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
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
Half Circle
Quarter Circle
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!