Circle Calculator — area, circumference and diameter from radius

How it works

Everything about a circle follows from its radius r — the distance from the centre to the edge — and the constant π (pi ≈ 3.14159), which links a circle's size to its area and perimeter:

• Diameter: 2r — all the way across, twice the radius.
• Circumference: 2πr — the distance around the edge.
• Area: πr² — the space enclosed.

The circumference grows in direct proportion to the radius, but the area grows with the square of it — so doubling the radius doubles the circumference but quadruples the area. That square is why a slightly bigger pizza is a lot more food.

Worked example

Take a circle of radius 5:

• Diameter = 2 × 5 = 10
• Circumference = 2 × π × 5 = 10π ≈ 31.42
• Area = π × 5² = 25π ≈ 78.54

Compare a radius of 10: the circumference doubles to ≈ 62.83, but the area becomes π × 100 ≈ 314.16 — four times as large, because area depends on r².

Frequently asked questions

How do I find the area of a circle?

Square the radius and multiply by π: A = πr². For r = 3, that's π × 9 ≈ 28.27. If you know the diameter instead, halve it to get the radius first (r = d ÷ 2), then apply the formula.

How do I find the circumference?

Multiply the radius by 2π: C = 2πr. For r = 3, that's 2π × 3 ≈ 18.85. Equivalently, since the diameter is 2r, the circumference is π × diameter — which is where π comes from: it's the ratio of a circle's circumference to its diameter.

What is π (pi)?

Pi is the constant ratio of any circle's circumference to its diameter, about **3.14159**. It's irrational — its decimals go on forever without repeating — so answers involving π are usually left as a multiple of π (like 25π) or rounded. It appears in both the area and circumference formulas.

What if I know the diameter, not the radius?

Halve it: the radius is the diameter ÷ 2. Then use the formulas as usual. Since this calculator takes the radius, enter half your diameter — a 10-unit diameter means a radius of 5.

Why does area grow with the square of the radius?

Because area covers two dimensions. Scaling a circle up by a factor stretches it in both directions, so the area scales by that factor squared. Tripling the radius makes a circle 9 times bigger in area but only 3 times bigger around — a key idea in how size and capacity relate.

How can I find the radius from the area or circumference?

Reverse the formula. From area: r = √(A ÷ π). From circumference: r = C ÷ (2π). So a circle of area 50 has radius √(50 ÷ π) ≈ 3.99, and one of circumference 20 has radius 20 ÷ (2π) ≈ 3.18.