What is the circumference of a circle?
Type a radius or a diameter to get the distance around the circle, or type the circumference to get the diameter back.
- Diameter
- 10 in
A circle of radius 5 in (diameter 10 in) has a circumference of 31.42 in.
- Circumference
- 31.42 in
Diameter: 10 in. A circle of radius 5 in (diameter 10 in) has a circumference of 31.42 in.
How to calculate
Finds the circumference of a circle from its radius or diameter (C = 2πr = πd), or the radius and diameter from the circumference.
Example with the default inputs (Radius 5 in): A circle of radius 5 in (diameter 10 in) has a circumference of 31.42 in.
Formula: C = 2πr = πd, where r is the radius and d = 2r is the diameter.
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Every length is in the unit shown next to it.
- Each value must be greater than 0.
Worked examples
Each example is checked against the calculator on every build.
- Radius 196.9 in gives Circumference 1,237 in, Diameter 393.7 in.Source: hand calculation in content.mdx: C = 2 × π × 5 = 10π = 31.4159
- Diameter 315 in gives Circumference 989.5 in, Radius 157.5 in.Source: hand calculation in content.mdx: C = π × 8 = 25.1327
- Circumference 1,732 in gives Diameter 551.4 in, Radius 275.7 in.Source: hand calculation in content.mdx: d = 44 ÷ π = 14.0056 (with π ≈ 22/7 it would be exactly 14)
How it works
The circumference C of a circle is the distance around it. π is defined as the ratio of the circumference to the diameter, so:
- C = πd, where d is the diameter
- C = 2πr, where r is the radius, because d = 2r
Type any one value and the calculator finds the other two:
- from the radius: d = 2r and C = 2πr
- from the diameter: r = d ÷ 2 and C = πd
- from the circumference: r = C ÷ 2π and d = C ÷ π
Assumptions
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Each value is greater than 0.
- Each box has its own length unit, converted through metres (1 in = 0.0254 m exactly). In one unit the numbers are the same in any unit: a radius of 5 cm gives 31.42 cm, and a radius of 5 in gives 31.42 in.
Worked examples by hand
Radius 5. C = 2 × π × 5 = 10π = 31.4159, and d = 2 × 5 = 10.
Diameter 8. C = π × 8 = 25.1327, and r = 8 ÷ 2 = 4.
Circumference 44. d = 44 ÷ π = 14.0056, and r = 14.0056 ÷ 2 = 7.0028. With π ≈ 22/7, the diameter would come out as exactly 14, which is why that textbook example is popular.
Other questions people ask
What is the formula for circumference?
C = 2πr, where r is the radius. Because the diameter is twice the radius, the same formula is C = πd. A 10 in pizza (diameter 10 in) has a crust 31.42 in long.
How do I get the diameter from the circumference?
Divide by π: d = C ÷ π. A tree trunk that measures 44 in around is 44 ÷ 3.14159 = 14.01 in across.
How do I get the radius from the circumference?
Divide by 2π: r = C ÷ 2π. A circumference of 44 in gives a radius of 7.00 in.
Is circumference the same as perimeter?
Yes. Circumference is the word for the perimeter of a circle: the length of its edge. It is a length, so it is in inches or centimetres, not square units.
Why do some books say the circumference of a 14 cm circle is exactly 44 cm?
They use 22/7 for π. 22/7 = 3.142857…, which is a little more than π = 3.141592…, so π × 14 is 43.98 cm, not 44 cm. This calculator uses the full value of π.
How do I measure the circumference of a round object?
Wrap a flexible tape or a string once around it, then measure the string. To check, measure the width across the middle and multiply by π.