Circumference of a Circle Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the circumference of a circle?
Answer
Circumference of a circle
C = 2 · π · r
Here r is the radius. The result comes out in units.
Where the formula comes from
C = 2 · π · r
π is defined as the ratio of a circle’s circumference to its diameter — that is what the number means. So C = π·d, and since d = 2r, C = 2πr. The formula is not derived from π; π is derived from it.
Worked examples
Let r = 5. Then the circumference of a circle ≈ 31.42 units.
Let r = 3.2. Then the circumference of a circle ≈ 20.11 units.
The common mistake
Asking for the "perimeter of a circle" and expecting a different formula. It is the same length under a different name — a circle’s perimeter IS its circumference, 2πr.
Other quantities: Circle
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- Gravel Calculator - Area to cubic yards, tons and coverage
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- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula
| If r = | Circumference |
|---|---|
| 1 | ≈ 6.28 units |
| 2 | ≈ 12.57 units |
| 3 | ≈ 18.85 units |
| 4 | ≈ 25.13 units |
| 5 | ≈ 31.42 units |
| 10 | ≈ 62.83 units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the circumference of a circle? (The answer is: C = 2 · π · r). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter