Ellipse Perimeter Calculator
Enter the lengths of the semi-axes to calculate the approximate perimeter of the ellipse using Ramanujan's second approximation.
Semi-major axis (a)
Semi-minor axis (b)
Quick Examples
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Solved Examples
The following are examples of problems solved by the calculator.
Calculate the perimeter of the ellipse with semi-axes a = 5 and b = 3.
Result
The perimeter (circumference) of the ellipse is:
$$ P \approx 25.527 $$
This calculator uses the formula known as Ramanujan's second approximation. First, we calculate an auxiliary parameter h based on the semi-axes:
$$ h = \dfrac{(a-b)^2}{(a+b)^2} $$
Then, we apply the main perimeter formula:
$$ P \approx \pi (a+b) \left( 1 + \dfrac{3h}{10 + \sqrt{4 - 3h}} \right) $$
Visually verify that the proportions of the semi-axes match the oval in your problem.
Find the perimeter of the ellipse given a = 2.5 and b = 1.5
Result
The perimeter or circumference of the ellipse is:
$$ P \approx 12.7635 $$
Determine the perimeter of the ellipse given its semi-axes \(a = \sqrt{5}\) and \(b = \sqrt{3}.\)
Result
The perimeter of the oval is:
$$ P \approx 12.5165 $$
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