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How to Find the Circumference of a Circle

Learn how to calculate the circumference (perimeter) of a circle using the radius or diameter. Master the formula C = 2πr with our interactive calculator and practice problems.

Circumference Formula
The fundamental formulas for calculating the circumference of a circle
C = 2πr
Using Radius
C = Circumference
r = Radius
π = Pi (≈ 3.14159)
C = πd
Using Diameter
C = Circumference
d = Diameter
π = Pi (≈ 3.14159)

Visual Guide:

r
Circumference Calculator
Calculate the circumference using either the radius or diameter of the circle
Practice Problems: Circle Circumference
Test your understanding with these circumference calculation problems
Problem 1 of 4Score: 0/0

A circular garden has a radius of 8 feet. What is the circumference?

Common Mistakes to Avoid
Learn from these frequent errors when calculating circumference
Mistake: Confusing radius and diameter
Using C = πr instead of C = 2πr when given the radius
Correct: Remember that diameter = 2 × radius
If radius = 5, then C = 2π(5) = 10π, not C = π(5) = 5π
Mistake: Using 3.14 instead of π in exact answers
Writing 31.4 instead of 10π when an exact answer is required
Correct: Leave π in the answer when asked for exact form
Exact: 10π units, Approximate: 31.42 units
Mistake: Forgetting units in the final answer
Writing just "31.42" instead of "31.42 cm" or "31.42 units"
Understanding π (Pi)
The mathematical constant that makes circles work
Definition

π = circumference ÷ diameter

This ratio is the same for every circle, no matter how big or small!

Common Values
Exact: π (infinite decimal)
Decimal: 3.14159...
Fraction: 22/7 (close approximation)
Simple: 3.14 (for quick calculations)
Historical Note

Ancient Greek mathematician Archimedes (287-212 BC) was one of the first to calculate π accurately by inscribing and circumscribing polygons around circles.

Fun Fact

π is an irrational number, meaning its decimal representation never ends and never repeats. Mathematicians have calculated π to over 100 trillion digits!

Real-World Applications
See how circumference calculations are used in everyday life and various industries

Tire Circumference

Calculate how far a car travels with each wheel rotation

Example
A tire with 15-inch radius travels 94.2 inches per rotation

Bicycle Wheels

Determine gear ratios and cycling distance calculations

Example
26-inch bike wheel has circumference of about 81.7 inches

Earth's Circumference

Measure the distance around our planet

Example
Earth's circumference at equator is approximately 40,075 km

Clock Design

Calculate the length of clock hands and dial markings

Example
Hour hand tip travels in a circle with circumference 2πr

Ferris Wheels

Design amusement park rides and calculate passenger travel

Example
100-foot diameter Ferris wheel has 314-foot circumference

Tree Trunk Measurement

Estimate tree age and health from trunk circumference

Example
Tree with 3-foot circumference has approximately 11.5-inch diameter
Related Problems
Continue learning with these related geometry topics
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