How to use the Circle Calculator (Area, Circumference)
- Choose what you know: radius, diameter, circumference or area.
- Enter the value.
- Read the area, circumference, radius and diameter.
- Keep the units consistent: lengths in one unit and area in its square.
Formula used
Area = π × r². Circumference = 2 × π × r. Diameter = 2 × r. From circumference r = C ÷ (2π); from area r = √(A ÷ π).
Worked example
Here is the Circle Calculator (Area, Circumference) worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| I know the | Radius |
| Value | 5 |
| Result | |
| Area | 78.539816 |
| Circumference | 31.415927 |
| Radius | 5 |
| Diameter | 10 |
The formulas
With radius r: diameter = 2r, circumference = 2πr and area = πr². For a radius of 5, the diameter is 10, the circumference 31.4159 and the area 78.5398.
The circumference can also be written as π times the diameter. That is where π comes from: the ratio of any circle’s circumference to its diameter.
Working backwards
If you only know the diameter, halve it: a diameter of 10 gives the same circle as a radius of 5, with area 78.5398. If you know the circumference, r = C ÷ 2π. A circumference of 100 gives a radius of 15.9155.
If you know the area, r = √(A ÷ π). An area of 100 gives a radius of 5.6419 and a circumference of 35.4491.
Everyday uses
Circle measurements come up when buying a round table cover, working out how much fencing goes around a circular bed, sizing a pizza, or finding how much paint a circular wall needs. Pizza is a good example: area grows with the square of the radius, so a 16 inch pizza has about 78% more area than a 12 inch one, not 33% more.
For a wheel, the circumference is the distance travelled in one turn, which is useful for odometers and bicycle computers.
Units and rounding
Lengths such as radius and circumference are in your chosen unit. The area is in square units, so centimetres give square centimetres. To convert the area to another square unit use the area converter, because converting a square unit is not the same as converting the length.
Results are shown to a reasonable number of digits. If you need an exact answer, keep π as a symbol: the area of a circle of radius 5 is exactly 25π.
Common circle questions
Doubling the radius quadruples the area but only doubles the circumference. That is why a pipe that is twice as wide carries four times as much, and why two small pizzas are less food than one large.
A half circle (semicircle) has half the area, πr² ÷ 2, but its perimeter is πr + 2r, because you must add the straight edge across the diameter. For a sector, scale both by the fraction of the circle: a 90° sector is a quarter of the circle.
Frequently asked questions
How do I find the area of a circle?
Square the radius and multiply by π. For a radius of 5 the area is 25π, about 78.54.
How do I find circumference from the diameter?
Multiply the diameter by π. A diameter of 10 gives a circumference of about 31.416.
What is the difference between radius and diameter?
The radius runs from the centre to the edge. The diameter runs across the whole circle through the centre and equals twice the radius.
Which value of π does it use?
The full double-precision value, 3.141592653589793, not a rounded one.
Can I find the radius from the area?
Yes. Choose area, enter it, and the calculator returns the radius as the square root of the area divided by π.
Why does doubling the radius quadruple the area?
Area depends on the radius squared, so doubling r multiplies the area by 2², which is 4.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.