Circumference Calculator
Choose the measure you already know, whether radius, diameter, circumference or area, and the calculator returns the other three, with the formulas written out step by step.
Last updated November 3, 2026
Above 0, up to 1,000,000,000.
Result
Circumference 31.4159, area 78.5398
| Measure | Value |
|---|---|
| Radius | 5 |
| Diameter | 10 |
| Circumference | 31.4159 |
| Area | 78.5398 |
Uses π = Math.PI (3.141592653589793). Results are rounded to at most 4 decimals for display only.
Show the work
Formula: d = 2r, C = 2πr = πd, A = πr². From C: r = C ÷ 2π. From A: r = √(A ÷ π).
- You entered radius = 5.
- Radius: r = 5.
- Diameter: d = 2 × 5 = 10.
- Circumference: C = 2 × 3.1416 × 5 = 31.4159.
- Area: A = 3.1416 × 5² = 78.5398.
Result: Circumference 31.4159, area 78.5398
How the circumference of a circle is calculated
d = 2r
C = 2πr = πd
A = πr²
The circumference C is the distance around the circle. It is always the diameter d multiplied by π, about 3.14159, which is why a circle with a diameter of 10 has a circumference of 31.4159. The area A is π times the radius squared.
This calculator uses the full precision of π that your browser provides, not a rounded value, and rounds only what it displays, to at most four decimals. Lengths come out in the unit you pick, and the area comes out in that unit squared, such as cm² or ft². Because every formula depends only on the radius, any one of the four measures fixes the other three.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Length Converter, Ratio Calculator and Geometry Calculator.
Radius, diameter and circumference
The radius runs from the centre to the edge, and the diameter runs across the circle through the centre, so the diameter is twice the radius. Once you know either one, the circumference follows directly.
The table below shows how the measures grow. Doubling the radius doubles the circumference, but it multiplies the area by four, because the radius is squared in the area formula.
Working back from the area or the circumference
If you only know the circumference, the radius is C ÷ 2π. A circumference of 100 gives a radius of 15.9155, a diameter of 31.831 and an area of 795.7747.
If you only know the area, the radius is the square root of A ÷ π. An area of 50 gives a radius of 3.9894, a diameter of 7.9788 and a circumference of 25.0663. Only positive values make sense, so zero and negative inputs are rejected.
Pi approximations compared
Many people use 3.14 or 22/7 for π. On a circle with a radius of 5, 3.14 gives a circumference of 31.4 and an area of 78.5. The fraction 22/7 gives 31.4286 and 78.5714. The full value gives 31.4159 and 78.5398.
So 3.14 is short by 0.0159 on the circumference and 0.0398 on the area, while 22/7 is too long by 0.0126 and 0.0316. For schoolwork either is usually fine. For a part that has to fit, use the full value.
Real-world uses
A wheel with a 26 inch diameter travels 81.6814 inches in one turn. A wheel with a 0.65 meter diameter needs about 4.8971 turns to cover 10 meters. A pipe with a 4 inch outer diameter needs 12.5664 inches of wrap or tape to go around it once.
A round fence ring with a radius of 3 meters needs 18.8496 meters of fencing and encloses 28.2743 square meters. Add a little extra for overlap or joints when you buy material, and measure in one unit throughout so the area is in the matching squared unit.
How to use the Circumference Calculator
- Choose what you know: radius, diameter, circumference or area.
- Enter the value, which must be above zero, and pick a unit if you want one.
- Read the radius, diameter, circumference and area. Areas are shown in squared units.
- Open Show the work to see each step, then Copy, Print or Share the result.
Worked example
A circle has a radius of 5. Its diameter is 2 × 5 = 10. Its circumference is 2 × π × 5 = 31.4159. Its area is π × 5² = 78.5398.
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
Frequently asked questions
What is the circumference formula?
The circumference is 2 times π times the radius, which equals π times the diameter. A radius of 5 gives 31.4159.
How do I find the radius from the circumference?
Divide the circumference by 2π. For a circumference of 100 the radius is 100 ÷ 6.2832, or 15.9155.
How do I find the circumference from the area?
First find the radius as the square root of the area divided by π, then multiply by 2π. An area of 50 gives a circumference of 25.0663.
Why do the results have squared units?
Area measures a surface, so it is in the unit multiplied by itself. A radius in centimeters gives an area in square centimeters, while the circumference stays in centimeters.
What happens if I enter zero or a negative number?
The calculator shows a message instead of a result, because a circle needs a size above zero. Values above one billion are also refused.