Circumference to Diameter Calculator
Enter a circumference to find the diameter, radius, and area of the circle, or enter a diameter to work the other way. The calculator solves both directions using the relationship C = pi x d. Switch between millimetres, centimetres, metres, inches, and feet - all four results update instantly.
Formula
Worked example
A circle has circumference 31.416 cm. Diameter = 31.416 / 3.14159 = 10.000 cm. Radius = 10 / 2 = 5 cm. Area = pi x 5^2 = 78.540 cm^2.
The relationship between circumference and diameter
Every circle, no matter its size, has the same ratio between its circumference and its diameter. That ratio is pi, approximately 3.14159265. This means if you divide any circle's circumference by its diameter you always get pi, and if you multiply any diameter by pi you get the circumference. The formula is simply d = C / pi in one direction, and C = pi x d in the other. This relationship was known to ancient mathematicians and remains one of the most elegant constants in all of mathematics.
How to use this calculator
Choose whether you want to find the diameter (from a known circumference) or find the circumference (from a known diameter). Enter the value you know, and the calculator instantly returns the other length, plus the radius and the enclosed area. Use the unit selector to work in millimetres, centimetres, metres, inches, or feet - the formulas are identical regardless of unit. The steps panel shows the arithmetic with your actual numbers, so you can check each stage of the working.
Diameter, radius, and area - what each one means
The diameter is the longest straight line you can draw through the centre of a circle, touching the edge on both sides. The radius is half the diameter, the distance from the centre to any point on the edge. The area is the total flat space enclosed inside the circle, calculated as pi times the radius squared. These three properties - along with circumference - fully describe any circle, and knowing any one of them lets you calculate all the others.
Practical uses: when do you need circumference and diameter?
Circumference and diameter conversions come up constantly in practical work. Cyclists and mechanics use wheel circumference to calibrate speedometers and calculate gear ratios. Plumbers and pipe fitters measure the outside circumference of a pipe with a tape measure and then divide by pi to get the outside diameter. Woodworkers and machinists wrap a tape around a cylinder to find its diameter without calipers. Gardeners calculate how much edging they need for circular beds by multiplying diameter by pi. Knowing the formula d = C / pi means any tape measure becomes an effective diameter gauge for any circular object.
Common circle sizes - circumference and diameter
| Object | Diameter (approx) | Circumference (approx) |
|---|---|---|
| Tennis ball | 6.7 cm | 21.0 cm |
| Baseball | 7.4 cm | 23.2 cm |
| Basketball | 24 cm | 75.4 cm |
| Soccer ball | 22 cm | 69.1 cm |
| Bicycle wheel (700c) | 622 mm | 1955 mm |
| Car tyre (16 in rim) | 40.6 cm | 127.5 cm |
| Standard manhole cover | 60 cm | 188.5 cm |
| Dinner plate | 27 cm | 84.8 cm |
| US quarter coin | 24.26 mm | 76.2 mm |
| Earth (equatorial) | 12 742 km | 40 030 km |
Reference values for everyday circles. Diameter and circumference are always related by pi.
Frequently asked questions
What is the formula to convert circumference to diameter?
The formula is d = C / pi, where d is the diameter, C is the circumference, and pi is approximately 3.14159. For example, a circumference of 62.832 cm gives a diameter of 62.832 / 3.14159 = 20 cm. You can also remember it as: diameter = circumference divided by 3.14159.
How do I find the diameter of a pipe or cylinder using a tape measure?
Wrap a flexible tape measure around the widest part of the cylinder to get the circumference. Then divide that measurement by pi (3.14159) to get the outside diameter. For example, if the circumference reads 15.71 cm, the outside diameter is 15.71 / 3.14159 = approximately 5 cm. This technique is widely used by plumbers and engineers because it is often easier to measure around a pipe than across it.
What is the relationship between radius and diameter?
The radius is exactly half the diameter: r = d / 2. Equivalently, the diameter is twice the radius: d = 2r. So once you know the diameter from the circumference (d = C / pi), you can immediately find the radius by dividing by 2. The circumference in terms of radius is C = 2 x pi x r.
How do I find the area of a circle from its circumference?
First find the diameter: d = C / pi. Then find the radius: r = d / 2. Finally calculate the area: A = pi x r^2. You can combine these into a single formula: A = C^2 / (4 x pi). For example, a circumference of 31.416 cm gives area = (31.416)^2 / (4 x 3.14159) = 987.0 / 12.566 = approximately 78.54 cm^2.
Does the unit I use change the formula?
No. The formula d = C / pi works in any unit as long as both the circumference and the diameter use the same unit. If you measure the circumference in inches, the diameter comes out in inches. If you use metres, the diameter is in metres. There is no conversion factor - just divide by pi.
Why is pi used in the circumference formula?
Pi is the ratio of a circle's circumference to its diameter - that is actually its definition. Every circle, large or small, has a circumference that is exactly pi times longer than its diameter. Pi is irrational (its decimal expansion never ends or repeats), but for most practical calculations 3.14159 is accurate to within 0.00001 percent, which is more than enough for any real-world measurement.