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, where C is circumference and d is diameter. Enter either measurement and get the other one, plus the radius, instantly, without needing to remember which way to multiply or divide. This conversion comes up any time you can measure around an object but need to know across it, or the reverse. Foresters wrap a tape measure around a tree trunk to estimate diameter, plumbers check pipe circumference to confirm a fitting size, and students converting between the two measurements in geometry problems all rely on the same fixed pi relationship. Because pi never changes, this conversion is exact for any circle, unlike many real-world measurements that only approximate a perfect shape.
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, so once you have one you have all three measurements.
- •The ratio between circumference and diameter is the same for every circle, from a coin to a planet, which is exactly what makes pi a constant.
How to Use
- 1Enter your measurement value. This can be a circumference or a diameter, in any unit.
- 2Choose the direction, circumference to diameter or diameter to circumference, depending on what you already measured.
- 3Click Calculate to read the converted value, with the radius shown alongside it.
- 4Use any unit you like, such as inches, centimeters, or feet. The answer comes out in the same unit you entered, since the conversion is a pure ratio.
- 5If you measured with a flexible tape around a curved object, that reading is the circumference, so choose circumference to diameter.
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 3.14159265358979. That definition makes the conversion a single division or multiplication in either direction. A circle with a circumference of 31.4 inches has a diameter of 31.4 divided by pi, which is about 9.995 inches, and its radius is half that, about 4.997 inches. Going the other way, a diameter of 10 inches gives a circumference of 10 times pi, or about 31.416 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.
A 20-inch diameter wheel
Multiply 20 by pi to get 62.831853, which rounds to 62.832 inches. This is the kind of figure used to calculate how far a wheel travels in one full rotation.
A small circumference under 1 unit
Dividing 3.14 by pi gives almost exactly 1, since pi rounded to 3.14 was historically used as a quick approximation before more decimal places were common.
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 |
Why pi is the same for every circle
No matter how large or small a circle is, dividing its circumference by its diameter always produces the same value, pi. A bicycle wheel and a dinner plate have completely different circumferences and diameters, but the ratio between those two measurements is identical for both.
This constant relationship is why circumference-to-diameter conversion never needs measurement-specific adjustment. The only source of error in real use comes from imperfect circles, such as a tree trunk that is slightly oval, not from the math itself.
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.
- Forgetting that the radius is half the diameter, not half the circumference, which is a common shortcut error when working quickly.
- Measuring an irregular or oval object and expecting an exact result. The formula assumes a true circle, so a slightly warped shape will produce a close but not perfect answer.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
<script src="https://calctide.com/embed.js" data-tool="circumference-to-diameter-calculator" async></script>Preview the embed at /embed/circumference-to-diameter-calculator/.