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Math

Area of a Sector Calculator.

Calculates the area of a sector of a circle given the radius and the central angle in degrees or radians.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Measure the radius of the circle.

  2. 2

    Measure the central angle of the sector in degrees.

  3. 3

    Square the radius and multiply by pi.

  4. 4

    Multiply by the angle and divide by 360 to get the area.

(pi * radius^2 * angle) / 360

Frequently asked questions

What if the angle is given in radians?

Convert radians to degrees by multiplying by 180/pi, then use the calculator.

Can the angle be greater than 360 degrees?

The calculator allows up to 360 degrees, but for angles beyond 360, the sector would overlap; the formula still works mathematically.

What units should I use for radius?

Any unit of length (e.g., cm, m, inches). The area will be in square units of that length.

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Results

Formula checked

Sector Area

13.09sq units

Arc Length5.24units
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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the area of a sector of a circle given the radius and the central angle in degrees or radians.

  1. Measure the radius of the circle.
  2. Measure the central angle of the sector in degrees.
  3. Square the radius and multiply by pi.
  4. Multiply by the angle and divide by 360 to get the area.

Formulas

The math behind this calculator, written out so you can verify the result.

Area of a Sector

A = (θ/360) × π × r²

The area of a sector is a fraction of the circle's area, proportional to the central angle θ out of 360°.

Example:

Input: r = 5, θ = 60°

Calculation: (60/360) × π × 5² = (1/6) × π × 25

Result: ≈ 13.09 square units

Real-world use cases

Where this calculation shows up in everyday life.

Pizza slice size

Find the area of a slice of pizza given its radius and the angle at the tip.

Example: A 12-inch pizza cut into 8 slices: each slice has angle 45°, area ≈ 14.14 sq in.

Land measurement

Calculate the area of a pie-shaped plot of land.

Example: A plot with radius 100 m and angle 30° has area ≈ 2618 m².

Design and fabrication

Determine material needed for a sector-shaped piece.

Example: A metal sheet sector with radius 2 m and angle 90° requires ≈ 3.14 m².

Tips and common mistakes

Tips

  • Ensure the angle is in degrees; if it's in radians, convert first.
  • Use consistent units for radius and area.
  • For a full circle (angle=360°), the formula gives πr², the circle's area.
  • Round the result to a reasonable number of decimal places for practical use.

Common Mistakes to Avoid

  • Forgetting to convert radians to degrees.
  • Using diameter instead of radius.
  • Not dividing by 360 when using degrees.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.