Circle calculator
Circumference, area, radius and diameter from any one of them
Choose what you know and type it. The example is a circle with a radius of 5.
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- Radius
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- Diameter
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- Circumference
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- Area
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Working, step by step
The circle formulas
Four measurements describe a circle, and any one gives the others. The radius r runs from the center to the edge. The diameter d runs edge to edge through the center, so d = 2r. The circumference, the distance around, is C = 2πr (or πd). The area is A = πr².
π (pi) is the number of times a circle's diameter fits around its edge, about 3.14159. It never ends, so answers with π are rounded. This page uses π to the full precision a browser holds, 3.141592653589793, and rounds answers to 10 significant digits. When you give the radius or diameter, it also shows the exact answer in terms of π: a radius of 5 gives a circumference of 10π and an area of 25π.
Working backwards
- From the circumference: r = C ÷ 2π. A circumference of 31.4 gives r ≈ 4.997.
- From the area: r = √(A ÷ π). An area of 50 gives r ≈ 3.989.
Units
Choose a unit if you want it shown. Lengths come out in that unit and the area in square units: a radius of 5 cm gives an area of about 78.54 cm². The page does not convert between units.
Real objects
To measure a round object, wrap a string or tape measure around it for the circumference and choose "Circumference". That is usually easier than finding the exact center.
Formula and sources
- Circumference and area of a circle: Common Core 7.G.B.4.
- π as the JavaScript constant Math.PI (the IEEE 754 double nearest to π, 3.141592653589793).
- Checked in test_maths.js: r = 5 → d = 10, C = 10π ≈ 31.41592654, A = 25π ≈ 78.53981634; d = 10 gives the same; C = 2π → r = 1; A = π → r = 1.