Enter any circle value to calculate all other properties.
Circle Formulas Explained
The circumference of a circle is C = 2πr, or π × diameter, so a circle 10 inches across measures 31.42 inches around. Going the other way, the radius is C ÷ 2π. Enter a radius, diameter, circumference or area above and the calculator returns the other three values, with each step shown.
The circumference is the perimeter of a circle: the total distance around its edge. All circle properties are linked through π (pi ≈ 3.14159), the ratio of any circle's circumference to its diameter. Enter any one value and this calculator derives the rest.
Circumference from Radius
Circumference from Diameter
Radius from Circumference
Area from Circumference
Circumference and Area by Diameter
Inches are used here, but the numbers work for any unit: a 10 cm circle is also 31.42 cm around. Area is in square units.
| Diameter | Radius | Circumference | Area |
|---|---|---|---|
| 1 | 0.5 | 3.14 | 0.79 |
| 2 | 1 | 6.28 | 3.14 |
| 3 | 1.5 | 9.42 | 7.07 |
| 4 | 2 | 12.57 | 12.57 |
| 5 | 2.5 | 15.71 | 19.63 |
| 6 | 3 | 18.85 | 28.27 |
| 8 | 4 | 25.13 | 50.27 |
| 10 | 5 | 31.42 | 78.54 |
| 12 | 6 | 37.70 | 113.10 |
| 14 | 7 | 43.98 | 153.94 |
| 16 | 8 | 50.27 | 201.06 |
| 18 | 9 | 56.55 | 254.47 |
| 24 | 12 | 75.40 | 452.39 |
| 36 | 18 | 113.10 | 1,017.88 |
Circumference grows in step with the diameter, but area grows with its square. A 16 inch circle is only a third wider than a 12 inch one, yet it has 1.78 times the area, which is why the pizza calculator compares pies by area.
How Much Precision Does Pi Need?
The calculator uses the full double precision value of π (about 16 significant digits). Hand calculations often use a shortcut. This is how far each shortcut drifts on a circle 100 feet across, whose true circumference is 314.16 ft.
| Value used | Decimal | Relative error | Error on a 100 ft circle |
|---|---|---|---|
| 3 | 3 | 4.5% low | 169.9 in short |
| 3.14 | 3.14 | 0.051% low | 1.9 in short |
| 22/7 | 3.142857 | 0.040% high | 1.5 in long |
| 3.1416 | 3.1416 | 0.0002% high | 0.009 in long |
| 355/113 | 3.1415929 | 0.0000085% high | 0.0003 in long |
For school work and most building jobs, 3.14 is plenty. Keep full precision until the last step and round only the final answer.
Worked Examples
Distance per wheel turn
A mountain bike wheel 29 inches in diameter travels π × 29 = 91.11 inches per turn. A mile is 63,360 inches, so the wheel turns about 695.5 times per mile.
Diameter of a tree from a tape
You wrap a tape around a trunk and read 94.2 inches. Diameter = C ÷ π = 29.98 inches, so the trunk is about 30 inches across. Foresters take this measurement at 4.5 feet above the ground.
Edging for a round garden bed
A bed 20 feet across needs π × 20 = 62.83 feet of edging. Its area is π × 10² = 314.16 ft², which tells you how much mulch or soil to cover it.
Everything from a circumference
Start with C = 50 cm. Radius = 50 ÷ 2π = 7.96 cm, diameter = 15.92 cm, and area = C² ÷ 4π = 198.94 cm².
Common Mistakes
- Doubling twice. C = πd or C = 2πr. Writing 2πd gives an answer twice too large.
- Mixing up circumference and area. Circumference is a length (in, ft, cm). Area is in square units and uses r².
- Rounding π too early. Rounding every intermediate step compounds the error. Round once at the end.
- A slanted tape. When measuring a pipe or trunk, keep the tape level and snug, or the reading will be too long.
- Semicircle perimeter without the straight edge. Half the circumference is only the curve. Add the diameter to close the shape.