How to Calculate the Area of ​​an Ellipse: 5 Steps

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How to Calculate the Area of ​​an Ellipse: 5 Steps
How to Calculate the Area of ​​an Ellipse: 5 Steps

The equation for the area of ​​an ellipse will look familiar if you've studied circles before. The most important thing to remember is that the ellipse has two important measurements that we need to measure, the larger radius and the smaller radius.


Part 1 of 2: Calculating the area

Calculate the Area of ​​an Ellipse Step 1

Step 1. Find the largest radius of the ellipse

It will be the distance from the center of the ellipse to the farthest point from it. Think of this measurement as the size of the "fat" part of the ellipse. Measure this distance if there is no diagram showing this length. We will call this value The.

You can also call this radius a semi-major axis

Calculate the Area of ​​an Ellipse Step 2

Step 2. Find the smallest radius

As you might have guessed, the smallest radius measures the distance between the center of the ellipse and the point closest to it. We will call this measure B.

  • This radius makes an angle of 90º with the larger radius, but it is not necessary to do operations with angles to solve the problem.
  • We can also call it "semi-minor axis".
Calculate the Area of ​​an Ellipse Step 3

Step 3. Multiply by pi

The ellipse area is The x B x π. Since you are multiplying two units of measure, the answer will be in square units.

  • For example, if an ellipse has a smaller radius of 3 units and a larger radius of 5 units, the area will be equal to 3 x 5 x π, which is approximately 47 square units.
  • If you don't have a calculator or yours doesn't have the symbol "π", consider its value as "3.14".

Part 2 of 2: Understanding Why the Method Works

Calculate the Area of ​​an Ellipse Step 4

Step 1. Think about the area of ​​a circle

You must remember that the area of ​​a circle is equal to π x r x r. What if we tried to find the area of ​​a circle as if it were an ellipse? We would measure the radius in one direction, getting r. Then, we would rotate 90º and measure the radius again, obtaining r again. Applying the formula, we get: π x r x r! As we can see, a circle is just a particular case of an ellipse.

Calculate the Area of ​​an Ellipse Step 5

Step 2. Imagine a circle being squeezed

It will take the shape of an ellipse. As it gets squeezed more and more, one of the spokes gets bigger while the other gets smaller. However, the area remains the same as nothing is coming out of the circle. Considering the two radii used in our equation, the one being squeezed will decrease as the one being stretched grows, meaning they cancel each other out and the area doesn't change.


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