Sector Area Calculator

Calculate the area of a circle sector with half the angle times radius squared. Includes degrees and radians, a worked example, and pizza-slice mental math.

Calculate area of sector

Formula

\\text{area} = \\\\frac{\\\\theta}{360} \\\\times \\\\pi r^2

Where r is the radius and θ is the central angle in degrees.

Worked example

Calculate the area of a sector with radius 10 cm and angle 60°:

\\text{area} = \\\\frac{60}{360} \\\\times \\\\pi \\\\times 10^2 = \\\\frac{1}{6} \\\\times \\\\pi \\\\times 100 \\\\approx \\\\frac{314.16}{6} = 52.36 \\\\text{ cm}^2

Result: 52.36 cm²

How to use

Enter the radius of the circle
Enter the central angle in degrees (0-360)
Click "Calculate" to see the sector area

Related formulas

Arc length: $\\\\frac{\\\\theta}{360} \\\\times 2\\\\pi r$
Perimeter: Add arc length plus two radii
Fraction of circle: θ/360 gives the proportion

Common use cases

Pizza slice area calculations
Land sector measurements
Engineering sector cuts
Graphics and design applications

FAQ

What if the angle is 360°? The sector becomes a full circle with area $\\\\pi r^2$ .

Can I use radians? Enter the angle in degrees. To convert radians: degrees = radians × 180/π.

What if I know the arc length? First find radius: r = arc length × 360 / (2π × θ), then use the formula.

How is this different from a segment? A sector includes the center point; a segment is the area between a chord and the arc.

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