Select an approximation formula below
The Ramanujan formula is a mathematical formula for approximating the perimeter of an ellipse, named after the famous Indian mathematician Srinivasa Ramanujan. It is given by:
P ≈ π(a + b) [ 3 - √(3a+b) - √(a+3b) ]
where P is the perimeter of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
The Ramanujan formula provides a good approximation of the perimeter of an ellipse, with an error of less than 0.5% for most practical purposes. It is particularly useful for hand calculations and other situations where more exact methods may be impractical or time-consuming.
Some real-life applications of the perimeter of an ellipse include calculating the perimeter of racetracks, the outer boundaries of satellite orbits, and the perimeters of curved architectural features such as arches and domes.
The first Ramanujan formula used for determining the perimeter of an ellipse
\(P\): 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
