π is the ratio of a circle’s circumference to its diameter, about 3.14159. You can rediscover it with a tape measure and a plate, with matchsticks on a floorboard or with random numbers – a great classroom experiment.
How to use the Pi Experiments Calculator
- Start by choosing your experiment
- Circumference C
- Diameter d
- Needle length l
- Distance between lines t
- Number of needles dropped
- Needles crossing a line
- Darts inside the circle
- Total darts
Results update as you type, and everything is calculated in your browser.
How it works
Enter the measurements of the experiment you did. The calculator gives your estimate of π and its error compared with the true value.
Inputs explained
| Field | What to enter |
|---|---|
| Start by choosing your experiment | Choose one: Measure a circle, Buffon’s needle, Monte Carlo darts |
| Circumference C | Units: cm, m, mm, in, ft, yd … |
| Diameter d | Units: cm, m, mm, in, ft, yd … |
| Needle length l | Units: cm, m, mm, in, ft, yd … |
| Distance between lines t | Units: cm, m, mm, in, ft, yd … |
| Number of needles dropped | A number |
| Needles crossing a line | A number |
| Darts inside the circle | A number |
| Total darts | A number |
Example values
How the main result changes when Circumference C changes and everything else stays at the example values above:
| Circumference C (cm) | Your estimate of π |
|---|---|
| 39.25 | 1.57 |
| 58.88 | 2.355 |
| 78.5 | 3.14 |
| 98.13 | 3.925 |
| 117.75 | 4.71 |
| 157 | 6.28 |
Formula
Circle: π ≈ C ÷ d
Buffon's needle: π ≈ 2·l·N ÷ (t·h)
Monte Carlo: π ≈ 4 × (darts inside the circle) ÷ (total darts)
Worked example
Inputs — Start by choosing your experiment: Measure a circle; Circumference C: 78.5 cm; Diameter d: 25 cm.
Results — Your estimate of π = 3.14; Error compared with π = -0.0507 %; True value of π = 3.1415926536.
Key terms
- π (pi)
- The ratio of a circle's circumference to its diameter.
Frequently asked questions
What is Buffon's needle?
Drop needles of length l on lines t apart (l ≤ t); the chance a needle crosses a line is 2l/(πt).
How many darts do I need for a good Monte Carlo estimate?
The error shrinks like 1/√N – with 10,000 darts the estimate is typically within about 0.02 of π.
Why does C/d give π?
That is the definition of π.
Who first computed π accurately?
Archimedes bounded it between 3 10/71 and 3 1/7 using polygons.