Circle Circumference Calculator

Calculate the circumference and area of a circle from radius or diameter: C = 2πr

Circumference Formulas

Circumference from radius: C = 2πr

Circumference from diameter: C = πd

Area: A = πr²

where: - r = radius (distance from center to edge) - d = diameter (distance across the circle, d = 2r) - π ≈ 3.14159

How to Calculate Circumference

1. Measure the radius or diameter: The radius is half the diameter
2. Using radius: Multiply 2 × π × radius
3. Using diameter: Multiply π × diameter
4. Both methods give the same result since diameter = 2 × radius

Understanding Circumference

Circumference is the perimeter of a circle — the total distance around its edge. The ratio of circumference to diameter is always π, regardless of the circle's size. This constant ratio is what defines the number π.

If you roll a circle along a straight line for one full rotation, the distance traveled equals the circumference. This relationship connects circular and linear measurements.

Real-World Applications

Circumference calculations are used in: - Wheels and tires: Distance traveled per rotation - Fencing: Amount of fencing for circular gardens or pools - Track and field: Calculating lap distances for curved tracks - Engineering: Belt and pulley systems - Sewing: Measuring hems for circular garments - Pizza: Crust length for different pizza sizes

Common Questions

What is the formula for circumference?

The circumference formula is C = 2πr or C = πd, where r is the radius and d is the diameter. Both formulas give the same result since d = 2r.

What is the relationship between circumference and diameter?

The circumference divided by the diameter always equals π (approximately 3.14159). This ratio is the same for every circle, regardless of size. This is the definition of π.

How do you find the radius from circumference?

To find the radius from circumference, use r = C / (2π). Divide the circumference by 2π (approximately 6.2832) to get the radius.