Circumference is the distance around a circle — its perimeter. Whether you're fencing a circular garden, calculating how far a wheel travels in one rotation, or finding pipe length, circumference is the formula you need.
The Formula
C = 2πr or C = πd
Two forms, same result. Use whichever is more convenient.
| Known Value | Use This Form | |------------|--------------| | Radius | C = 2πr | | Diameter | C = πd | | Area | r = √(A/π), then C = 2πr |
Step-by-Step Examples
Example 1: r = 5 cm
C = 2π(5) = 10π ≈ 31.42 cm
Example 2: d = 28 m
C = π(28) = 28π ≈ 87.96 m
Example 3: A = 78.54 sq m
- r = √(78.54/π) = √25 = 5
- C = 2π(5) = 31.42 m
Real-World Applications
Wheel Travel Distance
A car tire has diameter 60 cm. How far does the car travel per rotation?
C = π(60) = 188.5 cm = 1.885 m per rotation
At 1000 rotations: 1,885 m = 1.885 km
Fencing a Circular Garden
Garden radius 7m. How much fencing?
C = 2π(7) = 43.98 m of fencing
At ₹150/m: 43.98 × 150 = ₹6,597
Pipe Length for Circular Tank
Tank circumference = 12m. What's the diameter?
d = C/π = 12/3.14159 = 3.82 m
Running Track (Circular)
Standard 400m track (inner lane):
- C = 400m → r = 400/(2π) = 63.66 m
- Area enclosed = π(63.66²) = 12,732 sq m
Circumference Quick Reference
| Radius | Circumference | Diameter | Circumference | |--------|--------------|----------|--------------| | 1 | 6.28 | 2 | 6.28 | | 3 | 18.85 | 6 | 18.85 | | 5 | 31.42 | 10 | 31.42 | | 7 | 43.98 | 14 | 43.98 | | 10 | 62.83 | 20 | 62.83 | | 14 | 87.96 | 28 | 87.96 | | 50 | 314.16 | 100 | 314.16 |
The Relationship: C = πd Is the Definition of π
π is literally defined as circumference divided by diameter:
π = C/d
This ratio is the same for EVERY circle, regardless of size. That's what makes π a universal constant.
The Trench Truth: When a problem gives you the diameter, use C = πd directly — don't waste time dividing by 2 to get the radius and then multiplying by 2 again in 2πr. C = πd is one step instead of three. Work smarter.
Calculate circumference instantly with our circle calculator.
Related: Area Converter · Square Root Calculator · Derivative Calculator
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