition cases and worked examples you can verify.

Guide

Dijkstra's Algorithm

See how Dijkstra's algorithm finds shortest paths: the idea, a full worked table, why negative weights break it, and its running time. Try your own graph.

Guide

Big O Notation

Understand Big O notation with the formal definition, a short proof, five simple rules, a growth table and loop examples for finding an algorithm's complexity.

Guide

Propositional Logic

A clear introduction to propositional logic: the five connectives, converse and contrapositive, De Morgan's laws, and valid versus invalid arguments.

Guide

Discrete Math Formulas

A practical cheat sheet of discrete mathematics formulas for logic, sets, counting, sums, number theory, graphs and functions, each with a numeric example.

What makes these discrete mathematics calculators different

Discrete mathematics is usually taught through methods: build a truth table, run the Euclidean algorithm, trace Dijkstra's algorithm, simulate an automaton. If a calculator only prints the final result, you cannot tell where your own working went wrong. Each tool here is built to display the intermediate steps, and each topic page explains the ideas behind them.

How to use a topic page

Try the calculator. Enter an example (each input shows a sample) and read the steps it produces.
Read the study guide below the calculator: key ideas, two fully worked examples, common mistakes and where the topic is used in computing.
Test yourself. Each guide ends with short questions whose answers are hidden until you open them.

Who it is for

Computer science and mathematics students meeting these topics for the first time, anyone revising for an exam, and self-taught programmers who want to understand the mathematics behind algorithms, databases and hardware. Not sure of the order? The learning path groups the topics into five stages, and the glossary defines the common terms in plain language.

How we keep it accurate

Calculators run deterministic algorithms rather than generating answers, and the numbers in worked examples are checked automatically. Read the editorial and accuracy policy, or report a mistake if you find one.

Free accounts

Every calculator and study guide is open to everyone. A free account additionally unlocks the timed quizzes, practice problems with hints and full solutions, PDF export and a saved calculation history. Create an account or log in. The site is funded by advertising; see About for details.