math · 22 minutes · Official OETT Aligned
Distance Around a Circle
Radius, diameter, and circumference
What to know
- radius: center to edge
- diameter: all the way across the center
- circumference: distance around
Using the radius when the formula needs diameter gives only half the correct answer.
The core rule
Diameter = 2 × radius. Circumference = π × diameter, or 2 × π × radius.
Circumference means the distance around a circle. The radius goes from the center to the edge. The diameter goes across the whole circle through the center. Use about 3.14 for π unless the question gives another value. The answer uses inches or feet, not square units.
Worked examples
Example 1: easy
A 16-inch diameter has an 8-inch radius.
- Diameter is the full 16-inch width, so radius is 16 ÷ 2.
- The radius is 8 inches; multiplying 8 by 2 returns the labeled diameter.
The radius is half the distance across the center.
Example 2: medium
A 10-inch diameter has circumference about 31.4 inches.
- Use C = πd with diameter 10 inches.
- Calculate 3.14 × 10 = 31.4 inches and retain linear units.
Circumference is the distance around the circle.
Example 3: hard
A 7-foot radius gives circumference about 44 feet.
- Use C = 2πr with radius 7 feet.
- Calculate 2 × 3.14 × 7 = 43.96 feet, approximately 44 feet.
Twice the radius is the diameter.
Common mistakes
Circumference is π × radius.
Double the radius first, or use the diameter. Circumference is π × diameter.
Put it into practice
Use guided explanations, check your answers, and try a new variation.