What is the formula for the circumference of a circle?

C = 2πr, and because the diameter is twice the radius that is the same as C = πd. With a radius of 3 the multiple is 2 × 3, so the circumference is exactly 6π, which is 18.8496 to four decimal places. The same circle entered as a diameter of 6 gives the identical figures, and the area, πr² = 9π = 28.2743, is shown beside them.

How do I find the radius from the circumference?

Divide by 2π: r = C / (2π). Set the known measurement to Circumference and type it in. A circumference of 10π returns a radius of exactly 5, a diameter of 10 and an area of 25π, or 78.5398. A plain decimal works the same way: a circumference of 100 gives a radius of 50/π, which is 15.9155, and a diameter of 31.831.

Can it give the answer as a multiple of pi instead of a decimal?

Yes, that is the Exact cell, and it is the answer the decimal is rounded from. A radius of 3 gives 6π, a radius of 1/6 gives π/3, a radius of 3/4 gives 1.5π and a radius of π itself gives 2π². When you start from a circumference that is a plain decimal there is no tidy multiple of pi to be had, so the radius is written over pi instead: a circumference of 100 gives 50/π.

Is the circumference exact or rounded?

The working is exact and only the number on screen is rounded, to the number of places you choose between 0 and 10. A radius of 1/3 gives exactly 2π/3; shown to two places the decimal reads 2.09, and the exact form is still 2π/3. Paste that exact form back in as the circumference and the same circle comes back rather than one that has drifted: at four places, radius 0.3333, diameter 0.6667 and 2π/3 again. A circle too small for the places you picked is given to four significant figures instead of being printed as a zero.

What units does it work in?

Whichever you pick, and it changes the label rather than the number. A radius of 2.5 inches gives a circumference of 15.708 inches and an area of 19.635 square inches; the same 2.5 in centimetres gives the same figures in centimetres. Radius, diameter and circumference always share one unit and the area is in that unit squared, and nothing is converted behind the scenes. Leave the unit off and the page says so rather than inventing one.

Does it work out the area of the circle too?

Yes, as a secondary result rather than the headline: A = πr², from the same exact radius. A radius of 3 gives 9π, which is 28.2743, and a circumference of 10π gives 25π, which is 78.5398. If the area is what you came for, the area calculator covers every common shape.

What happens if I enter a negative number or zero?

It is refused with a message that names the problem instead of answering it: a negative measurement cannot describe a circle, and a radius of zero is a point rather than a circle. A fraction over zero is refused the same way. Measurements from 0.000000001 up to 1,000,000,000 are answered, and anything outside that says so.

Circumference Calculator

Enter whichever measure you have, the radius, the diameter or the circumference itself, and the circle comes back whole: circumference, exact form, diameter and area together. Every answer is given twice, as an exact form (a multiple of pi wherever the circle has one, such as 6π) and as a decimal rounded to between 0 and 10 places, because 6π and 18.8496 are the same circle and different homework. Fractions, mixed numbers and pi expressions are all read, so 3/4, 5 1/2, 6pi and 9.4248/pi are measurements here. The working is kept exactly and only the printed decimal is rounded, which is why feeding the exact circumference back in returns the circle you started with. Pick a unit and it is carried through to every figure, with the area in that unit squared and nothing converted behind your back. It runs in your browser, with no account and nothing uploaded.

Circumference18.8496radius 3 · exactly 6π · diameter 6

Known

Radius

Unit

Decimals

Circumference

18.8496

Exact

6π

Diameter

Area

28.2743

No unit chosen: radius, diameter and circumference all come back in the same unit you typed, and the area in that unit squared.

Radius 3C = 2πr
18.8496, exactly 6π
Diameter 6the same circle
18.8496, exactly 6π
Circumference 10πsolve back
radius 5, diameter 10

Accuracy. Exact geometry: C = 2 pi r, given both as a multiple of pi and as a decimal rounded to the number of places you choose. Only the displayed decimal is rounded, never the working, so solving back from the circumference returns the radius you started with. A negative measurement is refused rather than answered. Area is shown as a secondary result.

Common questions

What is the formula for the circumference of a circle?: C = 2πr, and because the diameter is twice the radius that is the same as C = πd. With a radius of 3 the multiple is 2 × 3, so the circumference is exactly 6π, which is 18.8496 to four decimal places. The same circle entered as a diameter of 6 gives the identical figures, and the area, πr² = 9π = 28.2743, is shown beside them.
How do I find the radius from the circumference?: Divide by 2π: r = C / (2π). Set the known measurement to Circumference and type it in. A circumference of 10π returns a radius of exactly 5, a diameter of 10 and an area of 25π, or 78.5398. A plain decimal works the same way: a circumference of 100 gives a radius of 50/π, which is 15.9155, and a diameter of 31.831.
Can it give the answer as a multiple of pi instead of a decimal?: Yes, that is the Exact cell, and it is the answer the decimal is rounded from. A radius of 3 gives 6π, a radius of 1/6 gives π/3, a radius of 3/4 gives 1.5π and a radius of π itself gives 2π². When you start from a circumference that is a plain decimal there is no tidy multiple of pi to be had, so the radius is written over pi instead: a circumference of 100 gives 50/π.
Is the circumference exact or rounded?: The working is exact and only the number on screen is rounded, to the number of places you choose between 0 and 10. A radius of 1/3 gives exactly 2π/3; shown to two places the decimal reads 2.09, and the exact form is still 2π/3. Paste that exact form back in as the circumference and the same circle comes back rather than one that has drifted: at four places, radius 0.3333, diameter 0.6667 and 2π/3 again. A circle too small for the places you picked is given to four significant figures instead of being printed as a zero.
What units does it work in?: Whichever you pick, and it changes the label rather than the number. A radius of 2.5 inches gives a circumference of 15.708 inches and an area of 19.635 square inches; the same 2.5 in centimetres gives the same figures in centimetres. Radius, diameter and circumference always share one unit and the area is in that unit squared, and nothing is converted behind the scenes. Leave the unit off and the page says so rather than inventing one.
Does it work out the area of the circle too?: Yes, as a secondary result rather than the headline: A = πr², from the same exact radius. A radius of 3 gives 9π, which is 28.2743, and a circumference of 10π gives 25π, which is 78.5398. If the area is what you came for, the area calculator covers every common shape.
What happens if I enter a negative number or zero?: It is refused with a message that names the problem instead of answering it: a negative measurement cannot describe a circle, and a radius of zero is a point rather than a circle. A fraction over zero is refused the same way. Measurements from 0.000000001 up to 1,000,000,000 are answered, and anything outside that says so.

Exact geometry: C = 2 pi r, given both as a multiple of pi and as a decimal rounded to the number of places you choose. Only the displayed decimal is rounded, never the working, so solving back from the circumference returns the radius you started with. A negative measurement is refused rather than answered. Area is shown as a secondary result.