How to use Probability Distribution Explorer

Choose a distribution and enter its parameters.
Set the value or probability range to evaluate.
Inspect the probability, tails and plotted range under the stated model.

Example: Probability Distribution Explorer

Probability Distribution Explorer: P(X = x) at x=5: 0.24609375.

You add

Distribution: binomial Binomial trials n: 10 Success probability p: 0.5 Normal mean: 0 Normal standard deviation: 1 Poisson mean λ: 3 Probability to evaluate: point Evaluation x: 5 Plot start x: 0 Plot end x: 10

You get

P(X = x) at x=5: 0.24609375. binomial: n=10, p=0.5 P(X = x): 0.24609375 Plot domain: 0 to 10 x Probability mass 0 0.0009765625 1 0.009765625 2 0.0439453125 3 0.1171875 4 0.205078125 5 0.24609375 6 0.205078125 7 0.1171875 8 0.0439453125 9 0.009765625 10 0.0009765625 The plot covers only the selected domain. Normal density is not a probability at one exact value. Discrete upper tails include x. Values below floating-point range may round to zero. 0 | 0.0009765625 1 | 0.009765625 2 | 0.0439453125

Options

Distribution assumptions: Binomial uses a fixed number of independent trials with one success probability. Poisson uses the entered rate; normal uses a mean and positive deviation.
Evaluation versus plot: Choose the probability operation separately from the displayed plot range. A short plot range can leave probability mass in unseen tails.

Supported inputs and limits

Binomial n is 0–1,000 and Poisson rate is 0–1,000; discrete plotting is capped at 201 points. Normal plots use 101 samples. Models assume independent trials or the chosen constant-rate/normal assumptions. A plotted range can omit tails, density is not point probability, and very small values can round to zero.

Where your input is processed

This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.

Density at a point is not a point probability

For a continuous normal model, the displayed height is density. Interval or tail probabilities describe areas under that density. Binomial and Poisson outputs use discrete masses at whole values. Keep the chosen model and operation with the result so those meanings do not get mixed.

Questions about Probability Distribution Explorer

Is a normal density the probability of one exact value?

No. A continuous distribution assigns zero probability to one exact value; probabilities belong to intervals.

Can the plot show every Poisson outcome?

No. Poisson outcomes are unbounded. The page shows a finite plotted range and states that limit.

Does the page select a distribution for my data?

No. Choose a model whose assumptions match the question you are studying.

Project manager: Tony Hines · Content updated 4 October 2026 · Report a problem