Quick and dirty transition from specific to relative humidity

Back to the retrieval of temperature/humidity profiles.
Our office forecasters are used to analyze humidity values as relative humidity, while IAPP algorithm retrieves specific humidity. Therefore conversion is needed.

Simple and quick way to do that:
Assume that we know temperature T (Celsiums), air pressure P (hPa) and specific humidity S (g/kg). These are actually the variables retrieved by IAPP. To calculate relative humidity f (%) we should know actual water vapor pressure e (hPa) and saturation water vapor pressure E (hPa).

Actual water vapor pressure e can be calculated as following:
e = S*P/622

Saturation pressure:
E = 6.107E(7.632*T/(241.9+T))

and finally relative humidity:
f = e/E*100

Voi la!
The equations were taken from A. Hrgian, "Physics of Atmosphere", 1978.