What this calculator does
The radius of a circle is the distance from the centre to any point on the edge, and every other circle measurement, diameter, circumference and area, can be worked back to it. It is often the number a formula actually needs, even when the measurement you have to hand is something else entirely.
This radius calculator leads with the radius itself, worked out from whichever measurement you already have: the diameter, the circumference, or the area. Enter one of the three and it converts straight to the radius, with the other measurements shown underneath.
The formula
If you know the diameter, the radius formula is simply r = d/2. If you know the circumference instead, r = C/2π, since circumference is 2πr. If you know the area, rearranging A = πr² gives r = √(A/π).
| Term | Meaning |
|---|---|
| r | Radius: the distance from the centre of the circle to its edge. |
| d | Diameter: the distance straight across the circle, twice the radius. |
| π | Pi, approximately 3.14159, the constant linking a circle’s radius to its circumference and area. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the diameter, circumference or area, whichever measurement you already have. |
| This value is the | Select which measurement the value above represents. |
When to use it
Working from a manufacturer’s diameter spec
Pipes, wheels and lids are usually sold by diameter, but a formula for stress, speed or clearance often calls for the radius, so how to find radius from a stated diameter is a common first step.
Working from a measured circumference
Wrapping a tape measure around a tree trunk, tank or column gives the circumference directly; how to calculate radius from that figure is the more useful number for area or volume work that follows.
Working from a known area
If a circular surface is specified only by its area, working back to the radius gives the size actually needed to cut or order material to match 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.
Radius formula from a diameter, across a range of sizes
The radius and circumference recovered from a range of diameter values.
| Diameter | Radius | Circumference |
|---|---|---|
| 2 | 1.000 | 6.283 |
| 5 | 2.500 | 15.708 |
| 10 | 5.000 | 31.416 |
| 20 | 10.000 | 62.832 |
| 50 | 25.000 | 157.080 |
| 100 | 50.000 | 314.159 |
Diameter, circumference or area: does it matter which you enter?
The number 10 entered once as a diameter, once as a circumference and once as an area, to show how the "this value is the" setting changes the radius calculator’s answer.
| The value 10 is the | Radius |
|---|---|
| Diameter | 5.000 |
| Circumference | 1.592 |
| Area | 1.784 |
Questions
What is a radius?
The radius is the distance from the centre of a circle to any point on its edge. It is half the diameter and appears in every circle formula, from circumference to area.
What is the radius formula?
From a diameter, r = d/2. From a circumference, r = C/2π. From an area, r = √(A/π). This calculator applies whichever one matches the measurement you enter.
How to find radius from circumference?
Divide the circumference by 2π, since circumference equals 2πr. For a circumference of 31.4, dividing by roughly 6.283 gives a radius of about 5.
How to calculate radius from area?
Divide the area by π, then take the square root: r = √(A/π). Squaring the radius and multiplying by π reverses the calculation back to the original area.
For the diameter as the headline figure instead, see the diameter calculator. For every circle measurement from a single input at once, see the full circle calculator.