Maths Geometry

Circle calculator

You know the
Value
Radius 5
From radius = 5
Everything else
Diameter 10
Circumference 31.415927
Area 78.539816
Circumference is linear · area is squared

Circumference is 2πr, so adding one metre of length to a rope wrapped around the Earth raises it by 1 ÷ 2π — about 16 centimetres — all the way round. The result is independent of the original radius, which is why the same 16 centimetres would apply to a rope around a tennis ball. It is the clearest demonstration there is that circumference scales linearly with radius while area does not.

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Diameter is twice the radius, circumference is 2πr, and area is πr². A circle of radius 5 has a diameter of 10, a circumference of 31.42 and an area of 78.54. Any one of the four gives the other three.

How to work with circles

1 Choose which measurement you have.
2 Enter it in any unit.
3 Read the other three.
4 Remember area is in square units while circumference is not.

Doubling the radius doubles the circumference and quadruples the area, because one is linear in r and the other goes with r². That single fact explains why a 16-inch pizza is more than twice the pizza of a 12-inch, why a wider pipe carries disproportionately more water, and why doubling the diameter of a telescope collects four times the light. It is the most useful piece of intuition in the whole of plane geometry.

Questions

2πr, or πd if you have the diameter.

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