Key takeaway: The circumference of a circle is the distance around it, equal to pi times the diameter, or two times pi times the radius.
Grade 77.G.B.4Geometry and Measurement
Definition of Circumference
The circumference is the perimeter of a circle: the length you would measure if you walked once around the edge or wrapped a tape measure around a can. It is a length, so it uses units such as inches, feet or centimeters.
This length grows in step with the size of the circle. Double the diameter and the rim doubles too. For that reason, dividing the rim by the diameter always gives the same number, pi. That fixed ratio is what produces the formulas below, and it lets you work in either direction: from a tape-measure reading to the diameter, or from the diameter to the tape-measure reading.
Formula and notation
Use the diameter or the radius, whichever you are given:
\[C = \pi d \qquad \text{or} \qquad C = 2\pi r\]
The two agree because \(d = 2r\). Answers are in linear units, not square units.
Key facts
- A circle with diameter 1 has a rim of exactly π, about 3.14.
- Doubling the radius doubles the distance around, but it quadruples the area inside.
- A wheel rolls one full rim length of ground with each complete turn.
- Answers are written in linear units such as feet, never square feet.
Circumference example
A bicycle wheel has a radius of 13 inches. Use 3.14 for pi to find the distance around the tire, and then the distance the bike travels in 10 full turns of the wheel.
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Circumference: \(C = 2\pi r \approx 2 \times 3.14 \times 13 = 81.64\) inches.
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Ten turns: \(10 \times 81.64 = 816.4\) inches.
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Convert: \(816.4 : 12 \approx 68\) feet.
The wheel’s circumference is about 81.64 inches, so ten turns carry the bike roughly 68 feet.
Common mistake
Watch out
Keisha computes \(3.14 \times 13 = 40.82\) inches for the same wheel and reports it as the tire’s distance around.
Why it is wrong
She used the radius in the diameter formula and left out the 2. Either double the radius first, \(d = 26\), and compute \(3.14 \times 26 = 81.64\), or use \(2\pi r\). Her 40.82 is only half way around the wheel.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Geometry and Measurement