Area of a Circular Sector Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the area of a circular sector?
Answer
Area of a circular sector
A = (deg / 360) · π · r²
Here r is the radius, deg is the angle in degrees. The result comes out in square units.
Where the formula comes from
A = (deg / 360) · π · r²
A sector is a slice of the disc, and the slice takes the same fraction of the area as its angle takes of the full turn. A quarter of 360° is a quarter of πr².
Worked examples
Let r = 6, deg = 90. Then the area of a circular sector ≈ 28.27 square units.
Let r = 4.5, deg = 120. Then the area of a circular sector ≈ 21.21 square units.
The common mistake
Feeding radians into a formula written for degrees. If the angle is given in radians the fraction is θ/2π, not θ/360, and the two differ by a factor of about 57.
Found an error in the calculation or the information?
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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 (deg = 90)
| If r = | Area |
|---|---|
| 1 | ≈ 0.79 square units |
| 2 | ≈ 3.14 square units |
| 3 | ≈ 7.07 square units |
| 4 | ≈ 12.57 square units |
| 5 | ≈ 19.63 square units |
| 10 | ≈ 78.54 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 circular sector? (The answer is: A = (deg / 360) · π · r²). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter