What is the area of a circle?
Type the radius or the diameter to get the area of the circle, or type the area to get the radius back.
- Diameter
- 10 in
A circle of radius 5 in (diameter 10 in) has an area of 78.54 in².
- Area
- 78.54 in²
Diameter: 10 in. A circle of radius 5 in (diameter 10 in) has an area of 78.54 in².
How to calculate
Finds the area of a circle from its radius or diameter (A = πr²), or the radius and diameter from the area.
Example with the default inputs (Radius 5 in): A circle of radius 5 in (diameter 10 in) has an area of 78.54 in².
Formula: A = πr², where r is the radius; with the diameter d = 2r, A = πd² ÷ 4.
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- The radius and diameter are in the length unit shown next to them, and the area is in the square unit shown next to it.
- Each value must be greater than 0.
Worked examples
Each example is checked against the calculator on every build.
- Radius 196.9 in gives Area 121,737 in², Diameter 393.7 in.Source: hand calculation in content.mdx: A = π × 5² = 25π = 78.5398
- Diameter 551.2 in gives Area 238,604 in², Radius 275.6 in.Source: hand calculation in content.mdx: r = 7, A = π × 7² = 49π = 153.9380
- Area 155,000 in² gives Radius 222.1 in, Diameter 444.2 in.Source: hand calculation in content.mdx: r = √(100 ÷ π) = 5.6419
How it works
The area A of a circle is the space inside it. With radius r (the distance from the centre to the edge):
A = πr²
The diameter is d = 2r, so the same area is A = πd² ÷ 4.
Type any one value and the calculator finds the other two:
- from the radius: A = πr² and d = 2r
- from the diameter: r = d ÷ 2, then A = πr²
- from the area: r = √(A ÷ π) and d = 2r
Assumptions
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Each value is greater than 0.
- Each box has its own unit. Lengths are converted through metres and areas through square metres (1 in = 0.0254 m exactly). In one unit the numbers match: a radius of 5 in gives 78.54 in², and a radius of 5 m gives 78.54 m².
Worked examples by hand
Radius 5. A = π × 5² = 25π = 78.5398, and d = 2 × 5 = 10.
Diameter 14. r = 14 ÷ 2 = 7, so A = π × 7² = 49π = 153.9380.
Area 100. r = √(100 ÷ π) = √31.8310 = 5.6419, and d = 2 × 5.6419 = 11.2838.
Other questions people ask
What is the formula for the area of a circle?
A = πr², where r is the radius. Square the radius first, then multiply by π. A radius of 5 cm gives 25 × 3.14159 = 78.54 cm².
How do I find the area from the diameter?
Halve the diameter to get the radius, then use A = πr². In one step, A = πd² ÷ 4. A 14 in pizza has an area of π × 7² = 153.94 in².
How do I find the radius from the area?
Divide the area by π, then take the square root: r = √(A ÷ π). An area of 100 m² gives r = √31.831 = 5.64 m.
Why does a 16 in pizza have more than twice the area of an 11 in pizza?
Area grows with the square of the size. A 16 in pizza has an area of π × 8² = 201 in², and an 11 in pizza has π × 5.5² = 95 in², so the larger one is about 2.1 times as much pizza.
What units is the area in?
Square units: if the radius is in inches, the area is in square inches (in²). Each box has its own unit switch, so you can type the radius in feet and read the area in square metres.
Is the area the same as πd?
No. πd is the circumference, the distance around the circle. The area is πr², the space inside it. They have different units: a length and a square length.