Diameter to Radius Calculator
This calculator converts between a circle's diameter and its radius, and works out the circumference and area at the same time, so you get all four key measurements from one figure. Diameter and radius are easy to mix up on a spec sheet, tyre sidewall or product listing, and getting the wrong one can throw out a calculation for pipe fittings, wheel clearances, garden beds, pools or manufacturing drawings. To use it, choose whether you are converting diameter to radius or radius to diameter, enter your measurement, and select the unit - millimetres, centimetres, metres, inches or feet. The calculator instantly returns the radius (centre to edge), the diameter (edge to edge through the centre), the circumference (distance around the circle) and the area (space inside the circle), all shown in the unit you entered. A full breakdown and the exact formulas used are listed below the results so you can see the working. Because the radius is always exactly half the diameter, the conversion carries no rounding error, though circumference and area figures are rounded slightly for display using full-precision pi. If you are working to tight tolerances, such as pipe fittings or structural components, treat the results as a helpful working figure and confirm critical measurements with a physical check or a qualified tradesperson.
1. Enter Your Measurement
2. What You Get
Enter the diameter or radius of any circle and this tool converts it to the other measurement straight away. It also works out the circumference (distance around the circle) and the area (space inside the circle) using the same unit you entered.
This is useful for pipe sizing, wheel and tyre measurements, round garden beds, pizza sizes, or any job where a spec sheet gives you one measurement and you need the other.
Full Breakdown
Formulas Used
How to Convert Diameter to Radius
The radius of a circle is always exactly half of its diameter. The diameter is the straight-line distance across a circle, passing through its centre, from one side to the other. The radius runs from the centre point to any point on the edge. Because the centre sits exactly halfway along the diameter, the relationship between the two is simple and fixed.
The Formula
| Conversion | Formula | Example |
|---|---|---|
| Diameter to radius | r = d ÷ 2 | 20 cm diameter = 10 cm radius |
| Radius to diameter | d = 2 × r | 10 cm radius = 20 cm diameter |
| Circumference (from radius) | C = 2πr | 10 cm radius = 62.83 cm circumference |
| Area (from radius) | A = πr² | 10 cm radius = 314.16 cm² area |
Common Uses
- Plumbing and pipes: pipe sizes are often given as diameter, but flow and fitting calculations sometimes need the radius.
- Wheels and tyres: tyre diameter is printed on the sidewall, but suspension and clearance calculations often use radius.
- Round garden beds and pools: working out materials or fencing length around a circular area.
- Manufacturing and engineering: converting between spec sheets that use diameter and formulas that require radius.
Frequently Asked Questions
How do you convert diameter to radius? Divide the diameter by 2. A circle with a diameter of 20 cm has a radius of 10 cm.
How do you convert radius to diameter? Multiply the radius by 2. A circle with a radius of 7 m has a diameter of 14 m.
Can I find the circumference and area from the radius or diameter? Yes, once you have the radius this calculator automatically works out the circumference (2 x pi x radius) and area (pi x radius squared) for you.
Related Calculators
- Essential Calculators: the full toolkit of everyday conversion and maths calculators.
- Circumference to Diameter Calculator: work backwards from circumference.
- Circumference Calculator: find the distance around any circle.
- Area of a Circle Calculator: work out the area from radius or diameter.
- Circle Calculator: solve for any circle measurement.
Sources: Standard Euclidean geometry definitions of radius, diameter, circumference and area, as used in NZ secondary school mathematics curricula (nzmaths.co.nz).
This calculator uses exact geometric formulas and full-precision pi. Results are rounded for display. Always double-check critical measurements (such as pipe fittings or structural work) with a physical measurement or a qualified tradesperson.