In aerospace engineering there are several definitions of altitude:
hg- geometric altitude : physical height above sea-level
ha- absolute altitude : height measured from center of earth
hgeo- geopotential altitude using variable g in the pressure height equation
where rE is the radius of the earth
hp- pressure altitude : height from the standard atmosphere table corresponding to the same value of pressure
: usually indicated by the mechanical altimeter
hT- temperature altitude : height from the standard atmosphere table corresponding to the same value of outside air temperature read on aircraft
= density altitude : height from standard atmosphere table corresponding to the same value of density (calculated using pressure and temperature reading along with the equation of state) - important for computing aerodynamic information at flight condition.