Circumference of Circle- Formula, Examples, and Practice Problems

What Is Circumference?

The circumference is the distance around a circle. That's it. If you walked along the edge of a circular track, the distance you covered is its circumference.

Unlike squares or rectangles, circles don't have straight sides you can measure with a ruler. You need a formula. Two formulas, actually.

The Two Circumference Formulas

Using the Radius

The most common formula uses the radius — the distance from the center of the circle to its edge:

C = 2πr

Where:

• C = circumference
• π (pi) ≈ 3.14159
• r = radius

Using the Diameter

If you know the diameter instead (the distance across the circle through the center), the formula simplifies:

C = πd

Where d = diameter

This works because the diameter is always exactly twice the radius. So 2πr equals π(2r), which is πd. Same result.

Understanding π (Pi)

Pi is a fixed number. It's the ratio of any circle's circumference to its diameter. No matter how big or small the circle, this ratio stays the same.

Pi ≈ 3.14159

For quick calculations, use 3.14. For precision work, use the π button on your calculator. The difference is small but matters in engineering and scientific contexts.

How to Calculate Circumference: Step-by-Step

Example 1: Using the Radius

Problem: Find the circumference of a circle with a radius of 5 cm.

Step 1: Plug values into C = 2πr

C = 2 × π × 5

Step 2: Calculate

C = 2 × 3.14 × 5

C = 31.4 cm

That's your answer. 31.4 cm.

Example 2: Using the Diameter

Problem: Find the circumference of a circle with a diameter of 12 inches.

Step 1: Plug values into C = πd

C = π × 12

Step 2: Calculate

C = 3.14 × 12

C = 37.68 inches

Done.

Example 3: Real-World Application

Problem: A bicycle wheel has a radius of 35 cm. How far does it travel in one revolution?

The distance in one revolution equals the wheel's circumference.

C = 2 × 3.14 × 35

C = 219.8 cm (about 2.2 meters per rotation)

This is why bicycle computers and car odometers work — they count rotations and multiply by circumference.

Quick Reference Table

Practice Problems

1. A circle has a radius of 8 cm. What is its circumference?

Answer: C = 2 × 3.14 × 8 = 50.24 cm

2. A circular garden has a diameter of 20 feet. What is the distance around it?

Answer: C = 3.14 × 20 = 62.8 feet

3. A pizza has a 14-inch diameter. What is its circumference?

Answer: C = 3.14 × 14 = 43.96 inches

4. A circular pond has a radius of 12 meters. What's the perimeter distance around it?

Answer: C = 2 × 3.14 × 12 = 75.36 meters

5. A Ferris wheel has a diameter of 50 feet. One full rotation takes 30 seconds. How far do you travel in 1 minute?

Answer: C = 3.14 × 50 = 157 feet per rotation. Two rotations = 314 feet

Common Mistakes to Avoid

• Using the wrong value for π. 22/7 works for rough estimates but introduces error. Stick with 3.14 or the π function on your calculator.
• Confusing radius with diameter. The radius is half the diameter. Double-check which one you're given.
• Forgetting to square the radius. This mistake happens in area problems, not circumference, but mixing up formulas leads to wrong answers.
• Dropping units. Always include units in your answer. 50.24 means nothing without "cm" or "inches."

When to Use Each Formula

Use C = 2πr when the radius is given or easier to measure.

Use C = πd when the diameter is given. It's one step less calculation.

Both formulas give identical results. Pick whichever requires less work.

The Bottom Line

Circumference comes down to two formulas: C = 2πr and C = πd. Know your radius or diameter, plug it in, multiply by 3.14, and you're done.

No excuses for getting this wrong on a test.