How to Find Radius from Circumference- Math Tutorial
The Formula You Actually Need
Finding radius from circumference is straightforward. No tricks, no complicated steps. Just one simple formula:
Radius = Circumference ÷ (2 × π)
That's it. If you know the circumference, you can find the radius in seconds.
Why This Works
The circumference of a circle is the distance around it. The relationship between circumference and radius is fixed:
Circumference = 2πr
So to reverse it and solve for r:
r = Circumference ÷ 2π
Using 3.14 for π, that's roughly dividing by 6.28. Using the more precise π value, that's dividing by 6.28318.
Step-by-Step Process
Here's how to actually do it:
- Write down your circumference value
- Multiply π by 2 (or just use 6.28 as your divisor)
- Divide the circumference by that number
- That's your radius
Real Examples
Example 1: Simple Calculation
Your circle has a circumference of 31.4 units.
31.4 ÷ 6.28 = 5
The radius is 5 units. ✓
Example 2: Using the Exact Formula
Circumference = 20π
Radius = 20π ÷ 2π
Radius = 10
When your circumference is given in terms of π, the π cancels out completely.
Example 3: Word Problem
A circular garden has a fence that measures exactly 44 feet. What's the radius of the garden?
44 ÷ 6.28 ≈ 7.01
Radius ≈ 7 feet
Quick Reference Table
| Circumference | Radius (using π = 3.14) |
|---|---|
| 6.28 | 1 |
| 12.56 | 2 |
| 18.84 | 3 |
| 31.4 | 5 |
| 62.8 | 10 |
| 100 | 15.92 |
| 200 | 31.85 |
Common Mistakes to Avoid
- Forgetting to divide by 2 — Some people divide by π alone. Wrong. You need to divide by 2π.
- Using wrong π approximation — 3.14 works fine. Don't overthink it unless your teacher specifies otherwise.
- Units confusion — If circumference is in inches, radius is in inches. Same units, no conversion needed.
How to Get Started
Pick a circumference value. Any value. Now apply the formula:
Radius = Circumference ÷ 6.28
Try these practice problems:
- C = 15.7 → r = ?
- C = 94.2 → r = ?
- C = 50 → r = ?
Answers: 2.5, 15, 7.96
That's all there is to it. Plug in the number, divide, done. No fluff needed.