In order to calculate the area and perimeter of an ellipse, you must first know the length of the ellipse’s semi-major axis (half the longest distance possible from one side of the ellipse to the other-cutting through the ellipse lengthwise) and the length of the semi-minor axis (half the shortest distance possible from one side of the ellipse to the other). Once you know these lengths, also sometimes referred to as the “radii” of the ellipse, you can calculate the area and perimeter with simple mathematical operations.
Square the ellipse’s semi-major and semi-minor axes, then add them together. So, if our ellipse has a semi-major axis of length 5 and a semi-minor axis of length 3, we have 5 squared = 25 plus 3 squared = 9 for a total of 34.
Divide the result from Step 1 by 2. To continue our example, we have 34 / 2 = 17.
Take the square root of the result from Step 2. How exact you must be in this calculation will vary depending on what the answer will be used for. In our example, we round to two decimal points, giving us Sqrt(17)=4.12.
Multiply the result from Step 3 by 2, which to continue our example gives us 4.12 * 2 = 8.24. Finally, multiply this result by pi to find the perimeter of the ellipse. It’s usually acceptable to estimate pi as 3.14. To conclude our example, 8.24 * 3.14 = 25.87
If the equation for the ellipse is in standard form, (x squared/A squared) + (y squared / B squared) = 1, you can easily identify the semi-major and semi-minor axes of the ellipse. They are A and B, with the smaller of the two being the semi-minor axis and the larger number representing the semi-major axis.
Multiply the length of the ellipse’s semi-major axis by the length of the semi-minor axis. So, if the ellipse has a semi-major axis of length 5 and a semi-minor axis of length 3, the result is 15.
Multiply the result from Step 1 by pi, or 3.14. To continue our example, we have 15 * 3.14 = 47.1.
Note the final result is the ellipse’s area in units squared. If the semi-major and semi-minor axes in our example ellipse were measured in inches, our answer would be 47.1 inches squared. If we don’t know what unit of measurement was used, you can simply note “units squared” and leave it at that.
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