Circle Sector Area

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Circle Sector Area Calculation:

  •  r =

    Radius of the circle

  •  θ =

    Angle of the sector in degrees

  •  A =

    Area of the sector in square units

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Circle Sector Area Formula

The sector of a circle is like a slice of pizza or pie. Its area can be calculated using the radius of the circle and angle of the sector, denoted by the Greek letter theta (θ). In this formula theta is measured in degrees, if theta is given in radians the second formula is used.

A = θ / 360 * πr2

Formula for calculating area of a sector given radians:

A = (θ / 2) * r2

Sector Area Formula
Area of a Sector Formula

Circle Sector Area Variables

To find the area of a sector two variables are needed, radius and angle.

Radius (r)
Radius of the circle. Measured from the center to the circumference.
Angle (θ)
Angle of the sector denoted by the Greek letter theta (θ).
Area (A)
Area of the sector in square units.

Circle Sector Area Solution

How do we find the area of the sector of a circle? Using a radius of 5 and an angle of 30 degrees the steps below will illustrate how the area of the sector is found.

  • A = θ / 360 * πr2
  • Start with the formula for sector area given angle in degrees
  • A = 30 / 360 * π52
  • Substitute in the known values
  • A = 30 / 360 * π25
  • Calculate the power
  • A = 0.0833 * π25
  • Calculate division
  • A = 0.0833 * 3.14159 * 25
  • Use a value of 3.14159 for π
  • A = 6.542361175
  • Calculate all the final multiplication
  • ~6.54 square units

A sector with a radius of 5 and angle of 30 degrees has an area of about 6.54 square units.

Circle Sector Area Example

What is the area of a sector with a radius of 8 inches and an angle of 1.57 radians?

  • A = (θ / 2) * r2
  • A = (1.57 / 2) * 82
  • A = (1.57 / 2) * 64
  • A = (0.785) * 64
  • 50.24

A sector with a radius of 8 inches and angle of 1.57 radians will have an area of 50.24 square inches. In square centimetres the area would be about 324.13 cm2 found using the square inches to square centimetres calculator.

Just wanted the area of a circle?

Circle area

Sector Area Formula