Circle Calculator
Area, circumference, radius and diameter from any one of them.
Area, circumference, radius and diameter from any one of them.
Area (units²)
78.5398
Circumference 31.4159 units
Every measure of a circle follows from any one of them, which is why this accepts whichever you have. Area is πr² and circumference is 2πr, so the area is also half the circumference times the radius — the same relationship that makes a circle's area the limit of a fan of thin triangles.
How the Circle Calculator works
Every measurement of a circle follows from any single one, so this accepts whichever you happen to have (radius, diameter, circumference or area) and returns the rest. Area is πr² and circumference is 2πr, which makes the area also half the circumference times the radius.
Also known as: area of a circle · circumference calculator · radius from area · circle area and circumference
Where the formulas come from
π is defined as the ratio of a circle's circumference to its diameter. Everything else follows: circumference is πd, and since d is 2r, it is also 2πr.
Area is πr², which can be seen by slicing the circle into thin wedges and interleaving them into something approaching a rectangle. That rectangle is half the circumference long and one radius tall, giving πr × r.
In practice
A radius of 5 gives an area of 25π — 78.54 square units — and a circumference of 10π, or 31.42.
Because all four measures are linked, any one determines the rest. That is why this page accepts whichever you have rather than insisting on the radius.
The commonest error is using the diameter where the radius belongs. It makes the area four times too large, and the result looks plausible enough to survive unchecked.
Where to go next
The Circle question rarely arrives on its own. These are the ones that usually come with it:
- Circle Sector Calculator — Sector area, arc length and chord from a radius and an angle.
- Arc Length Calculator — Arc length and chord, with the radian conversion shown.
- Ellipse Calculator — Area exactly, perimeter by Ramanujan's approximation.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
How do I find the area of a circle?
Multiply π by the radius squared. A radius of 5 gives 25π, or 78.54 square units.
How do I find the radius from the area?
Divide the area by π and take the square root. This page does it directly — choose 'Area' as your known value.
What is the difference between radius and diameter?
The diameter runs all the way across through the centre; the radius is half of it, from the centre to the edge. Confusing them is the single commonest circle error, and it makes the area four times too large.
Why is the circumference 2πr?
Because π is defined as the ratio of a circle's circumference to its diameter. Circumference is therefore π times the diameter, and the diameter is 2r.
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