Area of a Circle Calculator
Calculate the area, circumference, and diameter of a circle from its radius, diameter, or circumference. See also Area of Ellipse Calculator and Area of Sector Calculator.
How to Calculate the Area of a Circle
To find the area of a circle, measure the radius — the distance from the center to any point on the edge. Square the radius and multiply by π (pi ≈ 3.14159). If you know the diameter instead, divide it by 2 to get the radius first. If you know the circumference, divide by 2π to find the radius. This calculator handles all three input types automatically.
Circle Area Formula
A = π × r²
A = π × (d/2)² = π × d² / 4
A = C² / (4π)
Circumference: C = 2πr
Diameter: d = 2r
Example
Find the area of a circle with radius 5:
A = π × r²
A = π × 5²
A = π × 25
A ≈ 78.5398 square units
Circle Area Conversion Table
| Radius | Area | Circumference | Diameter |
|---|---|---|---|
| 1 | 3.1416 | 6.2832 | 2 |
| 2 | 12.5664 | 12.5664 | 4 |
| 3 | 28.2743 | 18.8496 | 6 |
| 4 | 50.2655 | 25.1327 | 8 |
| 5 | 78.5398 | 31.4159 | 10 |
| 6 | 113.0973 | 37.6991 | 12 |
| 7 | 153.9380 | 43.9823 | 14 |
| 8 | 201.0619 | 50.2655 | 16 |
| 9 | 254.4690 | 56.5487 | 18 |
| 10 | 314.1593 | 62.8319 | 20 |
| 15 | 706.8583 | 94.2478 | 30 |
| 20 | 1256.6371 | 125.6637 | 40 |
| 25 | 1963.4954 | 157.0796 | 50 |
| 50 | 7853.9816 | 314.1593 | 100 |
| 100 | 31415.9265 | 628.3185 | 200 |
Solved Examples: Area of a Circle
Example 1: Finding the Area of a 12-Inch Pizza
A pizza has a diameter of 12 inches. How much surface area does the pizza have?
Diameter = 12 inches, so radius = 12 ÷ 2 = 6 inches
A = π × r²
A = 3.14159 × 6²
A = 3.14159 × 36
A ≈ 113.10 square inches
Example 2: Circular Garden with Known Radius
You want to plant flowers in a circular garden bed with a radius of 4 meters. How much soil do you need to cover the area?
r = 4 meters
A = π × r²
A = 3.14159 × 4²
A = 3.14159 × 16
A ≈ 50.27 square meters
Example 3: Round Table Cover
A round dining table has a circumference of 3.77 meters. What is its area?
C = 3.77 m, so r = C ÷ (2π) = 3.77 ÷ 6.28318 ≈ 0.60 m
A = π × r²
A = 3.14159 × 0.60²
A = 3.14159 × 0.36
A ≈ 1.13 square meters
Example 4: Circular Swimming Pool Cover
A circular swimming pool has a diameter of 7.5 meters. What area of pool cover material is needed?
Diameter = 7.5 m, so radius = 7.5 ÷ 2 = 3.75 m
A = π × r²
A = 3.14159 × 3.75²
A = 3.14159 × 14.0625
A ≈ 44.18 square meters
Practice Questions
1. A circular clock face has a radius of 15 cm. What is its area?
Answer: A = π × 15² = 706.86 cm²
2. A manhole cover has a diameter of 60 cm. Find the area.
Answer: r = 30 cm, A = π × 30² = 2,827.43 cm²
3. A circular fountain has an area of 28.27 m². What is its radius?
Answer: r = √(A/π) = √(28.27/3.14159) = √9 = 3 meters
4. A circular rug has a circumference of 9.42 meters. What is its area?
Answer: r = 9.42/(2π) = 1.5 m, A = π × 1.5² = 7.07 m²
5. Two pizzas: one 16-inch diameter, one 12-inch diameter. Which has more total area?
Answer: 16": A = π × 8² = 201.06 in²; 12": A = π × 6² = 113.10 in². The 16-inch pizza is 77.8% larger.
6. A sprinkler waters in a circular pattern with radius 5.5 meters. What area does it cover?
Answer: A = π × 5.5² = π × 30.25 = 95.03 m²
Common Mistakes When Calculating Circle Area
Using the diameter instead of the radius
The formula is A = πr², not A = πd². If given the diameter, divide by 2 first. Using 10 instead of 5 gives you 4× the correct answer.
Forgetting to square the radius
A = πr² means π times r squared. Writing A = πr (without squaring) gives you the semi-circumference, not the area.
Confusing circumference with area
Circumference (C = 2πr) measures distance around the circle in linear units. Area (A = πr²) measures the space inside in square units.
Using π = 3 or rounding too early
Using 3 instead of 3.14159 introduces ~4.5% error. Always use at least π ≈ 3.14159 and only round the final answer.
Key Takeaways
- The area of a circle is A = πr², where r is the radius (half the diameter).
- If you know the diameter, use A = πd²/4. If you know the circumference, use A = C²/(4π).
- Doubling the radius quadruples the area (because area grows with the square of the radius).
- Area is always in square units — if the radius is in cm, the area is in cm².
- A 12-inch pizza has 113 sq inches but a 16-inch pizza has 201 sq inches — nearly double the food for 33% more diameter.
- Use π ≈ 3.14159 for calculations; only round at the very end to avoid compounding errors.
Frequently Asked Questions
What is the area of a circle?
The area of a circle is the total space enclosed within its boundary (circumference). It is measured in square units and calculated using the formula A = πr², where r is the radius.
How do I find the area if I only know the diameter?
Divide the diameter by 2 to get the radius, then use A = πr². Alternatively, use A = πd²/4 directly. For example, a circle with diameter 10 has area = π × 25 ≈ 78.54.
What is the value of π (pi)?
Pi (π) is approximately 3.14159265358979. It is the ratio of a circle's circumference to its diameter and is an irrational number — its decimal representation never ends or repeats.
Can I calculate the area from the circumference?
Yes. From the circumference C, find the radius as r = C/(2π), then compute A = πr². This simplifies to A = C²/(4π).
What units is the area in?
The area is in square units of whatever unit the radius is in. If the radius is in centimeters, the area is in square centimeters (cm²). If in meters, the area is in square meters (m²).