Circle Circumference and Pi
Roll the wheel one whole turn and see how far it got. Now measure that track using the wheel itself: three widths fit, and a little bit over. It comes out the same however big the wheel is.
3.14 times round
The way around is 3.14 diameters. It always is.
- Across (diameter)
- 2
- Radius (half of it)
- 1
- All the way around
- 6.28
- Round ÷ across
- 3.14
Any size you like
Or push the wheel along the line yourself.
Ready to try some? Circumference worksheets
Where it usually goes wrong
π gets filed as a number somebody decided on, or as 22/7 exactly, and the diameter and the radius get swapped in the formula. It is a measurement, not a decision: it is how many of a circle's own widths fit round its edge, and it comes out the same for a coin and for a planet.
Try this
- Roll the wheel one full turn and lay its own width along the track. Three fit, and a bit over.
- Press d = 0.5, then d = 1, then d = 2. Everything about the circle changes and the ratio does not.
- Read across and all-the-way-round together. The second is always the first times 3.14, which is the only thing the formula says.
Where this goes next
A number that stays the same while everything around it changes is the first constant most people meet, and constants are how the rest of mathematics gets anything done.
More about area and size
- Volume and Surface Area of a Boxvolume and surface area are two measurements that do not keep step
- Scale Factor and Areascaling a figure's sides by k scales its area by k², because area is a product of two lengths and both of them were multiplied by k
- Area of a Circlea circle cut into sectors and alternated into a strip settles toward a rectangle of height r and width πr as the sectors get thinner, which is where πr² comes from