The first calculator converts relative humidity to absolute humidity for a given temperature and barometric pressure. The next calculator does the opposite – converts absolute humidity to relative humidity for a given temperature and barometric pressure. Some theory and formulas are below the calculator.
First, it is hepful to define relative and absolute humidity. To follow, are a couple of definitions, taken from the Australian bureau of meteorology
Relative humidity (RH)
The ratio of the actual amount of water vapor in the air to the amount it could hold when saturated expressed as a percentage, or the ratio of the actual vapor pressure to the saturation vapor pressure expressed as a percentage.
Absolute humidity (AH)
The mass of water vapor in a unit volume of air. It is a measure of the actual water vapor content of the air.
Thanks to the World Meteorological Organization, we can find saturation vapor pressure given the temperature and atmospheric pressure (read more at Saturation vapour pressure)
From the relative humidity and saturation vapor pressure we can find the actual vapor pressure.
Then we can use the general law of perfect gases
In our case this is
where R is the universal gas constant defined as 8313.6, and Rv is the specific gas constant for water vapor defined as 461.5
Thus we can express mass to volume ratio as
which is absolute humidity.
So, for 25 degrees centigrade and 60% relativy humidity, one cubic meter of moist air contains about 14 grams of water, which corresponds to conversion table values I've found before.