The area of a circle is π times the radius squared. You need it to size pizza (a 16-inch pizza has 78% more area than a 12-inch one), to buy circular rugs or turf, to find pipe cross-sections and to work out the pressure on a piston.
How to use the Area of a Circle Calculator
- Radius r
- Every result field is editable: type into Area or any other result and Radius r plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter the radius or type into the diameter or circumference field. Changing the area field finds the radius that gives that area.
What each result means
- Area = pi×[Radius r]^2
- Diameter = 2×[Radius r]
- Circumference = 2×pi×[Radius r]
- Area in terms of π (number × π) = [Radius r]^2
Example values
How the main result changes when Radius r changes and everything else stays at the example values above:
| Radius r (cm) | Area (cm²) |
|---|---|
| 2.5 | 19.635 |
| 3.75 | 44.1786 |
| 5 | 78.5398 |
| 6.25 | 122.7185 |
| 7.5 | 176.7146 |
| 10 | 314.1593 |
Formula
A = πr² = πd²/4 = C²/(4π)
Worked example
Inputs — Radius r: 5 cm.
Results — Area = 78.539816 cm²; Diameter = 10 cm; Circumference = 31.415927 cm; Area in terms of π (number × π) = 25 π.
Key terms
- Area
- The space inside the circle.
Frequently asked questions
What is the area of a circle with a 10 cm diameter?
π × 5² ≈ 78.54 cm².
Why πr²?
Cutting a circle into thin wedges and rearranging them gives a near-rectangle of sides πr and r.
How do I find the radius from the area?
r = √(A/π).
Which is bigger: one 16" pizza or two 10" pizzas?
One 16" (201 in²) beats two 10" (157 in²).