Continuous
Standard Normal
μ = 0, σ = 1
P(X < 1.00)0.8413
Probability, made tangible
Hands on
with probability.
Grab a distribution. Point to the answer you want.
15 distributions
iPhone + iPad
Private by design
Drag to change the light.
See the distribution. Find the probability. Understand both.
Try it here
Probability at your fingertips.
The same ideas, in miniature. Move the controls to select an area under a standard Normal curve or outcomes from a Binomial distribution.
Discrete
Binomial
n = 20, p = 0.5
P(X = 10)0.1762
Live sample
Watch chance take shape.
One observation means very little. Let them arrive, and the theoretical shape gradually emerges from the noise.
0Observations
—Sample mean
Built for exploration
Start anywhere. Find your way.
Explore by touch
Swipe across a chart to select an area. Use two fingers for an interval, or tap an outcome on a discrete distribution.
Calculate both ways
Enter precise bounds to find a probability, or enter a probability to find its value.
Share the picture
Create a clean, labelled chart ready to save, copy or send.
Learn as you go
Every distribution has plain-language notes, key variables and an example.
The right shape for the question
Fifteen distributions.
One coherent studio.
NormalUniformExponentialLognormalChi-squared
Student’s tFBetaGammaWeibull
BinomialPoissonBernoulliGeometricNegative Binomial
Where should I start?
On first launch, take the five-step interactive tour or explore straight away. Tap ? at the top to revisit the tour at any time.
Where are the parameters?
On iPhone, tap the sliders button. On iPad, open Studio controls from the sidebar button. Number fields and increment controls change the current distribution; Reset restores its defaults.
How do I enter a precise range?
Tap the probability button, choose the region, then enter the bounds. Calculations retain full internal precision while long values are rounded where space is limited.
Can I find a value from a probability?
Tap the probability result. Enter a percentage or decimal, then choose a lower tail, central interval or upper tail.
How do I share a chart?
Tap Share chart below the chart.
Why does my sample differ from theory?
Random samples vary. Small samples can differ noticeably; larger samples usually approximate the theoretical shape more closely.
Why can’t a discrete distribution match every probability?
Discrete outcomes come in steps. The calculator shows the probability actually attained by the selected cutoff or interval.
Does the app collect data?
No account is required, and calculations and sampling run on your device. Read the privacy policy for full details.