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Probability distribution calculator

One calculator for the seven distributions you actually use — normal, binomial, Poisson, exponential, uniform, chi-square and Student's t. Pick the distribution and whether you want the density (PDF/PMF), the cumulative probability P(X ≤ x), or the quantile (the inverse, for a critical value), enter the parameters, and read the answer with the mean and variance.

Related tools

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Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.Dice Roll Probability CalculatorExact odds that a roll of nd s (+ modifier) meets a target — built by convolution, not simulated.Loot drop probability calculatorThe chance of getting a rare drop over many tries — the maths behind grinding for a mount, a shiny, or a knife skin. From the per-attempt drop rate and the number of attempts, it works out the probability of at least one (or several) drops, and how many runs you need for a 50%, 90% and 99% chance.Odds to probability converterConvert fractional odds into an implied probability and decimal odds.Probability calculatorCompute the probability of an event from favorable and total outcomes.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.Exponential Distribution CalculatorCompute exponential-distribution probabilities for waiting times from the rate λ, including P(X≤x), P(X>x) and a range.Gaussian Distribution GeneratorNormally-distributed numbers via Box–Muller, with an optional seed and the sample mean and SD.

Open Probability distribution calculator and you get an answer straight away, with no account to create. You will find it under Statistics & probability, with Binomial Probability Calculator and Dice Roll Probability Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Probability distribution calculator do?

One calculator for the seven distributions you actually use — normal, binomial, Poisson, exponential, uniform, chi-square and Student's t. Pick the distribution and whether you want the density (PDF/PMF), the cumulative probability P(X ≤ x), or the quantile (the inverse, for a critical value), enter the parameters, and read the answer with the mean and variance.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

How is Probability distribution calculator different from Binomial Probability Calculator?

They sit next to each other but answer different questions: Binomial Probability Calculator is the one to open when you need it to get P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Dice Roll Probability Calculator is the closest one after this: Exact odds that a roll of nd s (+ modifier) meets a target — built by convolution, not simulated.

What else is worth having open alongside it?

Loot drop probability calculator and Odds to probability converter — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.