Using the calculator
Type the radius as r = 4, the diameter as d = 8 or the area as A = 50, and the circumference is the answer at the top. If you type a plain number, set "A plain number is" to say which measurement it is.
The answer comes as a multiple of π where that's exact, 8π cm for a radius of 4, with the decimal beside it. Pick your unit under Units and the number of decimal places to round to. The radius, diameter and area are listed under the answer, and the working shows which formula was used.
For part of the way round, add an angle, like r = 4, θ = 90°, and switch Answer to Arc length. The arc length calculator opens that way.
The formula
C = 2πr, or C = πd. They're the same formula, since the diameter is twice the radius.
Both come from the definition of π itself. π is the circumference divided by the diameter, the same for every circle, so the circumference is π times the diameter.
From the area, find the radius first. A = πr² gives r = √(A/π), and then C = 2πr. Put together that's C = 2√(πA), so a circle with an area of 100 cm² has a circumference of 2√(100π) = 20√π, about 35.4491 cm.
Circumference for common sizes
| Diameter | Radius | Circumference | Exact |
|---|---|---|---|
| 1 | 0.5 | 3.14 | π |
| 2 | 1 | 6.28 | 2π |
| 5 | 2.5 | 15.71 | 5π |
| 10 | 5 | 31.42 | 10π |
| 12 | 6 | 37.70 | 12π |
| 20 | 10 | 62.83 | 20π |
| 24 | 12 | 75.40 | 24π |
| 50 | 25 | 157.08 | 50π |
| 100 | 50 | 314.16 | 100π |
Worked examples
A wheel 66 cm across. One turn rolls it forward πd = 66π cm, about 207.35 cm, so a kilometre takes about 482 turns.
Fencing a round pond with a radius of 3 m. C = 2π × 3 = 6π, about 18.85 m of fence.
Working backwards. A tree trunk measured with a tape at 1.5 m round has a diameter of 1.5/π, about 0.4775 m. Type C = 1.5 and set Answer to Diameter.
Where the letter π came from
The Welsh mathematician William Jones was the first known to use π on its own for this ratio, in his 1706 book Synopsis Palmariorum Matheseos. It wasn't taken up straight away.
Leonhard Euler took it up in his books of 1736 and 1748, and through them the symbol spread and became standard.
Questions
Is the circumference the same as the perimeter?
Yes. Circumference is the name for the perimeter of a circle.
Should I use 3.14 or 22/7 for π?
Use whatever your teacher or question says. The calculator uses π to double precision, so its decimals will differ a little from answers worked with 3.14: a radius of 10 gives 62.83 here and 62.8 with 3.14.
How do I find the diameter from the circumference?
Divide by π. Type C = your number and set Answer to Diameter.
Sources
Added and reviewed . What's new