What is the relationship between circumference and diameter?

The circumference is always π times the diameter: C = πd. This is why π (pi) is defined as the ratio of circumference to diameter.

How do I convert circumference to radius?

Use the formula r = C/(2π). Divide the circumference by 2π to get the radius.

Why is circumference proportional to radius?

Circumference is directly proportional to radius because C = 2πr. The constant 2π means that for every unit increase in radius, the circumference increases by 2π units.

Circumference Calculator

Calculate the circumference of a circle using radius or diameter. This calculator provides the formulas C = 2πr and C = πd with step-by-step solutions.

Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)

Circumference Calculator

Input Type

Radius (r)

How It Works

The circumference formula is C = 2πr, where r is the radius and π ≈ 3.14159.

Alternative formula using diameter: C = πd, where d is the diameter.

The circumference is the distance around the circle, also called the perimeter.

Circumference is directly proportional to the radius - doubling the radius doubles the circumference.

Common applications include calculating tire rotations, track lengths, and circular boundaries.

Step-by-step Examples

Example 1: Using Radius

Calculate the circumference of a circle with radius 7 units.

Given: r = 7
Apply formula: C = 2πr = 2π × 7 = 14π
Calculate: C ≈ 2 × 3.14159 × 7 ≈ 43.98 units

Example 2: Using Diameter

Find the circumference when diameter is 10 units.

Given: d = 10
Apply formula: C = πd = π × 10
Calculate: C ≈ 3.14159 × 10 ≈ 31.42 units

Common Mistakes

Forgetting to multiply by 2 in the formula C = 2πr (using πr instead).
Using diameter directly in the formula C = 2πr without converting to radius first.
Confusing circumference with area - circumference is a linear measurement, area is in square units.
Not maintaining unit consistency between radius/diameter and circumference.

Use Cases

Automotive: Calculating tire rotations and wheel travel distance.
Sports: Measuring track lengths and circular race courses.
Engineering: Determining the length of circular components and boundaries.
Mathematics: Solving geometry problems involving circles.
Construction: Calculating material requirements for circular structures.

Frequently Asked Questions

Common questions about circumference calculations.

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