Free Galton Board SimulatorThe bean machine, with live statistics.

Drop balls through rows of pegs and watch them build the bell curve, with the exact binomial distribution and a fitted normal curve over the slots.
Switch between real bouncing balls and the ideal 50/50 model, fast-forward thousands of balls, and read the mean, standard deviation and chi-squared test.

Binomial & normal curvesThousands of balls in secondsPNG, CSV & video

No sign-up No watermark Made for the classroom

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The simulation runs on your device; nothing you do here is uploaded.

THREE SIMPLE STEPS

How to use the Galton Board

Choose the board

Start with the classic 12-row board or change the rows, peg spacing, ball size and bounciness.

Drop the balls

Press Start, drop bursts of 10 or 100, or fast-forward 1,000 or 10,000 balls.

Compare with the theory

Read the histogram against the binomial counts and the normal curve, then export a PNG, CSV or video.

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Pay as you go

$1 in free credits for eligible new accounts. No card needed. Generators have separate account and credit requirements. The Plinko simulator is free.

Galton Board FAQ

What does a Galton board show?

That many small random left-or-right steps add up to a predictable shape: the binomial distribution, which looks more and more like the normal (bell) curve as the number of rows grows.

Who invented the Galton board?

Sir Francis Galton described it in 1889 as a way to show how the normal distribution arises from chance. It is also called a bean machine or quincunx, after the pattern of its pegs.

What distribution does a Galton board follow?

With n rows and a fair bounce at every peg, the slot number follows a binomial distribution with mean n/2 and standard deviation √n/2. The simulator draws these expected counts over the slots so you can compare.

Is the simulated board realistic?

Yes. In physics mode every ball bounces off the pegs under gravity, and like a real board its curve comes out a little wider than the ideal binomial. Switch to the ideal 50/50 model for exact coin flips.

Is it free for teachers and students?

Yes, completely free with no sign-up and no watermark. It runs in the browser on laptops, classroom computers and tablets.

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