Sector Area Calculator
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Sector area formula explained
A sector is the region inside a circle bounded by two radii and the arc between them. The area formula is A = ½ × r² × θ, where θ is measured in radians. This calculator lets you enter the angle in degrees and handles the conversion.
Sector area is useful for pie charts, circular gardens, fan-shaped pieces, pizza slices, rotating parts, and geometry problems involving part of a circle.
Worked example: radius 10 cm, angle 90°
90° = 1.5708 radians
A = ½ × 10² × 1.5708
Result: 78.5398 cm²
Degree shortcut
Another way to think about sector area is as a fraction of the full circle: A = (angle ÷ 360) × πr². A 90° sector is one quarter of the circle.
Common mistakes
- Using degrees directly in the radian formula without conversion.
- Confusing a sector with a segment. A segment is bounded by a chord and an arc.
- Entering an angle greater than 360° for a single sector.
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Step-by-step method
- Measure the radius.
- Measure the central angle.
- Convert the angle from degrees to radians, or let the calculator do it.
- Use half times radius squared times the radian angle.
Second example: radius 6 ft, angle 120°
120° = 2.0944 radians.
A = ½ × 6² × 2.0944
Result: 37.6991 ft²
Practical interpretation
A sector calculation is useful when only part of a circle is needed. A semicircle is a 180° sector, a quarter circle is a 90° sector, and a full circle is a 360° sector. The calculator gives the exact mathematical slice based on the radius and angle.
For real-world objects such as curved patios or fan-shaped panels, measure from the center point of the circle. If the outer edge is not part of a true circle, the sector formula becomes an estimate.
How to calculate this measurement
A sector is a slice of a circle. Its area depends on the radius and the central angle. The calculator accepts degrees and converts the angle to radians for the formula.