Circle Perimeter Calculator

Calculate circle perimeter (circumference) from radius, diameter, or area for full, half, and quarter circles

Calculate Circle Perimeter

Select the type of circle to calculate

Select the measurement you know

Enter a positive value to calculate the perimeter

Circle Perimeter Results

0
Radius (cm)
r
0
Diameter (cm)
d = 2r
0
Perimeter (cm)
full circle
0
Area (cm²)
A = πr²

Example Calculation

Circular Track Example

Problem: A circular running track has a radius of 50 meters.

Find: The perimeter (circumference) of the track.

Solution

Given: Radius (r) = 50 m

Formula: p = 2πr

Calculation: p = 2 × π × 50 = 100π ≈ 314.159 m

Answer: The track perimeter is approximately 314.16 meters.

Perimeter Formulas

Full Circle

p = 2πr (from radius)
p = πd (from diameter)
p = 2√(πA) (from area)

Half Circle

p = πr
p = πd/2

Quarter Circle

p = πr/2
p = πd/4

Quick Reference

Perimeter is also called circumference

π ≈ 3.14159... (infinite decimal)

Diameter = 2 × radius

Half circle perimeter = πr

Quarter circle perimeter = πr/2

Understanding Circle Perimeter

What is Circle Perimeter?

The perimeter of a circle, also known as circumference, is the distance around the circle. It's the length of the line that forms the circle's boundary. This measurement is fundamental in geometry and has countless practical applications.

Basic Formula

p = 2πr

Where p = perimeter, r = radius, π ≈ 3.14159

Alternative Forms

  • From diameter: p = πd
  • From area: p = 2√(πA)

Partial Circle Perimeters

Half Circle

For a semicircle, the perimeter is half of a full circle:

p = πr

Quarter Circle

For a quarter circle, the perimeter is one-fourth of a full circle:

p = πr/2

Real-World Applications

  • Track and field (running track length)
  • Fencing circular areas
  • Wheel and tire circumference
  • Pipe and cable length calculations

The Relationship Between π and Circumference

The number π (pi) represents the ratio of a circle's circumference to its diameter. This ratio is constant for all circles, regardless of size. In other words:

π = circumference ÷ diameter

This is why π appears in all circle formulas!