Circle Calculator

Enter any one of radius, diameter, circumference, or area, and get the other three instantly. Switch between meters, centimeters, feet, and inches — all four results share the same unit so you can compare directly.

Examples

Radius 5 m

Classic textbook example — radius 5 m yields area ≈ 78.54 m² and circumference ≈ 31.42 m.

What do you have?: Radius
Value: 5
Unit: Meters (m)

Area

78.54 m²

Circumference

31.42 m

Diameter

10.00 m

Radius

5.00 m

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How It Works

Formula

A = \pi r^2

C = 2 \pi r

d = 2\,r

d = C / \pi

r = \sqrt{A / \pi}

Variables, symbols and units

$r$: Radius (distance from center to edge)
$d$: Diameter (full width through the center)
$C$: Circumference (perimeter of the circle)
$A$: Area (region enclosed by the circle)
$\pi$: Pi — the ratio of circumference to diameter, ≈ 3.14159

Calculation method explained

Pick what you have, enter the value. The calculator solves for the radius first, then derives the other three using π. If circumference is the known value, diameter = circumference / π. All outputs are shown in the unit you selected — area in unit².

Examples

Radius 5 mRadius · 5 → 78.54 m²

Classic textbook example — radius 5 m yields area ≈ 78.54 m² and circumference ≈ 31.42 m.

What do you have?: Radius
Value: 5
Unit: Meters (m)

Area: 78.54 m²

Circumference 31.42 mCircumference · 31.42 → 78.56 m²

Measure around the circle: a 31.42 m circumference gives a 10.00 m diameter.

What do you have?: Circumference
Value: 31.42
Unit: Meters (m)

Area: 78.56 m²

Unit circle (radius 1)Radius · 1 → 3.14 m²

The reference circle of trigonometry — area = π, circumference = 2π.

What do you have?: Radius
Value: 1
Unit: Meters (m)

Area: 3.14 m²

Frequently Asked Questions

What's the formula for the area of a circle?

Area = π × r², where r is the radius. With r = 5, the area is π × 25 ≈ 78.54 square units. If you know the diameter d, use Area = π × (d/2)².

How are area and circumference related?

Both depend on the radius and π. Circumference = 2 × π × r is linear in r, while area = π × r² grows with the square of r. So doubling the radius doubles the circumference but quadruples the area.

What is π?

π (pi) is the ratio of any circle's circumference to its diameter — the same constant for every circle, ≈ 3.14159. It's irrational and shows up in every circle, sphere, and wave equation.

Why are radius and diameter listed separately if one is just twice the other?

Convenience. Real-world measurements often give you whichever is easier to measure — a pipe's diameter, a wheel's radius — and seeing both at once means you don't have to do the doubling or halving in your head.

What if I only know the circumference?

That is enough. Diameter = circumference / π, and radius = circumference / (2π). From there, the area follows automatically.

Circle Calculator

Radius 5 m

How It Works

Examples

Frequently Asked Questions

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