A circle has four common measurements — radius, diameter, circumference and area — and knowing just one of them is enough to derive all the others.
The four formulas
- Diameter = 2 × radius
- Circumference = 2π × radius
- Area = π × radius²
- Radius from area (the reverse direction) = √(area ÷ π)
Worked example
A circle with radius 5: diameter = 10, circumference = 2π×5 ≈ 31.416, area = π×5² ≈ 78.540.
Going backwards: from area to radius
If you only know the area is about 78.54, you can recover the radius by rearranging the area formula: radius = √(78.54 ÷ π) ≈ 5 — which matches the forward calculation above, confirming the two directions are consistent.
Common mistakes
- Using diameter where radius is required (or vice versa) in the area or circumference formula — since area scales with radius squared, using the diameter by mistake gives an area 4 times too large.
- Forgetting that deriving radius from area or circumference involves a square root or division by π, not a simple reversal of multiplication.
Enter any one known value (radius, diameter, circumference or area) to get all four with the Circle Calculator.
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