How to Calculate the Area of an Ellipse

Co-authored by David Jia

Last Updated: March 17, 2023 Fact Checked

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An ellipse is a two-dimensional shape that you might've discussed in geometry class that looks like a flat, elongated circle.^{[1]
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Research source} Calculating the area of an ellipse is easy when you know the measurements of the major radius and minor radius.

Part 1

Part 1 of 2:

Calculating the Area

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1
Find the major radius of the ellipse. This is the distance from the center of the ellipse to the farthest edge of the ellipse.^{[2]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021} Think of this as the radius of the "fat" part of the ellipse. Measure it or find it labeled in your diagram. We'll call this value a.
- You can call this the "semi-major axis" instead.^{[3]
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  Research source}
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Find the minor radius. As you might have guessed, the minor radius measures the distance from the center to the closest point on the edge.^{[4]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021}^{[5]
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Research source} Call this measurement b.
- This is at a 90º right angle to the major radius, but you don't need to measure any angles to solve this problem.
- You can call this the "semi-minor axis."
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Multiply by pi. The area of the ellipse is a x b x π.^{[6]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021} Since you're multiplying two units of length together, your answer will be in units squared.^{[7]
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Research source}
- For example, if an ellipse has a major radius of 5 units and a minor radius of 3 units, the area of the ellipse is 3 x 5 x π, or about 47 square units.
- If you don't have a calculator, or if your calculator doesn't have a π symbol, use "3.14" instead.

Part 2

Part 2 of 2:

Understanding Why it Works

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You might remember that the area of a circle equals πr², which is the same as π x r x r. What if we tried to find the area of a circle as though it were an ellipse? We would measure the radius in one direction: r. Measure it at right angles: also r. Plug it into the ellipse area formula: π x r x r! As it turns out, a circle is just a specific type of ellipse.^{[8]
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Imagine a circle being squeezed into an ellipse shape. As it's squeezed more and more, one radius gets shorter and the other gets longer.^{[9]
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Research source} The area stays the same, since nothing's leaving the circle. As long as we use both radii in our equation, the "squashing" and the "flattening" will cancel each other out, and we'll still have the right answer.

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How do I find A and B of an ellipse?

David Jia
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David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

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Expert Answer

To find A, measure from the center of the ellipse to the longest edge. For B, find the length from the center to the shortest edge.

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How do I calculate a half ellipse area?

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Since we know the area of an ellipse is πab, area of half the ellipse will be (πab)/2

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What is a 3-dimensional ellipse called?

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A 3-dimensional ellipse is called an "ellipsoid."

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