What this calculator does
Circumference is the distance around a circle: the circular equivalent of a rectangle’s perimeter. Whatever you are measuring, a wheel, a pipe, a running track or a garden bed, the circumference is fixed entirely by one number, the radius or diameter, because every circle has exactly the same proportions once scaled.
This calculator takes either the radius or the diameter, whichever you happen to have, and returns the circumference first, with the enclosed area given underneath as a secondary figure. If you want area as the headline result instead, the area of a circle calculator runs the same numbers the other way around.
The formula
The circumference formula is C = 2πr, or equivalently C = πd since the diameter is twice the radius. Multiplying the radius by 2π, or the diameter by π directly, gives the same answer either way; the calculator uses whichever one you entered.
| Term | Meaning |
|---|---|
| C | Circumference: the distance around the circle, 2πr or πd. |
| r | Radius: the distance from the centre to the edge. |
| d | Diameter: the distance across the circle through the centre, twice the radius. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the radius or the diameter, whichever measurement you have. |
| This value is the | Select whether the value above is a radius or a diameter. |
When to use it
Working out how far a wheel rolls
A wheel travels one circumference per full rotation, so the circumference from its radius or diameter converts a number of rotations directly into a distance.
Fencing or edging a circular bed
The circumference is the length of edging, fencing or trim needed to go once around a circular garden bed, pool or rug, before allowing for overlap or waste.
Checking a manufactured part
A pipe, lid or collar specified by diameter has a fixed, calculable circumference, useful for confirming a belt, band or gasket will actually fit around it.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does circumference change with the radius?
The circumference and enclosed area for a range of radius values.
| Radius | Circumference | Area enclosed |
|---|---|---|
| 1 | 6.283 | 3.142 |
| 2 | 12.566 | 12.566 |
| 5 | 31.416 | 78.540 |
| 10 | 62.832 | 314.159 |
| 20 | 125.664 | 1,256.64 |
| 50 | 314.159 | 7,853.98 |
Radius or diameter: does it matter which you enter?
A value of 10 entered once as a radius and once as a diameter, to show how the "this value is the" setting changes the result.
Questions
What is circumference?
Circumference is the total distance around the outside of a circle, measured along the curve rather than straight across it. It plays the same role for a circle that perimeter plays for a polygon.
How do you calculate circumference?
Multiply the radius by 2π, or multiply the diameter by π directly. Both give the same answer, since the diameter is always twice the radius.
What is the circumference formula in full?
C = 2πr, where r is the radius, or C = πd, where d is the diameter. π is approximately 3.14159, the fixed ratio of a circle’s circumference to its diameter.
Does circumference use the same π as area?
Yes, the same constant π appears in both the circumference formula (2πr) and the area formula (πr²), because π describes the fixed geometry of every circle regardless of its size.
For the area as the headline figure instead, see the area of a circle calculator. For every circle measurement worked out from a single input at once, see the full circle calculator.