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How to Calculate Relative Humidity from Absolute Humidity

Calculate Relative Humidity from Absolute Humidity - Formula, Example

Formula :
 Actual vapor density Relative Humidity = * 100% Saturation vapor density
Saturation vapor density :
 m M = * ps(t) V RT
Where,

m/V = density of water vapor, grams / ( cubic meters ) M = 18 grams/mol of water R = 0.0623665 mmHg x m3 / °C / mol T = 273.15 + Air Temperature ps = ps(t°C) = ( 0.61078 * 7.501 ) e ( 17.2694t / 238.3+t ) mmHg

Example:

Actual vapor density is 10 g/m3 at 20°C and find the saturation vapor density at that temperature and the relative humidity?

Given,

Air temperature= 20°C Actual vapor density= 10 g/m3

To Find,

Saturation vapor density Relative humidity

Solution:
Find ps value,
 ps = ( 0.61078 * 7.501 ) e ( 17.2694t / 238.3+t ) mmHg = (4.58146078)e(345.388)/(258.3) = (4.58146078)(2.718281828)1.337158343 = (4.58146078) * 3.808206498 = 17.4
Find m/V value,
 m/V = ( (18) / 0.0623665*(273.15+20) ) * 17.4 = ( (18) / 18.282739475 ) * 17.4 = 0.984535169 * 17.4 = 17.2
Find relative humidity :
 Actual vapor density Relative Humidity = * 100% Saturation vapor density = (10 / 17.2) * 100% = 0.581395349 * 100% = 58.13%