The formulas
Everything about a circle revolves around the number π (pi), approximately 3.14159. Pi is the ratio between the circumference and the diameter of every circle, large or small.
diameter d = 2 × r
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circumference = 2 × π × r = π × d
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area = π × r²
Here r is the radius: the distance from the centre to the edge. The diameter is the line straight through the centre from edge to edge, so it is twice the radius.
Worked examples
- Radius 5 cm: the area is π × 5² = π × 25 ≈ 78.54 cm² and the circumference 2 × π × 5 ≈ 31.42 cm.
- A 12-inch pizza: radius 6 in, area π × 6² ≈ 113 square inches.
- A round table with a circumference of 10 feet: the radius is 10 / (2π) ≈ 1.59 ft, so the diameter is about 3.18 ft (38 inches).
- A circular lawn of 1,000 square feet: the radius is √(1,000 / π) ≈ 17.8 ft.
Working backwards
If you don't know the radius but do know something else:
- from the diameter: r = d / 2
- from the circumference: r = circumference / (2π)
- from the area: r = √(area / π)
This is handy when you have measured around a tree, post or barrel with a tape measure: the circumference is easy to measure, the diameter of a thick trunk is not.
The pizza question: bigger is more than you think
Because the area grows with the square of the radius, a slightly larger circle gives a lot more. A 12-inch pizza has about 113 square inches, a 16-inch one about 201: almost 1.8 times as much pizza, although the diameter is only a third larger. Two 10-inch pizzas (about 157 square inches together) are less than one 16-inch pizza. Compare the price per square inch to find the better deal.
Units
Choose the unit you measured in. The circumference, radius and diameter come out in the same unit, the area in that unit squared (in², cm²). Careful when converting: 1 square foot is 144 square inches, not 12. For other conversions there is the unit converter.
In practice
- Garden and DIY: how much turf, paving or gravel do you need for a round patio or flower bed? Calculate the area and add a little extra for cutting waste.
- Volume: the volume of a round tank, well or rain barrel is the base area times the height. The cylinder calculator does this for you.
- Cycling: the circumference of your wheel determines how far you travel per revolution; bike computers ask for this value.
- School: check your homework, and for right triangles use the Pythagorean theorem calculator.
Semicircles and quarter circles
For half a circle, halve the area: a semicircle with a radius of 2 m has an area of π × 4 / 2 ≈ 6.28 m². The perimeter of a semicircle is half the circumference plus the straight edge (the diameter): π × 2 + 4 ≈ 10.28 m. For a quarter circle, take a quarter of the area. A sector with angle θ (in degrees) has an area of θ / 360 × π × r².
Frequently asked questions
How do you find the area of a circle?
Use π × r²: multiply the radius by itself and then by pi. With a radius of 4 cm that is π × 16 ≈ 50.27 cm².
How do you find the circumference of a circle?
Use 2 × π × r or π × d. A circle with a diameter of 10 cm has a circumference of about 31.42 cm.
What is the difference between radius and diameter?
The radius runs from the centre to the edge, the diameter from edge to edge through the centre. The diameter is twice the radius.
How do I get the diameter from the circumference?
Divide the circumference by π. A circumference of 100 cm gives a diameter of about 31.83 cm.
What exactly is pi?
An infinite, non-repeating number: 3.14159265… For most purposes 3.14 is accurate enough; the calculator is far more precise.
Why is the area in square units?
The circumference is a length, the area a surface. Surfaces are measured in square units.
Last reviewed: 2026-10-06. Results are estimates for information only.