First calculator converts relative humidity to absolute humidity for given temperature and barometric pressure. Next calculator does the opposite - converts absolute humidity to relative humidity for given temperature and barometric pressure. Some theory and formulas are below the calculator.
First, couple of definitions, taken from Australian bureau of meteorology
Relative humidity (RH)
The ratio of the actual amount of water vapour in the air to the amount it could hold when saturated expressed as a percentage or the ratio of the actual vapour pressure to the saturation vapour pressure expressed as a percentage.
The mass of water vapour in a unit volume of air. It is a measure of the actual water vapour content of the air.
Thanks to World Meteorological Organization we can find saturation vapour pressure given the temperature and atmospheric pressure (read more at Saturation vapour pressure)
From relative humidity and saturation vapour pressure we can find actual vapour pressure.
Then we can use the general law of perfect gases
In our case this is
where R is universal gas constant equals to 8313.6, and Rv - specific gas constant for water vapour equals to 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.