What is circumference?
The circumference is the perimeter of a circle: the distance once around it. The radius r runs from the center to the edge, and the diameter d goes all the way across through the center, so the diameter is twice the radius.
Every circle’s circumference is the same number of diameters long: π, which is 3.14159… That is why C = πd, and since d = 2r, C = 2πr. The area inside the circle is πr².
Source OpenStax · Prealgebra 2e, 9.5 Solve Geometry Applications: Circles and Irregular Figures ↗Common Core State Standards · Grade 7, area and circumference of a circle (7.G.B.4) ↗
How to find the circumference of a circle
Here it is with your numbers:
- C = 2 × π × 5
- C = 10π
- C = 31.4159
It means a string 31.4159 in long would go exactly once around the circle.
We keep π as π until the last step, then round, so the answer is exact to every decimal shown. Textbooks often use 3.14 instead, which can change the second or third decimal.
Circumference examples
Common circle sizes measured across (the diameter). Tap a row to try it.
| Diameter | Exactly | Circumference |
|---|---|---|
| 1 in | 1π | 3.1416 in |
| 2 in | 2π | 6.2832 in |
| 5 in | 5π | 15.7080 in |
| 10 in | 10π | 31.4159 in |
| 12 in | 12π | 37.6991 in |
| 14 in | 14π | 43.9823 in |
| 16 in | 16π | 50.2655 in |
| 20 in | 20π | 62.8319 in |
| 24 in | 24π | 75.3982 in |
FAQs
How to calculate the circumference?
Multiply the diameter by π, or twice the radius by π: C = πd = 2πr. A circle 10 inches across has a circumference of 10π, which is 31.4159 inches.
Source OpenStax · Prealgebra 2e, 9.5 Solve Geometry Applications: Circles and Irregular Figures ↗
Is the circumference 3.14 times the diameter?
Very nearly. The circumference is π times the diameter, and π is 3.14159…, a number whose decimals never end. 3.14 is π rounded, which is close enough for most homework; it makes a 20 inch circle 62.8 inches around instead of 62.8319.
What is the circumference of a 20 inch circle?
If 20 inches is the distance across (the diameter), the circumference is 20π, which is 62.8319 inches. If 20 inches is the radius, it is 40π, or 125.6637 inches.
How do I calculate diameter with circumference?
Divide the circumference by π: d = C ÷ π. A circle 47.1 cm around is 14.9924 cm across (OpenStax gets 15 cm because it uses 3.14 for π). Halve it for the radius.
What is the perimeter of a circle?
The perimeter of a circle is its circumference, the distance all the way around it: π times the diameter.
Sources
- OpenStax: Prealgebra 2e, 9.5 Solve Geometry Applications: Circles and Irregular Figures
- Common Core State Standards: Grade 7, area and circumference of a circle (7.G.B.4)