Area of a ellipse calculator
Enter the dimensions of a ellipse and read off its area, its perimeter and the quantities that follow from them.
Area
75.398 224m²
- Perimeter
- 31.730 875
- Eccentricity
- 0.745 355 99
- Distance between the foci
- 8.944 271 9
Show the working
- Semi-major axis = 6
- Semi-minor axis = 4
- Area = pi * 6 * 4 = 75.3982
- Perimeter = pi * (3*(6+4) - sqrt((3*6 + 4)*(6 + 3*4))) = 31.7309
- Eccentricity = 6 >= 4 && 6 > 0 ? sqrt(1 - 4^2/6^2) : 0 = 0.745 356
- Distance between the foci = 6 >= 4 ? 2*sqrt(6^2 - 4^2) : 0 = 8.944 27
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- area = pi a b
- perimeter = pi (3(a+b) - sqrt((3a+b)(a+3b))), Ramanujan's second approximation
- eccentricity = sqrt(1 - b^2/a^2)
The perimeter of an ellipse has no elementary closed form. Ramanujan approximation used here is accurate to better than one part in ten million for eccentricities up to about 0.9.
Lengths are entered in metres by default; switch any field to feet, inches or millimetres and the conversion is exact.