Discrete math calculators

Calculators for counting, sets, relations, logic and graphs, the topics of a first discrete mathematics or computer science course. They show the working, from the terms of an inclusion–exclusion sum to each step of Dijkstra’s algorithm.

Which calculator do I need?

You have or want	Use
How many ways to choose or arrange r items from n	Permutation and combination calculator
A closed form for a recurrence, or a count by inclusion–exclusion	Discrete math calculator
The union, intersection or complement of sets, with a Venn diagram	Set calculator
Whether a relation is reflexive, symmetric or transitive	Relation calculator
A truth table or the simplest form of a logic expression	Boolean algebra calculator
The shortest path or minimum spanning tree of a network	Graph theory calculator
A plot of y = f(x), with zeros and intersections	Graphing calculator

Counting

Count arrangements and selections, and solve the recurrences that counting problems lead to.

Permutation and combination calculator

nPr, nCr, with-repetition counts, letter arrangements and circular permutations, exactly.
Combination calculator

nCr with or without repetition, and a list of every combination for small sets.
Permutation calculator

nPr, nʳ with repetition, and the distinct arrangements of the letters in a word.
Discrete math calculator

Solve linear recurrences, count with inclusion–exclusion and apply the pigeonhole principle.

Sets, relations and logic

The language of discrete math: collections, the links between their members, and true-or-false statements.

Set calculator

Union, intersection, differences and complements of up to three sets, with a Venn diagram.
Relation calculator

Test a relation for the four properties and build its reflexive, symmetric and transitive closures.
Boolean algebra calculator

Truth tables, canonical SOP and POS, and Quine–McCluskey minimisation of a Boolean expression.

Graphs and plots

Networks of vertices and edges, and plots of functions on axes.

Graph theory calculator

Degrees, BFS and DFS, Dijkstra, Kruskal’s MST, Euler paths and a bipartite check for any edge list.
Graphing calculator

Plot up to four functions of x and find their zeros and intersections.

What the calculators cover

Counting is the largest topic. The permutation and combination calculator handles the standard cases in one place: with and without repetition, letter arrangements and circular seating. The discrete math calculator handles what those formulas cannot: recurrences, inclusion–exclusion and the pigeonhole principle. Sets, relations and Boolean logic come next. The graph theory calculator works on networks of vertices and edges.

“Graph” means two different things in mathematics. In graph theory it is a network. On the graphing calculator it is a plot of a function. Both are listed here because the words overlap, but they answer very different questions.

Worked comparison: four ways to pick 3 from 5

Order matters?	Repeats allowed?	Formula	Count
Yes	No	5P3 = 5!/2!	60
No	No	5C3 = 5!/(3! 2!)	10
Yes	Yes	5³	125
No	Yes	C(5 + 3 − 1, 3)	35

Decide on the two questions in the first two columns before choosing a formula. Most counting mistakes come from answering one of them wrongly. A 3-digit PIN from 5 digits is ordered with repeats (125). A 3-person committee from 5 people is unordered without repeats (10).

Inclusion–exclusion in one line

How many of the numbers 1 to 100 are divisible by 2 or 3? There are 50 multiples of 2 and 33 multiples of 3. The 16 multiples of 6 were counted twice, so the answer is 50 + 33 − 16 = 67. With three conditions you add back the triple overlap, and the discrete math calculator lays out every term.

Guides to read alongside

Standard deviation of a random variable

Counting outcomes of dice and other discrete distributions to find their mean and spread.
Statistics formulas

Reference formulas, including those for the binomial and other counting-based distributions.

Common questions

What is the difference between a permutation and a combination?

A permutation counts arrangements, where order matters, so ABC and CBA are different. A combination counts selections, where order does not matter, so they are the same. Each combination of r items corresponds to r! permutations, which is why nPr = nCr × r!.

How does the Boolean algebra calculator simplify an expression?

It builds the truth table, reads off the minterms, and applies the Quine–McCluskey method to find a minimal sum of products. The result matches what you would get from a Karnaugh map, and it works for more variables than a map can handle comfortably.

What input does the graph theory calculator need?

A list of edges, one per line, such as A B 4 for an edge from A to B with weight 4. You can choose a directed or undirected graph. It then runs searches, shortest paths, spanning trees and the Euler path and bipartite checks on that graph.

Written and reviewed by our editorial team. Last updated September 27, 2026. Method and sources: how these numbers are computed.