Circle Calculations- How to Find Radius from Circumference
What Is Radius and Why It Matters
The radius is the distance from the center of a circle to any point on its edge. It's half the diameter. That's it. No fancy definitions needed.
When you know the circumference, finding the radius is straightforward. You don't need to measure anything—just plug your number into a formula.
The Formula You Actually Need
Here it is:
Radius = Circumference ÷ (2 × π)
That's the whole thing. Circumference divided by 6.28318 (which is 2π). You can use 3.14159 for π if you want, but 2π is faster.
Step-by-Step: Finding Radius from Circumference
Method 1: Using π
Let's say your circumference is 31.4 units.
- Multiply π by 2 → 3.14159 × 2 = 6.28318
- Divide circumference by that number → 31.4 ÷ 6.28318
- Your answer is 5 units
That's it. Three steps. You can verify this: 2 × π × 5 = 31.4. It checks out.
Method 2: The Quick Approximation
If you don't need perfect precision, divide by 6.28 instead of 6.28318.
31.4 ÷ 6.28 = 5
Same answer. The difference only shows up in decimals, and most practical situations don't care about the fourth decimal place.
Real Examples
Example 1: Garden Fountain
Your circular fountain has a circumference of 15.7 feet. What's the radius?
15.7 ÷ 6.28 = 2.5 feet
Double it for diameter: 5 feet across.
Example 2: Pizza Pan
A pizza pan measures 37.7 inches around the edge. You need the radius for a recipe.
37.7 ÷ 6.28 = 6 inches
Your pan is 12 inches wide. Standard pizza size—makes sense.
Example 3: Tire
You measure a tire's circumference at 94.2 inches. What radius are you working with?
94.2 ÷ 6.28 = 15 inches
Radius of 15 inches means a 30-inch diameter. That's a large truck tire.
Quick Reference Table
| Circumference | Radius (using π = 3.14159) |
|---|---|
| 6.28 | 1.00 |
| 12.57 | 2.00 |
| 18.85 | 3.00 |
| 25.13 | 4.00 |
| 31.42 | 5.00 |
| 62.83 | 10.00 |
| 100 | 15.92 |
| 200 | 31.83 |
Common Mistakes That Waste Time
- Dividing by π instead of 2π. Some people see the circumference formula C = 2πr and panic. They solve for r and get r = C/π. That's wrong. r = C/(2π).
- Using diameter when radius is needed. If someone gives you the diameter, you don't need the circumference at all. Just halve it.
- Rounding too early. If you round π to 3.14 before dividing, you'll get small errors. Use the full value or divide by 6.28 instead.
When You'd Actually Use This
Construction: Cutting circular pieces to exact dimensions without measuring the center.
Engineering: Calculating wheel sizes when only the outer measurement is accessible.
Plumbing: Determining pipe radius from wrapped tape measurements.
Astronomy: Working with orbital distances when only the path length is known.
How to Get Started Right Now
Grab your circumference number.
Divide it by 6.28 (or 2π if you're being precise).
That's your radius.
If you're working with a calculator, just type: CIRCUMFERENCE ÷ 6.28318 = ANSWER
No need for anything else.
The Short Version
Radius = Circumference ÷ 6.28
That's the formula. That's the process. That's all you need to find radius from circumference.