How to Calculate the Area of an Ellipse

In 2D geometry, the ellipse looks like a long, flattened circle. It is very easy to calculate the area of an ellipse if you know the lengths of the major and minor axes.

Table of Contents

The area

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Calculate the length of the major axis of the ellipse. This is the distance from the center to the furthest point on the edge of the ellipse. You can think of this as the radius of the “flat” part of the ellipse. Measure or mark on the picture. We call this value a .

You can also call this value “semi-major axis”. ^{[1] X Research Source}

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Find the length of the minor axis. It’s not hard to guess, the minor axis is the distance from the center to the nearest point on the edge of the ellipse. ^{[2] X Research Source} This value is denoted by b .

This axis is perpendicular to the major axis, but you don’t need to calculate any angles to find the area.
You might call this “semi-baby shaft.”

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Multiply by pi. The area of the ellipse will be equal to a x b x π. Since you are multiplying two lengths, the final answer will be in squared units. ^{[3] X Research Sources}

For example, if the ellipse has a major axis with a length of 5 mm and a minor axis with a length of 3 mm, the area will be equal to 3 x 5 x π or 47 mm ² .
If you don’t have a calculator or a calculator without the π symbol, replace it with “3.14”.

Prove the formula for the area of an ellipse

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Remember the formula for calculating the area of a circle. The area of a circle is equal to π r ² or π x r x r . Try to calculate the area of the circle using the formula of the ellipse. Measure the radius of the circle, we have: r . Continue to measure another radius at an angle of 90º from the previous radius, still r . When we substitute the formula for the area of an ellipse, we get: π xrxr! So the circle is a special ellipse with the major and minor axes equal. ^{[4] X Research Sources}

Advice

If you want to rigorously prove the formula for the area of an ellipse, you need to use the integral operator calculus. ^{[5] X Research Sources}

Steps

The area

Prove the formula for the area of an ellipse

Advice

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