Report a Problem
Suggestions

# Calculate The Area Of An Elliptical Sector

Last updated: Saturday, June 24, 2023
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.
Hold & Drag
CLOSE
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
$$b$$
$$meter$$
Bookmark this page or risk going on a digital treasure hunt again