Circle questions come up everywhere — from geometry class to pizza orders to construction planning. Here are the most common questions, answered directly.
How do I find the area of a circle?
A = πr²
Multiply π by the radius squared.
| Radius | Area | |--------|------| | 1 | 3.14 | | 3 | 28.27 | | 5 | 78.54 | | 7 | 153.94 | | 10 | 314.16 | | 14 | 615.75 |
How do I find the circumference?
C = 2πr or C = πd
Use whichever is more convenient — if you know the diameter, use πd. If you know the radius, use 2πr.
What is pi (π)?
π is the ratio of circumference to diameter. Every circle, regardless of size, has C/d = π ≈ 3.14159.
Key facts:
- Irrational number (infinite, non-repeating decimal)
- Common approximations: 3.14, 22/7, 3.14159
- First 10 digits: 3.141592653
- NOT equal to 3.14 (that's an approximation)
How do I find the radius from the diameter?
r = d/2
The radius is always exactly half the diameter.
| Diameter | Radius | |----------|--------| | 4 | 2 | | 10 | 5 | | 14 | 7 | | 20 | 10 | | 28 | 14 |
How do I find the radius from the area?
r = √(A/π)
Take the area, divide by π, then take the square root.
Example: A = 78.54 → r = √(78.54/3.14159) = √25 = 5
How do I find the radius from the circumference?
r = C/(2π)
Example: C = 62.83 → r = 62.83/6.283 = 10
Common Circle Mistakes
| Mistake | Wrong | Right | |---------|-------|-------| | Using diameter in area formula | A = πd² | A = πr² = π(d/2)² | | Forgetting to square the radius | A = πr | A = πr² | | Confusing radius and diameter | r = d | r = d/2 | | Using 2πr for area | A = 2πr | C = 2πr, A = πr² |
The Trench Truth: The #1 circle mistake on exams: using the diameter instead of the radius in A = πr². If d = 10, the area is NOT π(100) = 314. It's π(25) = 78.54. Always halve the diameter first.
Related: Area Converter · Square Root Calculator · Derivative Calculator
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