Skip to content
Allin
Sign up · Sign in

Binomial Probability Calculator

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.

Related tools

All Statistics & probability tools →
Binomial Theorem Expansion CalculatorExpand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign.Negative Binomial Distribution CalculatorProbability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.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.Probability distribution calculatorOne 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.ANOVA Calculator (One-Way)Full one-way ANOVA table — SS, df, MS, F and p — plus η², ω² and Cohen's f, because a significant F on its own tells you nothing about how large the difference is. The equal-variance assumption is stated, not buried.

Binomial Probability Calculator works straight from this page — free, instant, nothing to install. You will find it under Statistics & probability, with Binomial Theorem Expansion Calculator and Negative Binomial Distribution 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 is Binomial Probability Calculator?

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.

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 Binomial Probability Calculator different from Binomial Theorem Expansion Calculator?

They sit next to each other but answer different questions: Binomial Theorem Expansion Calculator is the one to open when you need it to expand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Negative Binomial Distribution Calculator is the closest one after this: Probability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.

What else is worth having open alongside it?

Dice Roll Probability Calculator and Loot drop probability calculator — 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.