Galton Board Simulator

What is a Galton board?

A Galton board is an upright board with a funnel at the top, staggered rows of pegs in the middle and columns at the bottom. Victorian scientist Sir Francis Galton devised it in the 1870s and described it in his 1889 book Natural Inheritance. He called it a quincunx, after the five-dot pattern on a die that the pegs resemble. Today it's also known as a bean machine.

Each ball that falls through the pegs takes a random path, yet together the balls always build the same shape: tall in the middle, tapering at the edges. It's one of the clearest physical demonstrations of how randomness produces predictable patterns.

Why the balls form a bell curve

Every peg is a coin flip: the ball goes left or right with equal chance. By default this board has 11 rows, so each ball makes 11 independent choices, and the column it lands in depends only on how many of those were to the right. That's why there are exactly 12 columns.

Use the rows slider to try anywhere from 6 to 20 rows. With few rows the columns are wide and you can count the paths by hand. With 20 rows there are 21 narrow columns, and the pile follows the bell curve much more closely: the binomial distribution turning into the normal distribution right in front of you.

There is only one path to each outer column (all left or all right), but there are 462 different paths to each of the two middle columns. The counts follow the binomial distribution, and as the number of rows grows, the binomial distribution approaches the normal distribution, the famous bell curve. This is a simple, visible case of the central limit theorem: add up many small random effects and the total tends toward a bell curve.

How to use the simulator

1. Choose how many balls with the balls slider, from 50 up to 1,500 (smaller balls fit more).
2. Pick a ball size with the size slider. Bigger balls need more room, so the maximum count drops as the size goes up.
3. Set the number of rows from 6 to 20. A board with N rows has N + 1 columns, so more rows means narrower columns.
4. Press load to clear the board and refill the funnel.
5. Press play to pull the stopper. Press it again to pause. After a run finishes, play starts a fresh one.
6. Try a skin: Classic Pinball, Neon Arcade, Sunset Drive, Toxic Glow, Vintage Parlour, Steamworks, Candy Shop, Blueprint, or Frost. Each comes with its own dispenser, from a funnel to a gumball globe, its own sound effects, and its own decoration for the corners of the board no ball can reach.

Keyboard shortcuts: Space plays or pauses, L loads, F goes full screen, and M turns the sound on or off.

A fair, accurate simulation

Balls in the funnel are fully simulated, jostling against each other and the walls as they pour out. Through the pegs, every bounce is an exact 50/50 random choice; the bounce height varies for realism but never changes the direction. The dashed line on the board shows the theoretical distribution for the number of balls loaded, and the stats panel shows each run's mean and spread (σ). The expected spread is √rows / 2 columns, about 1.66 for the default 11 rows.

Embed the Galton board on your site

Teachers, bloggers and course designers can put this simulator straight into a lesson page, blog post or learning management system. The embed keeps your chosen skin, ball count, size and rows, resizes to fit any column width, and works on phones and tablets.

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