Circumference of a circle — Mathematics, 11–13 years
The circumference is the distance all the way around a circle. It is connected to the circle’s diameter by the constant π, so you can find the outside distance without measuring every point of the curve.
Distance around a circle
Imagine cutting a circular hoop at one point and pulling it straight. Its length is the circle’s circumference. If the diameter is d, the circumference is about 3.14 times d, written C = πd. Since the radius is half the diameter, it can also be written C = 2πr.
Why π appears
People needed to measure round objects such as wheels, wells and towers. They noticed that dividing a circle’s circumference by its diameter always gives nearly the same number, no matter how large the circle is. That number is π, about 3.14159, and it turns a curved measurement into a simple calculation.
Finding a bicycle wheel’s circumference
A bicycle wheel has a diameter of 70 cm. Use C = πd and take π ≈ 3.14. Then C ≈ 3.14 × 70 = 219.8 cm. One full turn moves the bicycle about 220 cm, or 2.2 m, along the ground, ignoring the small effect of the tyre pressing down.
Using the radius as the diameter
A frequent mistake is multiplying π by the radius when using C = πd. It feels natural because the radius is the measurement shown from the centre to the edge, but the formula needs the whole distance across the circle. If you know r instead, use C = 2πr, or double r first.
Measuring round paths
Circumference is useful when a belt goes around a wheel, a border surrounds a circular garden, or a machine part turns. Engineers use the wheel’s circumference to link rotations with distance: each complete turn covers one circumference. It is not the right tool for finding the space inside a circle; that is a different measurement.
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