How to Compute the Length of an Ellipse

A porthole is an example of an ellipse.

An ellipse is a curved line that forms a closed loop but has two points where the sum of the distance from any point on the line to those points is always constant. When you look at an ellipse it might remind you of a circle that has been flattened, because two ends of it extend outward or upward. To calculate the length, or circumference, of an ellipse you will need to know the width of the long axis and the length of the short axis.

Things You'll Need

• Calculator

Instructions

1. Square your long axis width and short axis length. For example, an ellipse has a long axis of 10 inches and a short axis of 8 inches. When you square both, your result is 100 inches and 64 inches, respectively.

2. Add together your two results from Step 1 and divide by 2. In this example, you would add together 100 and 64 to get a result of 164. Dividing that result by 2, you would get 82.

3. Take the square root of your result in Step 2. In this example, you would take the square root of 82; your result would be approximately 9.06.

4. Multiply your result from Step 3 by pi, which is approximately 3.14. In this example, you would multiply 9.06 by 3.14, and you would get a result of 28.45.

5. Multiply your result from Step 4 by 2. In this example, you would multiply 28.45 by 2; your result would be 56.9. The length of the ellipse is approximately 56.9 inches.

References

• Math Open Reference: Ellipse
• Approximate Circumference of an Ellipse