Circle Calculator: Circumference & Area
Know any one measurement of a circle — radius, diameter, circumference or area — and get the other three instantly.
- C = 2π × 5 = 31.4159 in
- A = π × 5² = 78.5398 in²
- Radius
- 5 in
- Diameter
- 10 in
- Circumference
- 31.4159 in
- Area
- 78.5398 in²
Why the area of a circle is πr²
Cut a circle into wedges like a pizza and lay them tip-to-tail. The more slices, the closer the strip gets to a rectangle: its height is the radius r, and its length is half the circumference, πr. So the area is πr × r = πr².
Strip ≈ 3.142r long × r tall
Circle formulas
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr² = πd²/4 = C²/(4π)
- From area to radius: r = √(A/π)
- From circumference to diameter: d = C/π
π is the same for every circle: the circumference is always about 3.14159 times the diameter. That fixed ratio is what makes the conversions above possible. For part of a circle, use the arc length and sector calculator.
Common sizes
| Diameter | Circumference | Area |
|---|---|---|
| 6 in | 18.8496 in | 28.2743 in² |
| 8 in | 25.1327 in | 50.2655 in² |
| 10 in | 31.4159 in | 78.5398 in² |
| 12 in | 37.6991 in | 113.097 in² |
| 14 in | 43.9823 in | 153.938 in² |
| 16 in | 50.2655 in | 201.062 in² |
| 18 in | 56.5487 in | 254.469 in² |
| 24 in | 75.3982 in | 452.389 in² |
So a 16 in pizza (201 in²) has more than twice the topping area of a 10 in pizza (78.5 in²).
Questions people ask
How do I find the circumference of a circle?
Multiply the diameter by π, or the radius by 2π. A circle with a 10 cm diameter has a circumference of about 31.42 cm.
How do I find the area from the circumference?
A = C² ÷ (4π). A circumference of 31.42 gives an area of about 78.54.
How do I find the diameter from the circumference?
Divide by π. Wrap a tape measure around a tree trunk, divide by 3.1416 and you have its diameter.
What value of π should I use?
The calculator uses full double precision. For hand work, 3.14 is fine to about 0.05%; 22/7 is slightly closer.
Stuck on a word problem?
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