Circumference to Diameter Calculator
Divide a circumference by pi (3.14159) to get the diameter, so a circumference of 31.4 means a diameter of about 10. This circumference to diameter calculator converts in both directions using the exact relationship C = pi x d. Enter either measurement and get the other one, plus the radius, instantly.
Quick answer
Circumference is the distance around a circle, diameter is the distance straight across through the center.
Diameter
9.99493
Diameter
9.99493
Circumference
31.4
Radius
4.997465
What this tells you
- •Circumference is the distance around a circle, diameter is the distance straight across through the center.
- •The two are locked together by pi. Circumference is always pi times the diameter, about 3.14159 times.
- •To go from circumference to diameter, divide by pi. To go the other way, multiply by pi.
- •The radius is always half the diameter.
How to Use
- 1Enter your measurement value.
- 2Choose the direction, circumference to diameter or diameter to circumference.
- 3Read the converted value, with the radius shown below it.
- 4Use any unit you like. The answer comes out in the same unit you entered.
How It Works
Formula
d = C / pi and C = pi x dPi is defined as the ratio of a circle's circumference to its diameter, roughly 3.14159. That makes the conversion a single division or multiplication. A circle with a circumference of 31.4 inches has a diameter of 31.4 / 3.14159, which is about 9.99 inches, and its radius is half that, about 5 inches.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Circumference 31.4 to diameter
Divide 31.4 by pi (3.14159) to get 9.995. The radius is about 4.997.
Diameter 10 to circumference
Multiply 10 by pi to get 31.416.
Tree trunk measuring 62.8 inches around
Wrap a tape around a trunk, divide by pi, and you have the trunk diameter without cutting anything.
Circumference to Diameter Quick Table
Common circumference values and the matching diameter, rounded to 2 decimals.
| Circumference | Diameter | Radius |
|---|---|---|
| 1 | 0.32 | 0.16 |
| 5 | 1.59 | 0.80 |
| 10 | 3.18 | 1.59 |
| 25 | 7.96 | 3.98 |
| 50 | 15.92 | 7.96 |
| 100 | 31.83 | 15.92 |
Common mistakes
- Multiplying by pi when you should divide. Circumference to diameter is division. If your answer got bigger, you went the wrong way.
- Using the radius formula by accident. C = 2 x pi x r uses the radius, while C = pi x d uses the diameter. Mixing them doubles or halves your answer.
- Rounding pi to 3. That introduces almost a 5 percent error, which matters for anything you plan to cut or build.