What this calculator does
Diameter to radius is the simplest relationship in circle geometry: the radius is exactly half the diameter, because the radius runs from the centre to the edge and the diameter runs all the way across, through the centre, covering that same distance twice. Radius vs diameter mix-ups are common precisely because the two are so closely related, easy to confuse under time pressure even though the maths is trivial.
This calculator converts in either direction, diameter to radius or radius to diameter, and shows the circumference and area of that same circle alongside the headline answer, so a single measurement gives the full picture of the circle it describes.
The formula
Diameter to radius divides by two: radius = diameter ÷ 2. Radius to diameter multiplies by two: diameter = radius × 2. Both are the same fixed 2:1 ratio read in opposite directions, with no other input needed.
| Term | Meaning |
|---|---|
| Radius | The distance from the centre of a circle to any point on its edge. |
| Diameter | The distance straight across a circle through its centre, equal to twice the radius. |
| Circumference | The distance around the outside of the circle, equal to π times the diameter. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the diameter or the radius, matching whichever direction is selected below. |
| Convert | Select whether you are converting diameter to radius, or radius to diameter. |
When to use it
Reading a spec sheet given in diameter
Pipes, wheels, screws and drill bits are usually specified by diameter, but a formula or a CAD tool might call for the radius instead. Converting once at the start avoids working with the wrong value throughout a calculation.
Checking a measurement taken with a ruler
A ruler naturally measures diameter, straight across the widest point, while some formulas are written in terms of radius. Converting the raw measurement avoids halving or doubling it twice by mistake further down the working.
Explaining the difference between radius and diameter vs a mix-up in someone else's working
When a shared calculation looks out by a factor of two, checking whether radius and diameter have been swapped somewhere is usually the first thing worth checking.
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 recovered from a range of diameters
A range of diameters converted to radius, with the circumference and area of each circle shown alongside.
| Diameter | Radius | Circumference |
|---|---|---|
| 4 | 2.000 | 12.566 |
| 8 | 4.000 | 25.133 |
| 12 | 6.000 | 37.699 |
| 20 | 10.000 | 62.832 |
| 50 | 25.000 | 157.080 |
| 100 | 50.000 | 314.159 |
The same value of 10 converted both directions
The number 10 run through both directions of the conversion, to show how the "convert" setting changes what the number is taken to mean.
| Direction | Result |
|---|---|
| Diameter to radius | 5.000 |
| Radius to diameter | 20.000 |
Questions
How do you convert diameter to radius?
Divide the diameter by 2. A diameter of 20 gives a radius of 10.
How do you convert radius to diameter?
Multiply the radius by 2. A radius of 10 gives a diameter of 20.
What is the difference between radius and diameter?
The radius runs from the centre of the circle to its edge; the diameter runs all the way across, through the centre. The diameter is always exactly twice the radius for the same circle.
Do radius and diameter use the same units?
Yes. Whatever unit the diameter is measured in, centimetres, inches, metres, the radius comes out in that same unit, since the conversion is just a factor of two with nothing else involved.
For circumference or area from either measurement, see the circumference calculator and the area of a circle calculator.