Galton Board
A Galton board (or bean machine) drops balls through a triangular array of pegs; at each peg a ball bounces left or right with equal chance, and the column it lands in is decided by how many rights it took on the way down. This simulator animates the balls falling and stacks them into bins, growing a histogram that converges on the normal distribution — the central limit theorem made physical. Adjust the number of rows, bias the pegs left or right, and overlay the theoretical binomial and normal curves to compare.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Each ball follows a binomial distribution: with r rows and a right-turn probability p, the expected bin is r·p and the counts approach a bell curve.
- The normal approximation to the binomial is why the pile is symmetric and bell-shaped when the pegs are fair (p = 0.5).
- Biasing the pegs shifts the whole pile sideways and, at the extremes, skews it — the mean moves to r·p.
- Runs 100% in your browser — simulations are computed locally on your device.
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