ToolCalcu

Circle Calculator

Know one measurement of a circle and find the rest. Enter the radius, diameter, circumference or area and the other three appear.

Your circle

Result

Please correct the highlighted fields.
Area
78.5398
Radius
5
Diameter
10
Circumference
31.4159

How the circle measurements are related

All four measurements come from the radius. The diameter is twice the radius, the circumference is 2π times the radius and the area is π times the radius squared.

When you enter another measurement, the calculator first works back to the radius: from the diameter by halving, from the circumference by dividing by 2π and from the area by taking the square root of area ÷ π.

Formulas used

Diameter = 2 × r
Circumference = 2 × π × r
Area = π × r²
r = Circumference ÷ 2π = √(Area ÷ π)

Worked example

A circle with a radius of 5:

  1. Diameter: 2 × 5 = 10
  2. Circumference: 2 × π × 5 = 31.4159
  3. Area: π × 5² = 78.5398

Radius 5: area = 78.5398, circumference = 31.4159, diameter = 10.

Assumptions and limits

  • The shape is a perfect circle.
  • The unit is only a label that is added to the results; it does not convert between units.
  • Values up to one billion are accepted.

Common questions

What is the difference between radius and diameter?

The radius is the distance from the center of a circle to its edge, and the diameter is the distance across the circle through the center, so the diameter is always twice the radius. Mixing them up is the most common source of wrong circle results, which is why this calculator asks which one you know.

Why does pi appear in both the circumference and the area?

Pi is the fixed ratio between a circle’s circumference and its diameter, about 3.14159. The circumference grows in proportion to the radius, while the area grows with the square of the radius, so doubling the radius doubles the circumference but quadruples the area.

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