Relative Humidity is measured using a device called a sling psychrometer. This consists of 2 side by side conventional thermometers, one of which (the wet bulb thermometer) has a wetted wick placed at the bottom, the other (the dry bulb thermometer) has no wetted wick.
When the psychrometer is swung around by its attached chain or handle, the air causes the water on the wick to evaporate which produces a lower temperature in the wet bulb thermometer. We now have a dry bulb and a wet bulb temperature which we can use to calculate relative humidity. The easiest way to do this is entering the dry and wet bulb temperatures into the calculator above and then click calculate. For example, if we have a dry bulb temperature of 20℃ and a wet bulb temperature of 15℃ what is the relative humidity? Using the calculator, we see that this is 58.4 %.

Now, let’s try using the above equation. (The equation is so complex, for ease of use, it has been split into 3 parts.)

We have
dry bulb temp (T_d) = 20℃ and wet bulb temp (T_w) = 15℃
What is the relative humidity?

Solving for e_d
e_d= 6.112 ✱ 2.71828^{(17.502 ✱ 20 ➗ 240.97 ✚ 20)}

e_d= 6.112 ✱ 2.71828^{(350.04 ➗ 260.97)}

e_d= 6.112 ✱ 2.71828^(1.3413)

e_d= 6.112 ✱ 3.8240

e_d= 23.372

Solving for e_w
e_w= 6.112 ✱ 2.71828^{(17.502 ✱ 15 ➗ 240.97 ✚ 15)}

e_w= 6.112 ✱ 2.71828^{(262.53 ➗ 255.97)}

e_w= 6.112 ✱ 2.71828^(1.0256)

e_w= 6.112 ✱ 2.7888

e_w= 17.045

Solving for relative humidity
rh = ([e_w ➖ .66875 ✱ (1 ✚ .00115 ✱ T_w) ✱ (T_d ➖ T_w)]➗ e_d) ✱100

rh = ([17.045 ➖ .66875 ✱ (1 ✚ .00115 ✱ 15) ✱ (20 ➖ 15)] ➗ 23.372) ✱100

rh = [17.045 ➖ .66875 ✱ 1.01725 ✱ 5] ➗ .23372

rh = [17.045 ➖3.4014] ➗ .23372

rh = 58.376

rh = 58.4%

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