Circumference: Step-by-Step Guide
The circumference of a circle is the distance around it. It is equal to pi times the diameter, or 2 times pi times the radius. Pi is a special number that is about 3.14. The radius is the distance from the center to the edge, and the diameter is the distance all the way across through the center.
Math Racer skill guide · Middle School · Grades 6-8
How to solve it, step by step
- Find the radius or the diameter. Check if the problem gives you the radius (r) or the diameter (d). The diameter is always twice the radius.\[d = 2r\]
- Choose the formula. If you know the diameter, use C = pi x d. If you know the radius, use C = 2 x pi x r.\[C = \pi d = 2\pi r\]
- Put in the number and work it out. Replace r or d with the number. You can leave pi as a symbol for an exact answer, or use 3.14 for a decimal answer.\[C = 2\pi (r)\]
- Write the units. Circumference is a length, so use the same units as the radius or diameter, like cm, m, or inches.\[C = 2\pi r \;\text{units}\]
Worked example
A circular track has a radius of 14 m. Find its circumference, both in terms of pi and as a decimal.
Step 1: The radius is 14 m.
Step 2: Since we know the radius, use C = 2 x pi x r.
Step 3: Put in the number: C = 2 x pi x 14 = 28 x pi.
Step 4: For a decimal, use pi = 3.14159: C = 28 x 3.14159 = about 87.96.
Step 5: Add the units: the circumference is 28 x pi meters, or about 87.96 meters.
Check: The diameter is 28 m. Circumference is a little more than 3 times the diameter: 3.14 x 28 = about 87.9. That matches.
Tips and common mistakes
- Circumference is a length, so use regular units like m or cm, not square units.
- Both formulas give the same answer. C = 2 x pi x r and C = pi x d are the same thing, since d = 2r.
- Leave your answer in terms of pi (like 28 x pi) unless the problem asks for a decimal.
- Do not mix up circumference and area. Circumference is 2 x pi x r. Area is pi x r x r.
- Quick estimate: pi is a little more than 3, so the distance around a circle is a little more than 3 times the distance across.
- If you know the circumference and need the radius, divide by 2 x pi.
- Always check whether the problem gave you the radius or the diameter. Mixing them up makes your answer twice as big or half as big.