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Calculate The Area Of An Elliptical Sector

Last updated: Saturday, June 24, 2023
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Select a type of sector below
Circular Sector
Elliptical Sector

The area of a sector is the portion of a circle enclosed by two radii and an arc. It is a useful concept in fields such as geometry, physics, and engineering. For example, in civil engineering, the area of a sector can be used to calculate the amount of land needed for a circular parking lot or a roundabout. In physics, the area of a sector can be used to calculate the amount of solar energy received by a solar panel, which is proportional to the area of the panel facing the sun. Additionally, the area of a sector is used in various calculations involving circles and angles.

The formula for determining the area of an elliptical sector is defined as:
\(A\) \(=\) \(\int_{\theta_1}^{\theta_2} \dfrac{a^2 \cdot b^2}{2 \cdot (b^2 \cdot cos^2(\theta) + a^2 \cdot sin^2(\theta))}d\theta\)
\(A\): the area of the sector
\(\theta_1\): The angle of between the a axis and the first leg of the sector.
\(\theta_2\): The angle of between the a axis and the second leg of the sector.
\(a\): the length of axis a
\(b\): the length of the axis b
The SI unit of area is: \(square \text{ } meter\text{ }(m^2)\)

Find \(A\)

Use this calculator to determine the area of an elliptical sector using the lengths of the axes and the angles.
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The angle of between the a axis and the first leg of the sector.
\(\theta_1\)
\(degree\)
The angle of between the a axis and the second leg of the sector.
\(\theta_2\)
\(degree\)
the length of axis a
\(a\)
\(meter\)
the length of the axis b
\(b\)
\(meter\)
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