What this calculator does
A circle is defined entirely by one measurement. Give any of radius, diameter, circumference or area and the other three follow, because all four are linked through π: the ratio of circumference to diameter, identical for every circle that has ever existed.
This calculator works from whichever measure you happen to have, which matters in practice. Measuring a diameter across a pipe or a circumference around a tree is often far easier than measuring a radius, since finding the exact centre is the hard part.
The formula
Every conversion runs through the radius. Area grows with the square of the radius while circumference grows linearly, which is why doubling a circle’s width quadruples its area: the single most consequential fact about circles in practice.
| Term | Meaning |
|---|---|
| r | Radius: centre to edge. |
| d | Diameter: edge to edge through the centre, equal to 2r. |
| C | Circumference: the distance around, equal to 2πr. |
| A | Area: the space enclosed, equal to πr². |
| π | Approximately 3.14159, the ratio of circumference to diameter. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | The measurement you have. |
| This value is the | Which measurement it is. The calculator works out the other three from it. |
When to use it
Sizing a circular area
A round table, patio or garden bed. Enter the diameter you can measure and read the area for materials or seating.
Working with pipes and cylinders
Flow capacity depends on cross-sectional area, which scales with the square of the diameter. A pipe twice as wide carries roughly four times the flow, not twice.
Measuring a tree or a post
Wrap a tape around it to get the circumference, then work back to the diameter: far easier than trying to measure across a trunk.
Comparing round items by size
The area comparison is what matters for pizzas, pans and tabletops. A 14-inch pizza has nearly twice the area of a 10-inch one despite sounding only slightly larger.
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.
Circle measurements by radius
The full set of measurements at a range of radii.
| Radius | Area | Circumference | Diameter |
|---|---|---|---|
| 1 | 3.142 | 6.283 | 2.000 |
| 2 | 12.566 | 12.566 | 4.000 |
| 5 | 78.540 | 31.416 | 10.000 |
| 10 | 314.159 | 62.832 | 20.000 |
| 25 | 1,963.50 | 157.080 | 50.000 |
| 50 | 7,853.98 | 314.159 | 100.000 |
Working back from a circumference
Measurements derived from a wrapped tape reading: the usual field measurement.
| Circumference | Diameter | Radius | Area |
|---|---|---|---|
| 10 | 3.183 | 1.592 | 7.958 |
| 31.4159 | 10.000 | 5.000 | 78.540 |
| 50 | 15.915 | 7.958 | 198.944 |
| 100 | 31.831 | 15.915 | 795.775 |
| 200 | 63.662 | 31.831 | 3,183.10 |
| 314.159 | 100.000 | 50.000 | 7,853.97 |
Questions
How do I find the area from the diameter?
Halve the diameter to get the radius, then square it and multiply by π. Equivalently, area equals πd² ÷ 4, which avoids the halving step.
Why does doubling the radius quadruple the area?
Because area depends on the radius squared. Doubling the radius gives 2² = 4 times the area. The same square relationship applies to any shape scaled uniformly.
What exactly is π?
The ratio of any circle’s circumference to its diameter: the same for every circle. It is irrational, meaning its decimal expansion never terminates or repeats, so every calculation with it is an approximation.
How do I find the radius from the area?
Divide the area by π, then take the square root. This calculator does it directly if you select area as your input.
What is the area of the square around a circle?
The enclosing square has sides equal to the diameter, so its area is 4r². The circle fills about 78.5 per cent of it, a figure worth knowing when cutting circles from sheet material.
For a wedge rather than a whole circle, see the sector and arc calculator. For three dimensions, use the cylinder or sphere calculator.