Circumference of a Circle
The perimeter (boundary length) of a circle.
Formula
Variables
Example
A circle of radius 5 has circumference C = 2π·5 ≈ 31.4 units.
How it works
This formula gives the distance all the way around a circle, using only its radius. It works because every circle has the same shape: the circumference is always a fixed multiple of the radius, and that constant multiple is 2π. Since π is about 3.1416, the boundary length is a little more than six times the radius.
When to use it
Use this when you need the perimeter of any circular object, such as a wheel, a round table, a pipe, or a track. It is also useful in geometry problems whenever the radius is known and you need the distance around the circle.
Worked example, step by step
A circle has radius 8 cm. Use C = 2πr C = 2 × π × 8 C = 16π C ≈ 16 × 3.1416 C ≈ 50.3 cm So, the circumference is about 50.3 cm.
Common mistakes to avoid
- Using the diameter as if it were the radius without adjusting the formula
- Forgetting to include π in the calculation
- Mixing up area formulas with circumference and using πr² instead
Did You Know?
The ratio of any circle's circumference to its diameter is always π — a constant that has been computed to trillions of digits.
Share this formula
More in Geometry & Trigonometry
View allPythagorean Theorem
BasicRelates the sides of a right triangle.
Area of a Circle
BasicThe area enclosed by a circle.
Equation of a Circle
IntermediateThe standard form of the equation of a circle with centre (h, k) and radius r.
Area of a Rectangle
BasicArea of a rectangle.
Area of a Triangle
BasicArea of a triangle from base and height.
Area of a Trapezoid
BasicArea of a trapezoid with parallel sides a and b.