How to find a circle's circumference
The circumference is the distance around a circle: C = 2 × π × r, where r is the radius. For a radius of 5, C = 2 × π × 5 = about 31.42 units. You can also write it as C = π × diameter.
The formula comes straight from the definition of pi. For every circle, no matter its size, the distance around it divided by the distance across it is the same constant, roughly 3.14159. Rearranging that relationship gives C = π × d, and because the diameter is twice the radius, C = 2πr. If you only know the circumference and need the width across, the circle diameter calculator reverses the formula.
How to use this calculator
Enter the radius. If you only know the diameter, halve it first (radius = diameter ÷ 2). The result is in the same unit you used for the radius — inches, cm, m, and so on.
The single most common mistake is entering the diameter where the radius is expected, which doubles the answer. If a result looks twice as large as it should, that is almost always the cause. Circumference scales linearly with the radius: double the radius and the circumference doubles too, unlike area, which quadruples.
From diameter or area
From the diameter d, circumference = π × d. To find the area instead, square the radius and multiply by pi with the semicircle area calculator for half-circles, or work the sector portion with the sector area calculator.
You can also run the formula backwards. If you measure a circumference with a tape and want the radius, divide by 2π: a rope 31.42 units long laid in a circle encloses a radius of 5 units.
Frequently asked questions
- What is the formula for circumference?
- C = 2 × π × r, where r is the radius. Equivalently, C = π × diameter.
- What is the circumference of a circle with radius 5?
- About 31.42 units (2 × π × 5).
- How do I find circumference from the diameter?
- Multiply the diameter by pi (about 3.14159). For a diameter of 10, the circumference is about 31.42.
- What units is circumference in?
- The same length unit as the radius — inches, cm, metres, and so on.
- Is the circumference the same as the perimeter?
- Yes — circumference is simply the name given to the perimeter of a circle. The word is reserved for curved closed shapes, while perimeter is the general term used for polygons such as rectangles and triangles.