Circumference (Perimeter) of a Circle Calculator
Quickly calculate the distance around a circle using the radius or diameter.
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How to Calculate the Perimeter of a Circle
In geometry, the perimeter of a circle is formally known as the circumference. It represents the linear distance around the outside edge of the circle. Understanding how to calculate this is essential for fields ranging from basic construction to advanced engineering and physics.
The Fundamental Formula
The circumference is directly proportional to the size of the circle and the mathematical constant π (Pi), which is approximately 3.14159. There are two primary ways to calculate it depending on the information you have:
- Using Radius: $C = 2 \times \pi \times r$
- Using Diameter: $C = \pi \times d$
Step-by-Step Calculation Guide
- Identify your measurement: Determine if you are starting with the radius (distance from center to edge) or the diameter (distance from edge to edge through the center).
- Choose the formula: If you have the radius, multiply it by 2 and then by π. If you have the diameter, simply multiply it by π.
- Apply the constant: Use 3.14 for a rough estimate, or use the π button on a calculator for high precision.
- Label your units: Since perimeter is a measure of length, your result should be in the same units as your input (inches, centimeters, meters, etc.).
Realistic Examples
Example 1: The Bicycle Wheel
A standard bicycle wheel has a radius of 35 centimeters. To find the distance the bike travels in one full rotation:
Formula: $2 \times 3.14159 \times 35$
Result: 219.91 cm
Example 2: The Circular Table
You have a circular dining table with a diameter of 1.5 meters. You want to buy a decorative trim for the edge:
Formula: $3.14159 \times 1.5$
Result: 4.71 meters
Frequently Asked Questions
What is the difference between perimeter and circumference?
"Perimeter" is a general term for the path surrounding a two-dimensional shape. "Circumference" is the specific name given to the perimeter of a curved geometric figure, most commonly a circle.
Is Pi exactly 3.14?
No, Pi is an irrational number, meaning it goes on forever without repeating. 3.14 or 22/7 are common approximations used for simple math, but digital calculators use many more decimal places for accuracy.