<ol>
<li>Compute saturated vapor pressure, <span class="math-container">$e_{sat}$</span>, at <span class="math-container">$t_1$</span> and <span class="math-container">$t_2$</span>.  There are <a href="https://en.wikipedia.org/wiki/Vapour_pressure_of_water" rel="nofollow noreferrer">many approximations</a>; personally, I learned this one (where <span class="math-container">$e_{sat}$</span> is in kPa and <span class="math-container">$T$</span> is in Celsius):
<span class="math-container">$$ e_{sat}=0.611\exp\left(\frac{17.27T}{237.3+T}\right) $$</span></li>
<li>Vapor pressure <span class="math-container">$e = e_{sat}(t_1)\cdot r_1$</span></li>
<li>Expected relative humidity at <span class="math-container">$t_2$</span>, <span class="math-container">$\hat{r}_2 = \frac{e}{e_{sat}(t_2)} = r_1\frac{e_{sat}(t_1)}{e_{sat}(t_2)}$</span></li>
</ol>

CC BY-SA 4.0
2024-09-04T19:20:38.680Z
2024-09-04T19:20:38.680Z
damp_civil
<p>Consider this scenario: Two sensors are placed in a room to track temperature (in degrees Celsius) and relative humidity over time. The room's temperature varies throughout the day and so does the relative humidity (in general).</p>
<p>Given an earlier measurement of temperature <span class="math-container">$t_1$</span>, the corresponding relative humidity <span class="math-container">$r_1$</span>, and a current temperature <span class="math-container">$t_2$</span>, I would like to calculate (or at least approximate) the corresponding relative humidity <span class="math-container">$\hat{r}_2$</span> that would be measured, if nothing but the temperature changed (i.e. the absolute humidity and the atmospheric pressure are constant). With <span class="math-container">$\hat{r}_2$</span> at hand, I would compare it to <span class="math-container">$r_2$</span> to draw some conclusions (e.g. the absolute humidity or pressure must have changed if <span class="math-container">$\hat{r}_2 \neq r_2$</span>).</p>
<p>If it is necessary, or at least meaningful to also include values for atmospheric pressure <span class="math-container">$p_1, p_2$</span>, that would be OK for me.</p>
<p>To summarize: Is there a (closed form) function of <span class="math-container">$t_1, t_2$</span> and <span class="math-container">$r_1$</span>, to calculate/approximate <span class="math-container">$r_2$</span>? Alternatively, is there a function of <span class="math-container">$t_1, t_2, p_1, p_2$</span> and <span class="math-container">$r_1$</span> to calculate/approximate <span class="math-container">$r_2$</span>? I would assume yes, as <a href="https://en.wikipedia.org/wiki/Psychrometrics#Terminology" rel="nofollow noreferrer">psychrometric charts</a> seem to be almost the solution to my problem.</p>

<hydrology>
How to calculate relative humidity r2 in a room at temperature t2, if given a previous pair of temperature t1 and rel. humidity r1?
user3389669
# How to calculate relative humidity r2 in a room at temperature t2, if given a previous pair of temperature t1 and rel. humidity r1?

(Asked by: username_0 on 2024-09-04)

Consider this scenario: Two sensors are placed in a room to track temperature (in degrees Celsius) and relative humidity over time. The room's temperature varies throughout the day and so does the relative humidity (in general).

Given an earlier measurement of temperature $t\_1$, the corresponding relative humidity $r\_1$, and a current temperature $t\_2$, I would like to calculate (or at least approximate) the corresponding relative humidity $\hat{r}\_2$ that would be measured, if nothing but the temperature changed (i.e. the absolute humidity and the atmospheric pressure are constant). With $\hat{r}\_2$ at hand, I would compare it to $r\_2$ to draw some conclusions (e.g. the absolute humidity or pressure must have changed if $\hat{r}\_2 \neq r\_2$).

If it is necessary, or at least meaningful to also include values for atmospheric pressure $p\_1, p\_2$, that would be OK for me.

To summarize: Is there a (closed form) function of $t\_1, t\_2$ and $r\_1$, to calculate/approximate $r\_2$? Alternatively, is there a function of $t\_1, t\_2, p\_1, p\_2$ and $r\_1$ to calculate/approximate $r\_2$? I would assume yes, as [psychrometric charts](https://en.wikipedia.org/wiki/Psychrometrics#Terminology) seem to be almost the solution to my problem.

**Tags:** hydrology


---

## 1 answers

### Answer by username_1 on 2024-09-04. Score: 2 | Accepted answer

1. Compute saturated vapor pressure, $e\_{sat}$, at $t\_1$ and $t\_2$. There are [many approximations](https://en.wikipedia.org/wiki/Vapour_pressure_of_water); personally, I learned this one (where $e\_{sat}$ is in kPa and $T$ is in Celsius):
   $$ e\_{sat}=0.611\exp\left(\frac{17.27T}{237.3+T}\right) $$
2. Vapor pressure $e = e\_{sat}(t\_1)\cdot r\_1$
3. Expected relative humidity at $t\_2$, $\hat{r}\_2 = \frac{e}{e\_{sat}(t\_2)} = r\_1\frac{e\_{sat}(t\_1)}{e\_{sat}(t\_2)}$


---

