Find the circumference (perimeter) of a circle.
The radius is multiplied by 2π.
Circumference: 2 × π × radius
Circumference is the length of the boundary of a circle: how far you would walk if you went once around its edge. This calculator takes the radius and returns 2πr, which is the same as π times the diameter.
It is the circle version of perimeter, and it answers practical questions such as how much lace is needed to trim a round tablecloth, how far a bicycle moves in one turn of its wheel, how much fencing a circular garden bed needs, or how long a running track's inner lane is on the curved part. Students learn it in Class 7 and use it again for arc lengths, the curved surface of a cylinder and speed problems involving wheels. The only input is the radius, so halve a diameter before entering it.
1. Find the radius r. If you know the diameter d, use r = d ÷ 2.
2. Multiply the radius by 2 to get the diameter, if you do not already have it.
3. Multiply the diameter by π: C = πd = 2πr.
4. Use π ≈ 3.14159 for accuracy, or 22/7 if the problem asks for it.
5. Give the answer in the same length unit as the radius.
6. For a fraction of the circle, an arc, multiply the circumference by (angle ÷ 360°).
Every circle, large or small, has the same ratio of circumference to diameter. That constant ratio is what we call π, so C ÷ d = π by definition, and C = πd follows at once. Since d = 2r, this becomes C = 2πr. The fact that all circles are similar shapes, scaled copies of one another, is what guarantees the ratio never changes. π ≈ 3.14159, so the circumference is a little more than three diameters.
Circumference is a length, so it scales directly with the radius. Doubling the radius doubles the circumference, unlike the area, which quadruples. A surprising result follows: if you wrap a rope snugly around the Earth and then want it 1 metre above the ground everywhere, you need only about 2π ≈ 6.28 metres of extra rope. The extra length depends only on the change in radius, not on how big the circle was to begin with.
When a wheel rolls without slipping, each full turn moves it forward by one circumference. A cycle wheel of radius 35 cm covers about 2.2 m per turn, so the number of turns for a journey is the distance divided by the circumference. An arc subtending angle θ at the centre has length (θ ÷ 360°) × 2πr. In radians this is simply rθ, which is why a full turn is 2π radians: the full arc is 2π radii long.
Ramesh is fitting a new rubber tyre strip around a cycle rickshaw wheel that has a radius of 32 centimetres.
Answer: Circumference 201.0619
Entering the diameter as the radius, which doubles the answer.
Using πr², the area formula, and getting square units for a length.
Forgetting the factor 2 and computing only πr, which is half the circumference.
Adding the diameter to the circumference when asked for the perimeter of a full circle. That is only needed for a semicircle.
Expecting an exact textbook match when the book used 22/7 and the calculator uses full-precision π.
Finding the distance a wheel travels per rotation for speed and odometer problems.
Buying edging, lace, ribbon or fencing for round objects and garden beds.
Measuring the girth of trees, pillars and pipes from their radius.
Designing circular tracks and roundabouts.
Computing arc lengths for sectors, clock hands and curved paths.
What's the difference between circumference and area?
Circumference measures the distance around the edge of the circle. Area measures the space inside it. They use related, but different, formulas.