Circle Calculator
Circles are everywhere a boundary has no corner: pizza cuts, pipework, wheels, round tables and plot boundaries. Three numbers describe one — radius from centre to edge, circumference around it, area inside — and each pair converts into the other through the constant π, about 3.14159. Enter the radius here, pick the unit you think in, and all three come back in that unit, with the area correctly squared.
Enter values
Results
- Area
- 78.5398 cm²
- Circumference
- 31.4159 cm
- Diameter
- 10 cm
How is the Circle calculated?
One number field takes the radius, the distance from the centre to the edge, and a menu selects the length unit: centimetres, metres or feet. The calculator squares the radius for the area, doubles it and multiplies by π for the circumference, and doubles it again for the diameter. Because the geometry stays inside one unit, the area lands in unit squared — a centimetre radius gives square centimetres, a metre radius gives square metres.
Formula
A = π r² gives the area, C = 2 π r the circumference and d = 2 r the diameter, with r the radius you enter. π is the circle constant ≈ 3.14159265, the ratio of any circle's circumference to its diameter. All three share one unit: if r is in metres then C and d are metres and the area is square metres.
Example
A circular patio with a 5 metre radius: the area is π × 5² = π × 25 ≈ 78.5398 m², the circumference is 2 × π × 5 ≈ 31.4159 m of edging, and the diameter measures 2 × 5 = 10 m. The same circle drawn in centimetres keeps its shape but changes only its labels: a 5 cm radius gives 78.5398 cm² of paper and a 31.4159 cm pencil line. Edging for a 2 m radius bed costs 2 × π × 2 ≈ 12.5664 m.
Things to remember
One radius in, three answers out — that is the leverage π provides, and the reason round tanks are quoted by diameter while floor space is quoted in area. Watch the square on the area: doubling the radius quadruples the square metres, not doubles them. When the measurement you have is a diameter, halve it first.
Frequently Asked Questions
How do you find the area of a circle from its radius?
Square the radius and multiply by π. A 5 m radius gives 25π ≈ 78.5398 m². If you measured the diameter instead, halve it first: a 10 m diameter circle has a 5 m radius and the same 78.5398 m² of floor.
What is the circumference of a circle?
The distance once around its edge, calculated as 2πr. At a 5 cm radius that is 10π ≈ 31.4159 cm. Equivalently it is π times the diameter, which is the historical definition of π itself.
Why does the area come back in square units?
Because area multiplies two lengths: r² turns centimetres into square centimetres before π joins in. Keep radius and result in the unit you chose — a 5 cm radius yields 78.5398 cm², never a mixture of centimetres and square metres.
If I double the radius, what happens to the area?
It quadruples. The radius is squared, so two times the radius gives four times the area — a 10 m radius circle covers about 314.1593 m², exactly four times the 78.5398 m² of the 5 m version. The circumference, being linear, merely doubles.
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