Circle Calculator
All four measurements describe the same circle, so any one of them gives the other three. That is the whole reason to have this rather than a formula sheet.
Area
78.5398
- Radius
- 5.0000
- Diameter
- 10.0000
- Circumference
- 31.4159
- Area
- 78.5398
- All four describe the same circle, so any one of them gives the other three. That is the whole reason to have this rather than a formula sheet.
- The units are whatever you typed. Length stays in those units and area comes back in them squared — enter centimetres and the area is square centimetres.
- Doubling the radius quadruples the area, because the radius is squared. It is why a sixteen-inch pizza is more than twice the food of a twelve-inch one.
About circle calculations
Two formulas cover everything. The circumference is 2πr and the area is πr². Both work from the radius, so the first step with any other measurement is to get back to it — halve a diameter, divide a circumference by 2π, or take the square root of an area over π.
The most useful thing to understand here is that area grows with the square of the radius. Doubling the radius quadruples the area. A sixteen-inch pizza is not a third more food than a twelve-inch one; it is nearly eighty per cent more, and pricing rarely reflects that.
Circumference, by contrast, grows in step with the radius. Double the radius and the circumference doubles. That difference between linear and squared growth is why a large circle encloses so much more than its edge would suggest.
Pi is the ratio of any circle's circumference to its diameter, and it is the same for every circle of any size — which is what makes these formulas work universally. It has no exact decimal form, so every answer here is a rounding of an irrational number.
What it works out
- Any one measurement giving the other three
- Radius, diameter, circumference and area
- Whatever unit you type, with area in it squared
The formula
Circumference = 2πr Area = πr²
A radius of 5 gives a diameter of 10, a circumference of 31.416 and an area of 78.540.
Working backwards is the same arithmetic rearranged. From a circumference, the radius is C ÷ 2π. From an area, it is the square root of A ÷ π. Once you have the radius, everything else follows.
The squared term in the area formula is where the interesting behaviour is. Going from a radius of 5 to a radius of 10 doubles the circumference from 31.4 to 62.8 and quadruples the area from 78.5 to 314.2.
That is the pizza arithmetic. A 12-inch pizza has an area of 113 square inches; a 16-inch has 201. It is 78% more food for a name that sounds 33% larger, and it is why the bigger pizza is almost always better value.
The units are whatever you typed. Enter centimetres and the circumference is centimetres while the area is square centimetres.
- r
- The radius — centre to edge.
- d
- The diameter — all the way across, which is twice the radius.
- π
- About 3.14159. The ratio of circumference to diameter, the same for every circle.
A worked example
A circle with a radius of 5.
That works out to 78.5398 .
- Radius
- 5.0000
- Diameter
- 10.0000
- Circumference
- 31.4159
- Area
- 78.5398
Questions
How do I find the area of a circle?
Multiply pi by the radius squared. A radius of 5 gives an area of 78.54. If you have the diameter, halve it first — using the diameter by mistake gives four times the right answer.
What is the circumference formula?
2πr, or πd if you have the diameter. Both give the same thing, since the diameter is twice the radius.
How do I find the radius from the area?
Divide the area by pi and take the square root. An area of 78.54 gives 25 under the root, so the radius is 5.
If I double the radius, what happens to the area?
It quadruples, because the radius is squared. The circumference only doubles. That gap between linear and squared growth is why large circles hold so much more than they look like they should.
Is a 16-inch pizza much bigger than a 12-inch?
Nearly 78% bigger by area — 201 square inches against 113 — for a name that sounds a third larger. The larger size is almost always better value per square inch.
What is pi exactly?
The ratio of any circle's circumference to its diameter, about 3.14159. It is irrational, so it has no exact decimal form and every calculation using it is rounded somewhere.
What are the units of the answer?
Whatever you typed. Lengths stay in those units and the area comes back in them squared — centimetres in, square centimetres out.