Circle Calculator

How to use the circle calculator

1. Choose what you know. Pick the radius, diameter, circumference or area.
2. Enter the value. Use any positive number. The label and unit change to match your choice.
3. Pick a unit (optional). The unit is only used to label the results. Areas are shown in square units automatically.
4. Read the results. You get the radius, diameter, circumference and area, plus the working step by step.

Results are rounded to 4 decimal places and use the full value of π, so they may differ slightly from answers worked out with π ≈ 3.14.

To measure a real object, wrap a tape around it for the circumference, or measure straight across the widest point through the center for the diameter. Then let the calculator find everything else.

Circle formulas

Every measurement of a circle follows from its radius (r), the distance from the center to the edge. The number π (pi) is about 3.14159.

• Diameter: d = 2r
• Circumference: C = 2πr = πd
• Area: A = πr² = πd² ÷ 4

Working backward gives the radius from any other value:

• From the diameter: r = d ÷ 2
• From the circumference: r = C ÷ 2π
• From the area: r = √(A ÷ π)

Worked examples

From the radius. A circle with a radius of 5 cm has a diameter of 10 cm, a circumference of 2 × π × 5 ≈ 31.4159 cm, and an area of π × 5² ≈ 78.5398 cm².

From the circumference. A round table measures 94.25 in around the edge. The radius is 94.25 ÷ 2π ≈ 15 in, the diameter is about 30 in, and the area is about π × 15² ≈ 706.9 in².

From the area. A circular patio covers 100 ft². The radius is √(100 ÷ π) ≈ 5.6419 ft, so the diameter is about 11.28 ft and the circumference about 35.45 ft.

Circumference vs area

The circumference is the distance around the circle, measured in ordinary length units such as cm or ft. The area is the flat space inside the circle, measured in square units such as cm² or ft². Doubling the radius doubles the circumference but makes the area four times larger.