Circumference Calculator
FAQs
- What is the circumference of a circle?
- The circumference is the distance around the outside of a circle — its perimeter. For a circle with radius r, the circumference equals 2πr.
- What is the formula for circumference?
- C = 2πr (using radius) or C = πd (using diameter). Both give the same result because diameter is exactly twice the radius.
- How do I find the circumference if I know the area?
- First derive the radius from the area: r = √(A/π). Then plug into C = 2πr. This calculator does both steps for you.
- Why does π appear in every formula?
- π is defined as the ratio of any circle's circumference to its diameter — about 3.14159. Because every circle scales the same way, π shows up whenever you connect a circle's radius/diameter to its perimeter or area.
- Can I enter the diameter instead of the radius?
- Yes — pick any one of the four quantities (radius, diameter, circumference, area) and the other three update automatically.
- What's the difference between circumference and area?
- Circumference is a length (the boundary), measured in linear units like centimetres. Area is a surface, measured in square units like cm². For a circle of radius r, C = 2πr and A = πr².
What is circumference?
The circumference of a circle is the distance around its outside — its perimeter. It is one of the most fundamental measurements in geometry, used everywhere from engineering and architecture to manufacturing and astronomy. For any circle, the ratio of its circumference to its diameter is the mathematical constant π (pi), approximately 3.14159.
Circumference formula
C = 2πr (using radius)
C = πd (using diameter)
Both formulas give the same answer because diameter is exactly twice the radius: d = 2r.
Worked example
A circle with radius 5 cm has a circumference of:
C = 2π × 5 = 10π ≈ 31.4159 cm
And an area of:
A = π × 5² = 25π ≈ 78.5398 cm²
All four circle quantities
| Quantity | Symbol | Formula |
|---|---|---|
| Radius | r | r = d ÷ 2 = C ÷ (2π) = √(A÷π) |
| Diameter | d | d = 2r = C ÷ π |
| Circumference | C | C = 2πr = πd |
| Area | A | A = πr² = π(d÷2)² = C² ÷ (4π) |
How to use this calculator
- Enter any one of the four values: radius, diameter, circumference, or area.
- Pick the unit you're using (mm, cm, m, in, ft, etc.).
- The other three quantities update automatically — that's it.
Common mistakes
- Confusing radius and diameter. Radius is from the centre to the edge; diameter is the full width across. Diameter is always twice the radius.
- Forgetting to square the radius for area. Area uses r², not r — a circle with radius 10 has an area 4× larger than one with radius 5, not 2×.
- Mixing linear and square units. Circumference is in cm; area is in cm². The calculator labels the area unit with a small ² so you don't lose track.
- Treating π as exactly 3.14. Fine for rough estimates, but the calculator uses the full Math.PI precision (≈ 3.141592653589793).
For non-circular shapes (ellipses, ovals, irregular curves) this calculator does not apply — you'll need a different tool. For the path length of an arc (a portion of a circle), use the Arc Length calculator.