Select an approximation formula below
Euler's formula provides a more accurate calculation of the perimeter of an ellipse compared to the naive formula, which assumes the ellipse is a circle and results in a larger error as the eccentricity of the ellipse increases.
Calculating the perimeter of an ellipse is important in various fields such as engineering and architecture, where ellipses are used to model curved surfaces and shapes. For example, the perimeter of an ellipse can be used to calculate the amount of fencing needed to enclose a curved area or the amount of material needed to construct an elliptical arch.
Euler's formula is one of the many approximation formulas used for determining the perimeter of an ellipse. Its relative error is approximately +11%
\(P\): the perimeter of the ellipse
\(a\): the length of the major axis
\(b\): the length of the minor axis
\(\pi\): A mathematical constant with an infinite decimal tail
The SI unit of perimeter is \(meter\text{ }(m)\)
Find \(P\)
Use this calculator to determine the perimeter of an ellipse when both lengths of the minor and major axis are given.
the length of the major axis
the length of the minor axis
\(\pi\) : A mathematical constant with an infinite decimal tail
