Probability Distribution Calculator
Interactive calculator for seven probability distributions. Adjust parameters with sliders and watch the curve, shaded area, probability and quantiles update instantly.
7 distributions · drag the sliders to reshape the curve · every setting is kept in the URL
Pick a distribution, drag the parameter sliders and watch the curve, the shaded area and the probability move together. Every setting lives in the address bar, so the link you copy reopens exactly this screen.
P(X ≤ 0) = 0.500000
Parameters
What to calculate
Type in either box — the other one is solved for you.
Result
Related probabilities
Distribution summary
Which distribution should I use?
| Distribution | Use it when | Parameters | Mean | Variance |
|---|---|---|---|---|
| A continuous measurement clusters around an average. | μ, σ | μ | σ² | |
| A fixed number of independent yes/no trials. | n, p | np | np(1−p) | |
| Counting events in a fixed interval of time or space. | λ | λ | λ | |
| Small samples where the population σ is unknown. | ν | 0 | ν/(ν−2) | |
| Goodness-of-fit and independence tests. | k | k | 2k | |
| Waiting time between events that happen at a constant rate. | λ | 1/λ | 1/λ² | |
| Every value in a range is equally likely. | a, b | (a+b)/2 | (b−a)²/12 |
Same calculation in code
from scipy.stats import norm norm.cdf(0, loc=0, scale=1) # 0.5
Type in the value box to get a probability, or type in the probability box to get the value — you never have to switch to an "inverse" mode.
How to use
- Pick a distribution from the tabs.
- Set the parameters with the sliders or type exact values.
- Choose what to calculate: a left tail, a right tail, an interval or the density.
- Enter a value to get its probability, or enter a probability to get the matching value.
- Copy the result or share the URL — it carries every setting.
FAQ
Which probability distribution should I use?
Counting successes in a fixed number of trials → binomial. Counting events in a fixed interval of time or space → Poisson. A continuous measurement that clusters around an average → normal. Waiting time between events → exponential. A small sample with an unknown population σ → Student’s t. Goodness-of-fit or independence tests → chi-square. Every value in a range equally likely → uniform.
How accurate are these results?
The normal CDF uses the Hart/West rational approximation (absolute error 1.8e-16), the inverse normal uses Acklam plus one Halley step (relative error 1.5e-10), and the incomplete gamma and beta functions land around 1e-12. The display stops at 12 decimals because anything beyond that would not be guaranteed.
Why is P(X ≤ x) different from P(X < x)?
In a continuous distribution P(X = x) is 0, so the two are identical. In a discrete distribution such as the binomial or Poisson they differ by exactly P(X = x). The boundary toggle switches between them.
Can I share a calculation with my students?
Yes. The distribution, its parameters, the mode and the boundary values all live in the address bar, so copying the URL and sending it reopens exactly the same screen.
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