Report a Problem
Suggestions

# Calculate The Perimeter Of An Ellipse

Last updated: Saturday, April 29, 2023
Select an approximation formula below
Naïve Formula
Euler's Formula
Kepler's Formula
Peano's Formula
Ramanujan Formula 1
Ramanujan Formula 2

The perimeter of an ellipse is a bit more complex than that of a circle. It cannot be expressed using a simple formula like that of the circle's circumference. However, there are several approximate formulas that can be used to estimate the perimeter of an ellipse, depending on the desired level of accuracy.

This calculator uses the Naive Formula, while this formula is relatively simple, it is only an approximation and may not be accurate for highly eccentric ellipses. In those cases, more advanced methods may be required to calculate the perimeter. Nonetheless, the naive formula can be a useful tool for estimating the perimeter of an ellipse in many practical applications.

The Naive Formula is one of the many approximation formulas used for determining the perimeter of an ellipse, it has a relative error of approximately -21.5%.
$$P$$ $$=$$ $$\pi$$ $$\cdot$$ $$(a$$ $$+$$ $$b)$$
$$P$$: 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.
Hold & Drag
CLOSE
the length of the major axis
$$a$$
$$meter$$
the length of the minor axis
$$b$$
$$meter$$
$$\pi$$ : A mathematical constant with an infinite decimal tail