# How to calculate relative humidity from specific humidity and temperature?

If I know specific humidity and temperature at a location, can I calculate relative humidity using these two?

• check the answers here – engineer Jul 17 '15 at 5:41
• Thank you @engineer.. But how about the pressure? Because I don't have known pressure, but I have a SLP at that location. Can I use it? – Kay Jul 17 '15 at 6:14
• Quick advice: In English, only the first word of a sentence and proper nouns are capitalized. – DanielSank Jul 17 '15 at 7:22
• There are dozens of tables and applet calculators available via a simple Google search. – Carl Witthoft Jul 17 '15 at 13:21

## 1 Answer

From Psychrometry in Refrigeration & Air Conditioning

Let $t_d$ be D.B.T. (dry bulb temperature) & $t_w$ be W.B.T. (wet bulb temperature) and $p_s$ & $p_w$ are saturation pressures at D.B.T. & W.B.T. respectively (refer to "Steam Table" for saturation pressures at given temperatures) then using Carrrier's Equation, the partial pressure ($p_v$) of water vapor is given as $$p_v=p_w-\frac{(p_b-p_w)(t_d-t_w)}{1544-1.44t_w}\tag 1$$ Where, $p_b$ is barometric pressure

Now, use the formula for given specific humidity say $W$ given as $$W=0.622 \left(\frac{p_v}{p_b-p_v}\right)$$ $$\implies p_b=\frac{0.622p_v}{W}+p_v$$ Substitute the value of $p_b$ in the eq(1) to get the value of $p_v$ Then apply the formula of $\color{blue}{\text{Relative Humidity}\ \phi}$ as follows $$\color{blue}{\phi=\frac{p_v}{p_s}}$$

Where, $p_v$ (partial pressure) & $p_s$ (saturation pressure at D.B.T.) are known.