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
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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
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 |
FAQ
What is the formula for the circumference of a circle?
Circumference of a circle C = 2 · π · r
Where does this formula come from?
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.
What is the most common mistake here?
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.
How do I use this formula?
Put your own numbers in place of the letters. With r = 3.2, for instance, the formula C = 2 · π · r gives ≈ 20.11 units.
See Also
- Area of a Circle Formula
- Area of a Hexagon Formula
- Area of a Parallelogram Formula
- Area of a Regular Polygon Formula
- Area of a Rectangle Formula
- Area of a Rhombus Formula
- Area of a Circular Sector Formula
- Area of a Square Formula
- Area of a Trapezoid Formula
- Area of a Triangle Formula
- Diameter of a Circle Formula
- Perimeter of a Regular Polygon Formula
- Perimeter of a Rectangle Formula
- Perimeter of a Semicircle Formula
- Perimeter of a Square Formula
- Perimeter of a Triangle Formula
- Surface Area of a Cone Formula
- Surface Area of a Cube Formula
- Surface Area of a Cylinder Formula
- Surface Area of a Pyramid Formula
- Длина окружности круга
- Circunferencia del círculo
- Circunferência do círculo