Circumference to Diameter Calculator
This calculator converts a circle's circumference into its diameter, radius, and area, useful whenever you can wrap a tape measure around something but cannot easily measure straight across it, such as a pipe, a tree trunk, a fence post, a wheel, or any round object where the centre is hard to reach. Enter the circumference you have measured, choose the unit it is in (millimetres, centimetres, metres, inches, or feet), and pick how many decimal places you want in the answer. The calculator instantly applies the standard geometry formula, diameter equals circumference divided by pi, and returns the diameter, along with the radius and the circle's area, shown both in the result tiles and in a step-by-step breakdown so you can see exactly how each figure was reached. A worked example using a circumference of 31.416 cm, giving a diameter of 10 cm, a radius of 5 cm, and an area of 78.540 square centimetres, sits alongside your own figures for reference. It is handy for trades and DIY jobs like sizing pipe fittings or round stock, estimating timber volume from a trunk's girth, checking wheel and tyre dimensions, or any classroom or workshop task involving circles. Because the formula is exact, your result is only as accurate as the circumference you feed in, so measure carefully and keep your units consistent throughout.
1. Circumference
2. Result
Step-by-Step Calculation
Worked Example (Default)
How to Convert Circumference to Diameter
The circumference of a circle is the distance around its edge. The diameter is the distance from one side of the circle straight through its centre to the other side. These two measurements are always related by the mathematical constant pi (π = 3.14159...):
C = π × d ⇒ d = C / π
To find the diameter from the circumference, you simply divide the circumference by pi. To find the radius, divide by 2π (or halve the diameter). The area then follows from A = πr².
Formula Reference
| What you want | Formula | Example (C = 31.416 cm) |
|---|---|---|
| Diameter | d = C / π | 31.416 / 3.14159 = 10.000 cm |
| Radius | r = C / (2π) | 31.416 / 6.28318 = 5.000 cm |
| Area | A = πr² | π × 5² = 78.540 cm² |
Common Applications
- Pipe and tube sizing: Measuring the circumference of a pipe with a tape measure is often easier than measuring its diameter directly. Divide by pi to get the outer diameter.
- Tree and post diameters: Wrap a tape around a tree trunk or fence post to measure circumference, then calculate the diameter to determine timber volume or post fit.
- Wheel and tyre sizing: Knowing a wheel's circumference lets you calculate the diameter and confirm the correct tyre fit.
- Engineering and manufacturing: Round stock, shafts, and circular flanges are sometimes measured at their perimeter; converting to diameter is a routine step.
- Astronomy: The equatorial circumference of Earth is approximately 40,075 km, giving a diameter of 40,075 / π = 12,756 km.
Unit Notes
The circumference and diameter will always be in the same unit. Area will be in that unit squared. For example, a circumference in centimetres gives a diameter in centimetres and an area in square centimetres (cm²). This calculator supports millimetres, centimetres, metres, inches, and feet.
Quick Reference: Circumference to Diameter
| Circumference | Diameter | Radius | Area |
|---|---|---|---|
| 3.142 cm | 1.000 cm | 0.500 cm | 0.785 cm² |
| 6.283 cm | 2.000 cm | 1.000 cm | 3.142 cm² |
| 15.708 cm | 5.000 cm | 2.500 cm | 19.635 cm² |
| 31.416 cm | 10.000 cm | 5.000 cm | 78.540 cm² |
| 62.832 cm | 20.000 cm | 10.000 cm | 314.159 cm² |
| 314.159 cm | 100.000 cm | 50.000 cm | 7,853.982 cm² |
Related Calculators
- Maths and Stats Calculators: browse all maths tools.
- Circumference Calculator: calculate circumference from diameter or radius.
- Area of a Circle Calculator: find circle area from radius or diameter.
- Arc Length and Sector Area Calculator: arc and sector calculations.
- Annulus Calculator: the area between two concentric circles.
Method: Standard circle geometry. Formula d = C / π is exact for an ideal circle (Euclidean geometry). Pi is taken as 3.14159265358979 (15 significant figures) for all calculations.
This calculator uses exact circle geometry. Results are rounded to the number of decimal places you select. For physical measurements, the accuracy of your result depends on the precision of the circumference you measure.