KinexiaLEARN PHYSICS

Measure π by Rolling

No formulas handed to you — just cans, string, and a ruler. Measure your way to π and learn how physicists handle error.

Safety:

No hazards. Watch for sharp can edges — use tape to cover any rough rims.

Materials

  • 3 to 5 round objects (cans, lids, plates) of different sizes
  • String or a flexible tape measure
  • A ruler with millimeter marks
  • Tape and a marker
  • Paper for a data table

Procedure

1

Measure circumference and diameter

Wrap string once around the object's widest part, mark it, and measure the length — that is the circumference. Measure the diameter straight across the center. Record both to the nearest millimeter.

2

Roll one revolution

Mark a start line on the object and the table. Roll it exactly one full revolution and measure the distance traveled — a second, independent circumference.

3

Repeat and average

Repeat the roll three times per object and average. Compute C/d for each object using both methods.

4

Compute the ratio

List all your C/d values. How far is each from 3.14159? Which objects gave the best and worst results, and why?

5

Count your trustworthy digits

Decide how many digits of your average you actually trust, given your millimeter ruler. That is your significant-figure count.

What to observe

  • Every object's circumference-to-diameter ratio lands near 3.14.

  • Small objects give noisier ratios than large ones.

  • Averaging repeated rolls tightens the result toward 3.1416.

Why it happens

For any circle, circumference divided by diameter is the constant π≈3.14159\pi \approx 3.14159. Your measurements will scatter around it because rulers and rolling both have uncertainty — reading to the nearest millimeter on a 10 cm roll is already a 1% error. Averaging several trials shrinks random error (∝1/N\propto 1/\sqrt{N}), which is why physicists repeat measurements. The number of trustworthy digits in your result is the lesson of significant figures, and every physics calculation inherits exactly this kind of uncertainty.

Try variations

  • Have a friend measure the same object blind — how much do your values disagree?

  • Try a very large circle (a bike wheel) and a tiny one (a coin). Does size change the accuracy?