Circumference calculator.
Find the distance around a circle. Enter the radius or the diameter and the calculator returns the circumference, along with the diameter, radius and area.
Circle size
LiveCircumference equals 2 times pi times the radius, or pi times the diameter. Enter either measurement and pick which one it is.
Circumference
31.416
distance around the circle
Uses pi to full floating-point precision. Units match whatever unit you enter. Calculations run in your browser; nothing you enter is stored.
How it works
Around the circle
The circumference is the distance all the way around a circle, its perimeter. It is tied to the radius by the constant pi: the circumference is 2 times pi times the radius, or equivalently pi times the diameter, since the diameter is twice the radius.
Pi is about 3.14159, so a circle with a radius of 5 has a circumference of about 31.42. Double the radius and the circumference doubles with it, because the relationship is linear.
Reference
Radius to circumference.
The circumference for a few radius values, using pi.
| Radius | Circumference |
|---|---|
| 1 | 6.283 |
| 2 | 12.566 |
| 5 | 31.416 |
| 10 | 62.832 |
| 0.5 | 3.142 |
The full guide
The complete guide to circumference.
What circumference is, how it relates to diameter and pi, and how to find the area too.
What circumference means
Circumference is just another word for the perimeter of a circle, the total length of its boundary. If you unrolled a circle into a straight line, the circumference is how long that line would be.
It is always in the same units as the radius or diameter you put in, whether centimetres, inches or metres.
The role of pi
Pi is the ratio of any circle’s circumference to its diameter, the same for every circle. That is why circumference equals pi times the diameter, or 2 times pi times the radius. Pi is irrational, about 3.14159, so circumference answers are usually rounded.
This constant is one of the most important numbers in mathematics, appearing far beyond circles.
Radius, diameter and circumference
The diameter is twice the radius, the full width across the circle through the centre. Because of that, the two circumference formulas are equivalent. If you know the circumference, you can work backwards: divide by 2 pi to get the radius.
This calculator lets you enter either the radius or the diameter and handles the conversion.
Circumference versus area
Circumference measures the distance around the circle, while area measures the space inside it. They use different formulas: circumference is 2 pi r, but area is pi times the radius squared. The calculator reports both so you do not mix them up.
Area grows with the square of the radius, so it climbs much faster than the circumference as the circle gets bigger.
The formula
Two pi
r.
Circumference is 2 times pi times the radius, or pi times the diameter; the area is pi times the radius squared.
All geometry tools ›# Circle
circumference = 2 × pi × r
diameter = 2 × r
area = pi × r^2
# r = 5
C = 31.416, area = 78.540Questions
Circumference questions.
How do I calculate the circumference of a circle?
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Multiply 2 times pi times the radius, or pi times the diameter. Enter the radius or diameter above and the calculator gives the circumference instantly.
What is the formula for circumference?
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C equals 2 pi r, where r is the radius, or C equals pi d, where d is the diameter. Both give the same answer because the diameter is twice the radius.
How do I find the radius from the circumference?
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Divide the circumference by 2 pi. For example, a circumference of 31.42 divided by 2 pi gives a radius of about 5.
What is the difference between circumference and area?
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Circumference is the distance around the circle, found with 2 pi r. Area is the space inside, found with pi r squared. This calculator shows both.
Is this circumference calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The circumference calculator works from either the radius or the diameter and shows the area too.