Area of Circle
Calculate the area of a circle from its radius. Get instant results in square meters, square feet, and square yards, free online.
How to Use the Circle Area Calculator
- Enter the radius of the circle.
- Select the unit of measurement.
- View the area instantly in square meters, square feet, and square yards.
Features of the Circle Area Calculator
- Instantly calculates the area of a circle from its radius.
- Supports 10 units of measurement, from nanometers to miles.
- Shows results simultaneously in square meters, square feet, and square yards.
- Free to use with no sign-up required.
Circle Area Formula
The area of a circle is found by multiplying π (pi) by the square of its radius.
Circle Area (A) = π × r²
Where r is the radius, the distance from the center of the circle to its edge, and π ≈ 3.14159.
Circle Area Reference Table
| Radius (r) | Area (A = π × r²) |
|---|---|
| 0.5 | 0.7854 |
| 1 | 3.14159 |
| 2 | 12.56637 |
| 3 | 28.27433 |
| 5 | 78.53982 |
| 10 | 314.15927 |
How to Calculate the Area of a Circle
To find the area of a circle, square the radius and multiply the result by π.
Suppose you have a circle with a radius of 5. Area = π × 5² = π × 25 ≈ 78.53982.
Thus, the area of the circle is approximately 78.53982 square units.
Solved Examples on Circle Area
1. Area From a Whole-Number Radius
Example: Find the area of a circle with radius 10 meters.
Area = π × 10² = π × 100 ≈ 314.15927 m².
2. Area From a Decimal Radius
Example: Find the area of a circle with radius 0.5 meters.
Area = π × 0.5² = π × 0.25 ≈ 0.7854 m².
3. Converting Radius Units Before Calculating
Example: Find the area of a circle with radius 10 feet.
Area = π × 10² = π × 100 ≈ 314.15927 ft², which converts to approximately 29.18635 m².
4. Area From a Small Radius
Example: Find the area of a circle with radius 2 meters.
Area = π × 2² = π × 4 ≈ 12.56637 m².
1. What is the formula for the area of a circle?
The area of a circle is A = π × r², where r is the radius and π is approximately 3.14159.
2. How is circle area different from circle circumference?
Area measures the space enclosed within the circle, calculated as π × r², while circumference measures the distance around the circle’s edge, calculated as 2 × π × r. Area is expressed in square units; circumference is expressed in linear units.
3. How do I find the area if I only know the diameter?
Divide the diameter by 2 to get the radius, then apply the area formula. Alternatively, the area can be written directly in terms of diameter as A = π × (d/2)², or A = (π × d²) ÷ 4.
4. Why does doubling the radius quadruple the area?
Because the radius is squared in the area formula, doubling it multiplies the area by 2² = 4. For example, a circle with radius 2 has 4 times the area of a circle with radius 1 (12.56637 vs. 3.14159).
5. Can the radius be negative or zero?
No. A radius must be a positive number, since a negative or zero radius doesn’t correspond to a real circle with any enclosed area.
6. Where is circle area used in practice?
Circle area calculations are used in construction for round surfaces and pipes, in landscaping for circular garden beds, and in manufacturing for sizing circular parts and components.