Why is it always 3.14?
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 round is 3.14 diameters. It always is.
- Across (diameter)
- 2
- Radius (half of it)
- 1
- All the way round
- 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.