Our Galton board simulator recreates the most famous probability experiment online: hundreds of balls drop from a hopper, bounce through a maze of pegs and pile up in the bins, drawing a bell curve. Choose how many balls and rows this virtual bean machine has and check, bin by bin, how close the result gets to the theory.
- Balls collected
- Mean bin
- Standard deviation
Results bin by bin
| Bin | Balls | Share | Expected |
|---|
How to use the Galton board simulator
Running the machine takes a few seconds. No sign-up and nothing to install.
Choose balls and rows
Set how many balls fill the hopper, from 200 to 1,000, and how many rows of pegs the board has, from 6 to 16. Each row adds one bin.
Set speed and tilt
Adjust how fast the balls leave the hopper and how far the board leans back: at 90° it stands upright, and the flatter it lies, the slower the balls fall.
Press Start
Watch the balls bounce off the pegs and collide with each other. You can pause and resume the fall whenever you like.
Read the result
Under each bin you see its ball count and its share of the total. Compare them with the theoretical curve, then press Reset to run the experiment again.
Release speed and board tilt can be changed while the machine is running. The number of balls and rows stays locked until the run finishes or you reset it, because changing either means building a new board.
What is a Galton board and how does it work
A Galton board, also known as a bean machine or quincunx, is a device that shows how chance, repeated many times, produces an orderly and predictable result. The British scientist Francis Galton devised it in the 1870s and described it in his book Natural Inheritance (1889).
The experiment is simple: identical balls are dropped down a board with staggered rows of pegs. At each peg a ball is deflected left or right with equal probability. No single path can be predicted, yet the balls always end up forming the same shape: many in the middle and fewer and fewer towards the edges.
The three parts of a Galton board
Hopper
The funnel-shaped reservoir at the top. It holds all the balls and lets them out, a few at a time, right above the first peg.
Pegs
They form a triangle of staggered rows. On every hit, a ball is deflected left or right at random.
Bins
They collect the balls at the end of the run. A board with n rows of pegs has n + 1 bins, and the height of each pile shows how many balls landed there.
From single bounces to the binomial distribution
To reach a given bin, a ball has to be deflected to the right an exact number of times. There is only one path to an end bin: turning the same way at every peg. There are many different paths to the middle bins, which is why they collect more balls. The number of paths to each bin is a binomial coefficient, the same numbers found in Pascal’s triangle.
A Galton board with 6 rows has 26 = 64 possible paths, shared out like this:
| Bin | Paths that reach it | Probability |
|---|---|---|
| 1 | 1 | 1.56% |
| 2 | 6 | 9.38% |
| 3 | 15 | 23.44% |
| 4 (middle) | 20 | 31.25% |
| 5 | 15 | 23.44% |
| 6 | 6 | 9.38% |
| 7 | 1 | 1.56% |
This spread is the binomial distribution. The simulator works it out for the number of rows you choose: it draws it as the theoretical curve over the bins and lists it in the Expected column of the results table.
Why the bell curve appears
The more rows a board has, the closer the binomial distribution gets to the normal distribution, the familiar bell curve. This follows from the central limit theorem: the sum of many small, independent random effects tends to spread out in a bell shape, whatever the source of each effect.
On a board with n rows, the mean falls on the middle bin and the standard deviation is √n / 2 bins: 1.73 with 12 rows and 2 with 16. The simulator computes both from the balls as they land and shows them next to the theoretical values, so you can watch them converge as the number of balls grows.
That is why the Galton board is used to explain things as different as measurement errors, the heights of a population or the small variations in a manufacturing process.
Advantages of our Galton board simulator
We built this online Galton board to stay true to the real experiment and to be easy to use, in class or out of curiosity.
Real physics
Balls fall under gravity, bounce off the pegs, collide with each other and stack up in the bins. No path is decided in advance.
Live theoretical curve
The expected distribution is drawn over the bins, so you can see at a glance how close each pile gets to the theory.
Results bin by bin
Count and share under every bin, live mean and standard deviation, and a table with the expected values.
Your own experiment
Balls, rows, release speed and board tilt: four controls to set up the test you want.
Free, no sign-up
No account, no usage limit and nothing to install. Open the page and start the machine.
Works on any device
Runs in the browser on a computer, tablet or phone, and the board adapts to the size of the screen.