The circumference is the perimeter of a circle. It tells you how far a wheel travels in one turn, how long a round fence or table edge is, and how to size a ring or belt.
How to use the Circumference Calculator
- Radius r
- Every result field is editable: type into Circumference or any other result and Radius r plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter the radius or type into the diameter, circumference or area field.
Tips
- Radius is half the diameter – double-check which one you measured.
- Keep π exact until the end, or use at least 3.14159.
- Arc length and sector area need the central angle in radians in the formulas.
- Type any result to work backwards to the radius.
Common mistakes to avoid
- Using the diameter in a formula that needs the radius.
- Forgetting to square the radius when finding the area.
- Using degrees in s = rθ, which needs radians.
What each result means
- Circumference = 2×pi×[Radius r]
- Diameter = 2×[Radius r]
- Area = pi×[Radius r]^2
- Circumference in terms of π = 2×[Radius r]
Example values
How the main result changes when Radius r changes and everything else stays at the example values above:
| Radius r (cm) | Circumference (cm) |
|---|---|
| 2.5 | 15.708 |
| 3.75 | 23.5619 |
| 5 | 31.4159 |
| 6.25 | 39.2699 |
| 7.5 | 47.1239 |
| 10 | 62.8319 |
Formula
C = 2πr = πd = 2√(πA)Worked example
Inputs — Radius r: 5 cm.
Results — Circumference = 31.415927 cm; Diameter = 10 cm; Area = 78.539816 cm²; Circumference in terms of π = 10 π.
Key terms
- Circumference
- The distance around a circle.
Frequently asked questions
How far does a 70 cm wheel travel per turn?
π × 70 ≈ 219.9 cm.
How do I measure circumference?
Wrap a string or tape around the object.
What is circumference ÷ diameter?
Always π.
Is circumference the same as perimeter?
Yes, for a circle.
What formula does the Circumference Calculator use?
C = 2πr = πd = 2√(πA).