# Pi Experiments Calculator

URL: https://speedycalculator.com/calculators/math/pi/
Last updated: 2026-10-30

> The pi experiments calculator estimates π from your own experiments: measuring a circle, dropping needles on lined paper (Buffon's needle) or throwing random darts at a square (Monte Carlo).

## Inputs

- Start by choosing your experiment
- Circumference C (cm, m, mm, in, ft, yd, km, mi)
- Diameter d (cm, m, mm, in, ft, yd, km, mi)
- Needle length l (cm, m, mm, in, ft, yd, km, mi)
- Distance between lines t (cm, m, mm, in, ft, yd, km, mi)
- Number of needles dropped
- Needles crossing a line
- Darts inside the circle
- Total darts

## Results

- Your estimate of π
- Error compared with π
- True value of π

## Formula

```
Circle: π ≈ C ÷ d
Buffon's needle: π ≈ 2·l·N ÷ (t·h)
Monte Carlo: π ≈ 4 × (darts inside the circle) ÷ (total darts)
```

## Explanation

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

FieldWhat to enterStart by choosing your experimentChoose one: Measure a circle, Buffon's needle, Monte Carlo dartsCircumference CUnits: cm, m, mm, in, ft, yd …Diameter dUnits: cm, m, mm, in, ft, yd …Needle length lUnits: cm, m, mm, in, ft, yd …Distance between lines tUnits: cm, m, mm, in, ft, yd …Number of needles droppedA numberNeedles crossing a lineA numberDarts inside the circleA numberTotal dartsA 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 π39.251.5758.882.35578.53.1498.133.925117.754.711576.28

## 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.

## FAQ

**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.


## Sources

- [Wolfram MathWorld – Buffon's needle problem](https://mathworld.wolfram.com/BuffonsNeedleProblem.html)
- [Wolfram MathWorld – Pi](https://mathworld.wolfram.com/Pi.html)