How this calculator works
Each experiment produces a ratio that should equal pi when the measurements are perfect. For the pizza, cutting it in half exposes the radius, so half the crust length divided by the radius gives the same ratio as circumference divided by diameter. For the pendulum, the period of a small swing is T = 2π√(L/g), so pi follows from the measured period and length. Round objects use circumference over diameter directly, averaged across every object you measure. The hot dog method is Buffon's needle: a stick of length equal to the line spacing crosses a line with probability 2/π, so 2 × tosses ÷ crossings estimates pi.
Formula
Pizza: π ≈ (C/2) ÷ r. Pendulum: π ≈ (T/2)√(g/L), with g = 9.80665 m/s². Round objects: π ≈ mean(Cᵢ/Dᵢ). Hot dogs: π ≈ 2N/X, where N is the number of tosses and X the number crossing a line.
Worked example
A pizza with a crust length of 31.4159 cm on each half and a radius of 10 cm gives π ≈ 31.4159 ÷ 10 = 3.14159. A hot dog experiment with 100 tosses and 64 crossings gives π ≈ 200 ÷ 64 = 3.125.
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Frequently asked questions
Why do my estimates differ from pi?
Measurements carry error, and each model has simplifying assumptions. The pizza ratio is exact in principle but limited by how well you measure a curved crust. The pendulum formula assumes a small swing, a light string and a point mass. Buffon's needle converges slowly, so a few hundred tosses usually give only two reliable digits.
Which experiment is most accurate?
The round-object method is usually the most reliable with a short ruler, because circumference and diameter are both easy to measure and errors tend to cancel across several objects. The pendulum needs precise timing of many swings.
What is the hot dog experiment really?
It is a physical version of Buffon's needle problem. Frozen hot dogs have a length close to the width of a tile floor, so tossing them and counting line crossings estimates pi from the ratio 2 × tosses ÷ crossings.
How many digits should I trust?
Trust only the digits your measurement precision supports. A ruler to the nearest millimetre on a 10 cm object supports about three digits; a stopwatch over twenty swings supports two or three. More decimals in the answer do not mean more accuracy.