The forecast says the humidity is 90%. Ninety percent of what? Relative humidity compares the vapor in the air with the saturation amount at the air's current temperature. Because saturation depends so strongly on temperature, relative humidity can change all day while the amount of vapor stays the same.
Key idea
$$\text{RH} = \frac{e}{e_s(T)} \times 100\%$$ where $e$ is the vapor pressure and $e_s(T)$ is the saturation vapor pressure at the air temperature $T$. At 100% the air is saturated.
Why it works
The top of the fraction is the vapor that is really there. The bottom is the saturation amount, which grows fast when the air warms. Warm the air and the bottom grows, so RH falls, even though not one molecule of vapor left. Cool the air and RH rises. That is why RH is usually highest around dawn, the coolest time of day, and lowest in mid-afternoon.
| Temperature | 0 °C | 5 °C | 10 °C | 15 °C | 20 °C | 25 °C | 30 °C | 35 °C |
|---|---|---|---|---|---|---|---|---|
| $e_s$ (hPa) | 6.1 | 8.7 | 12.3 | 17.0 | 23.4 | 31.7 | 42.5 | 56.3 |
Worked example: Finding RH
Air at 25 °C has a vapor pressure of 15.9 hPa. What is its relative humidity?
- Saturation at 25 °C: $e_s = 31.7$ hPa.
- RH = $15.9 \div 31.7 \times 100\% \approx 50\%$.
Answer: About 50%
Worked example: Which air has more vapor?
A cold morning: 5 °C and 100% RH. A desert afternoon: 35 °C and 20% RH. Which air holds more water vapor?
- Cold morning: $e = 1.00 \times 8.7 = 8.7$ hPa.
- Desert afternoon: $e = 0.20 \times 56.3 \approx 11.3$ hPa.
- The "dry" desert air has about 30% more vapor than the "saturated" morning air.
Answer: The desert air
Worked example: Same air, warmer
Saturated air at 10 °C (RH 100%) warms to 25 °C without gaining or losing vapor. What is its new RH?
- The vapor stays at $e = 12.3$ hPa (saturation at 10 °C).
- At 25 °C, $e_s = 31.7$ hPa, so RH = $12.3 \div 31.7 \approx 39\%$.
Answer: About 39%
Common mistake
Reading high relative humidity as "lots of water vapor." RH is a ratio, and its bottom changes with temperature. A cold morning at 100% can have less vapor than a hot desert afternoon at 20%. Check: multiply RH by $e_s$ at each temperature before comparing two places or times.
Heating cold air dries it out in relative terms. Outdoor air at 0 °C and 80% RH has $e \approx 4.9$ hPa. Heated to 21 °C indoors, where $e_s \approx 24.9$ hPa, its RH drops to about 20%, which is why indoor air feels so dry in winter.