Area of a Circle Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the area of a circle?
Answer
Area of a circle
A = π · r²
Here r is the radius. The result comes out in square units.
Where the formula comes from
A = π · r²
Cut the disc into many thin wedges and lay them alternately point-up and point-down: they comb together into something that gets closer and closer to a rectangle as the wedges get thinner. Its height is the radius r, and its base is half the circumference, πr. Multiply them and you have πr².
Worked examples
Let r = 5. Then the area of a circle ≈ 78.54 square units.
Let r = 3.2. Then the area of a circle ≈ 32.17 square units.
The common mistake
Putting the diameter where the radius belongs. It makes the answer four times too big, because the radius is squared: a circle 10 across has area π·5², not π·10². Halve the diameter first.
Other quantities: Circle
Found an error in the calculation or the information?
Related Calculations
- Circumference of a Circle Formula
- Diameter of a Circle Formula
- Area of a Rectangle Formula
- Area of a Square Formula
- Area of a Triangle Formula
- Area of a Trapezoid Formula
- Area of a Parallelogram Formula
- Area of a Rhombus Formula
- Area of a Hexagon Formula
- Area of a Regular Polygon Formula
- Area of a Circular Sector Formula
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula
| If r = | Area |
|---|---|
| 1 | ≈ 3.14 square units |
| 2 | ≈ 12.57 square units |
| 3 | ≈ 28.27 square units |
| 4 | ≈ 50.27 square units |
| 5 | ≈ 78.54 square units |
| 10 | ≈ 314.16 square units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a circle? (The answer is: A = π · r²). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter