Probability & Counting calculators
Combinations, permutations, tests and distributions.
4 Event Probability Calculator: All, None, At Least One, Exactly k
Work out the probability that all four, none, at least one, or exactly one, two or three of four independent events happen.
Binomial Distribution Table Calculator (Full PMF and CDF Table for n and p)
Generate a complete binomial probability table for any n and p, with the cumulative columns you would look up in a textbook and charts of the shape.
Binomial Probability Calculator with Steps (Exact, Cumulative, Mean and SD)
Calculate exact and cumulative binomial probabilities, with every step of the formula shown and the distribution plotted.
Birthday Paradox Calculator: Shared Birthday Probability and Group Size
Discover how likely it is that two people in a group share a birthday, and how many people you need for any target probability. It works for any number of days, not only 365.
Combination and Permutation Calculator (nCr, nPr)
Work out how many ways you can choose r items from n, in any order (combinations) or in a specific order (permutations), with or without repetition.
Combinations with Repetition Calculator (Multichoose, Stars and Bars)
Count the ways to choose r items from n types when the same type can be picked more than once and order does not matter, with the stars-and-bars working.
Gamma Distribution Calculator: PDF, CDF, Percentiles, Mean and Variance
Work with the gamma distribution: probabilities for any x or interval, density, percentiles, mean, variance and shape measures, with the curve plotted.
Geometric Distribution Calculator: Trials Until First Success
Model the number of trials until the first success. Get exact and cumulative probabilities, the expected wait and how many tries give a 95% chance.
nCr Calculator: Combinations C(n, r) with Steps, Pascal’s Triangle and Formula
Calculate nCr, the number of ways to choose r items from n when order does not matter, with exact big-number arithmetic and full working.
nPr Calculator: Permutations P(n, r) with Steps, Factorials and Circular Arrangements
Count ordered arrangements: how many ways can r items be picked from n and arranged in order? Exact answers with the working shown.
Probability of 3 Events Calculator: All, None, At Least One, Exactly
Enter the probabilities of three independent events to find the chance that all happen, none happen, at least one happens, or exactly one or two happen.
Probability Calculator: Chance, Odds, At Least Once and Exactly k Times
Find the chance of an event, convert it to odds, and see what happens over repeated tries: at least once, exactly k times and how many tries you need.
Z-Test Calculator (One-Sample)
Test whether a sample mean differs from a claimed population mean when the population standard deviation is known. You get the z-score, p-value, critical values and a decision.