# Perimeter of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

## Perimeter of an Ellipse

The formula is an approximation that is about 5% of the true value as long as "a" is no more than 3 times longer than "b".

### Perimeter of an Ellipse formula

$$p \approx 2\pi \sqrt { \frac{1}{2} \left(a^2 + b^2 \right) }$$          $$perimeter \;\approx\; 2 \;\;x\;\; Pi \; \sqrt { \; \frac{1}{2} \; \left( \; axis \; a^2 \;+\; axis \; b^2 \; \right) }$$

Where:

$$p$$ = perimeter

$$a$$ = length semi-major axis

$$b$$ = length semi-minor axis

$$\pi$$ = Pi