Everything about a circle from one number
A circle has four measurements that people need: the radius (centre to edge), the diameter (edge to edge through the centre), the circumference (the distance around) and the area (the surface inside). Any one of them fixes the other three, because they are all tied together by π, about 3.14159.
This circle calculator takes whichever one you have and works out the rest, with the formula and each step shown. It helps with homework, with cutting a round table top, ordering a round rug, or sizing a pipe, a planter or a cake tin.
How to use it
- Choose what you know: radius, diameter, circumference or area.
- Type the number.
- Pick a unit if you want it shown, or leave it as No unit.
- Read the other three measurements. Area comes in square units, the rest in plain units.
The calculator keeps full precision behind the scenes, so working back and forth between the four measurements gives the same circle every time, even when the number you start from is rounded.
To measure a real circle, a tape around the outside gives the circumference, which is often easier than finding the exact centre for the radius.
The circle formulas
diameter = 2 × radius
circumference = 2 × π × radius = π × diameter
area = π × radius²
radius = circumference ÷ (2 × π) = √(area ÷ π)π is the ratio of any circle’s circumference to its diameter. It never ends or repeats, so answers are rounded; this calculator keeps full precision inside and shows four decimal places.
Worked example: a radius of 5 cm
- Diameter: 2 × 5 = 10 cm
- Circumference: 2 × π × 5 = 31.4159 cm
- Area: π × 5² = π × 25 = 78.5398 cm²
A circle with a 5 cm radius is 10 cm across, 31.4159 cm around, and covers 78.5398 cm². Going backwards works the same way: type 31.4159 as the circumference and you get a radius of 5 cm again.
Quick reference
| Radius | Circumference | Area |
|---|---|---|
| 1 | 6.2832 | 3.1416 |
| 2 | 12.5664 | 12.5664 |
| 5 | 31.4159 | 78.5398 |
| 10 | 62.8319 | 314.1593 |
| 12 | 75.3982 | 452.3893 |
Notice how area grows much faster than circumference. Doubling the radius doubles the distance around but makes the area four times larger, because the radius is squared. A 12 inch pizza has four times the surface of a 6 inch one, not twice.
Common slips
- Putting the diameter into π × r². Halve it first.
- Mixing up 2πr and πr². The first is a length around the edge; the second is a surface.
- Rounding π to 3.14 for a big circle. On a 10 metre circle, that alone is out by more than a centimetre around the edge.
- For part of a circle, such as a curved edge, use the arc length calculator.
Frequently asked questions
How do I find the area of a circle?
Square the radius and multiply by π: area = π × r². For a radius of 3, that is π × 9, about 28.27 square units. If you only have the diameter, halve it first. Choose From the diameter above and the calculator does that step for you.
How do I find the circumference of a circle?
Multiply the diameter by π, or the radius by 2π. A circle 10 cm across has a circumference of about 31.42 cm. It is the distance you would measure by running a tape around the outside edge, which is also a handy way to check a real object.
How do I find the radius from the circumference?
Divide the circumference by 2π, which is about 6.28319. A circumference of 50 cm gives a radius of about 7.96 cm. Choose From the circumference above, type the distance around, and the calculator gives the radius, the diameter and the area as well.
What is the difference between radius and diameter?
The radius runs from the centre to the edge. The diameter runs right across, through the centre, so it is always twice the radius. Pipes, wheels and tins are usually sold by diameter, while most formulas use the radius, so it is easy to mix them up.
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