Circle Area Explorer — see where πr² comes from
Cut a circle into slices, unfold them into a near-rectangle, and watch the most famous area formula in maths build itself.
Every maths textbook states that the area of a circle is π × r × r, and most students simply memorise it. This explorer shows why it is true. A circle is cut into equal slices, like a cake. The slices are laid out in a row, points alternating up and down, and the row slowly straightens into something that looks more and more like a rectangle. The thinner the slices, the closer the match.
Try it: first cut the circle into just 4 pieces and unfold — the strip is all wobbly. Now try 32 pieces. The more pieces you cut, the straighter the strip gets, until it is almost a perfect rectangle.
How to play
Drag the first slider to choose how many slices to cut, then drag the second slider (or press the unfold button) to lay them out. Watch the dashed frame: its height is the radius, and its length is half the way around the circle.
What you learn
A rectangle has area length times height, so the strip has area (π × r) × r — which is exactly πr². Because cutting and rearranging never changes area, the circle must have the same area. You have not memorised the formula; you have seen where it lives.
Want more? Browse the whole Interactive Geometry Lab for nine hands-on math toys, or build a personalised math adventure for your child with the free Game Builder. Everything is free, with no sign-up.
✓ Last checked November 2, 2026 — we re-test this tool every week to make sure it still works.