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 Distribution Calculator With Steps and Terms
See every term of the binomial distribution you add up, for exact, at most, at least and between probabilities.
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.
Binomial Calculator with Steps: Percentile, Mode, Find n
Work backwards from a probability: find the binomial percentile k, the most likely number of successes, or how many trials you need, with each step shown.
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.
CDF Probability Calculator: Less, More, Between
Turn a CDF into the probability you need: less than, more than, between two values, or outside them. Works for normal, t, chi-square, binomial and Poisson.
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.
Combination Notation Calculator: C(n,k), nCr and (n choose k)
Type a combination in whatever notation you have, C(10,3), 10C3 or 10 choose 3, and get the value with the equivalent notations and steps.
Combination Probability Calculator: Choose r From N Items
Use combinations to find the probability of picking exactly k special items when you choose r items without replacement.
Combination Sum Calculator: Σ C(n, k) Over a Range of k
Add up combinations C(n, k) over a range of k, such as the number of ways to choose at most r items from n.
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.
Cumulative Distribution Function (CDF) Calculator
Find the cumulative distribution function value F(x) = P(X ≤ x) for five common distributions. You also get the upper tail and the density or probability at x.
Distinguishable Permutations Calculator (Repeated Items)
Count the distinguishable permutations of a word or a set with repeated items. Enter letters or group sizes and get the number of different arrangements.
Distribution Mean Calculator: Expected Value and Variance
Find the mean of a probability distribution. Enter a table of values and probabilities, or pick a standard distribution and its parameters.
Expected Value and Variance Calculator for Discrete Data
Enter outcomes and their probabilities to get the expected value, variance and standard deviation with a full working table.
Experimental vs Theoretical Probability Calculator
Compare theoretical probability with the experimental probability from your trials. You get both values, the difference, the expected count and a quick check of whether the gap is unusual.
Exponential Distribution Calculator: Probability and Mean
Calculate waiting-time probabilities from a rate or a mean, with median, variance, percentiles and density charts.
Find Probability Calculator: Normal, Binomial, Poisson and More
Find a probability under the normal, binomial, Poisson, uniform, exponential or t distribution in one place.
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.
Genotype Probability Calculator: Punnett Square for 1 to 3 Genes
Enter the genotype of each parent to get the probability of every offspring genotype and phenotype. Supports one, two or three genes with complete dominance.
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.
Independent Event Probability Calculator: And, Or, At Least
Combine the probabilities of any number of independent events to get P(all), P(none), P(at least one) and P(exactly k).
Indicated Probability Calculator: Chance of the Event You Pick
Find the probability of the event you indicate from a list of outcomes and how many of each there are.
Mean of a Random Variable Calculator (Expected Value)
Find the mean of a discrete random variable from its values and probabilities. The mean is the expected value, and you can also get the mean of aX + b.
Monte Carlo Probability Calculator (Dice, Coins, Birthday)
Estimate a probability by simulation. Pick dice, coins or the birthday problem, set the number of trials, and compare the Monte Carlo estimate with the exact answer.
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.
Normal Approximation to the Binomial Calculator
Approximate binomial probabilities with a normal curve and compare them with the exact answer, with and without continuity correction.
Normal Distribution Calculator: Probability, Z-Score and Area
Find normal probabilities for any mean and standard deviation, with z-scores and a shaded bell curve.
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.
Poisson Distribution Calculator: Exact and Cumulative
Calculate the probability of k events in a fixed interval from the average rate λ.
Probability Calculator for 1 Event: Single and Repeated Trials
Work out the probability of one event, and how that chance builds up when you repeat it.
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.
Conditional Probability Calculator: P(A|B), P(A and B), Bayes
Find the probability of A given B, the joint and union probabilities, and whether the events are independent.
Probability of A or B Calculator (Union of Two Events)
Find the probability of A or B. Choose independent, mutually exclusive or overlapping events and get the union, the intersection and the other regions.
Probability of a Sample Proportion Calculator (z and Exact)
Find the probability that a sample proportion falls below, above or between values, given the true population proportion and the sample size.
Probability Z Score Calculator: Left, Right and Two-Tail
Convert a z-score, or a raw score with its mean and standard deviation, into a normal probability.
Sample Mean Probability Calculator (Central Limit Theorem)
Find the probability that a sample mean falls below, above or between values, using the mean, standard deviation and sample size of the population.
Uniform Distribution Calculator: Probability, Mean, Variance
Find probabilities, the mean and the variance for a continuous uniform distribution on [a, b].
Variance of a Probability Distribution Calculator
Find the variance of a named probability distribution straight from its parameters.
Variance of a Random Variable Calculator + Steps
Find the variance and standard deviation of a discrete random variable from its values and probabilities. It also gives the variance after a linear change aX + b.
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.