# How Does a Barometer Work?

Level 3 (with higher mathematics)
A simple barometer works by using the barometer formula, which relates the height $$h$$ above the ground to the air pressure $$\mathit{\Pi}$$ prevailing at that height:
Here $$H ~=~ 8005 \, \mathrm{m}$$ and the mean air pressure at sea level is $$\mathit{\Pi}_0 = 101 \, \mathrm{kPa} = 1 \, \mathrm{bar}$$. The formula states that the air pressure decreases exponentially with increasing height $$h$$.
So an barometer measures the air pressure $$\mathit{\Pi}$$ and calculates from it the height at which this air pressure prevails: