An ellipse is a two-dimensional shape that looks like a flat circle. The equation for finding the area of an ellipse will be familiar to you if you have studied circles before. The most important thing to remember is that an ellipse has two important lengths that you must measure: the major radius and the minor radius.
Part 1 of 2: Calculate the area
Step 1. Find the largest radius of the ellipse
This is the distance from the center of the ellipse to the farthest edge of the ellipse. Think of this as the radius of the "fat" part of the ellipse. Measure it or find the measurement on your diagram. We will call this measure, value to.
You can also call it "semi-major axis"
Step 2. Find the minor radius
As you probably already realized, the smallest radius measures the distance from the center to the closest point on the edge. We will call this measure, value b.
- The smaller radius is 90º from the larger radius, but you don't have to measure the angle to solve this problem.
- You can also call it "semi minor axis".
Step 3. Multiply it all by pi
The area of an ellipse is to x b x π. Since you are multiplying two units of length, your answer will be in square units.
- For example, if an ellipse has a radius greater than 3 units and a radius less than 5 units, the area of the ellipse is 3 x 5 x π, or approximately 47 square units.
- If you don't have a calculator or if your calculator doesn't have the symbol for π, use "3.14".
Part 2 of 2: Understand how it works
Step 1. Think about the area of a circle
Remember that the area of a circle is equal to π r2, which is equal to π x r x r. What if we try to find the area of a circle as if it were an ellipse? We must measure the radius in one direction: r. Measure it at a right angle: which is also r. Enter those dimensions into the formula for the area of the ellipse: π x r x r. With this we realize a circle is a specific type of ellipse.
Step 2. Imagine a circle being squashed
Imagine a circle being squashed so that it looks like an ellipse. As you squash it more and more, one radius will get smaller while the other gets longer. The area remains the same, since nothing leaves the circle. As long as you use both radii in the equation, the "squash" or "flatten" the circle cancel each other out and you will still get the correct answer.