The Magnus Formula, Explained Simply
Your weather app gives you temperature and relative humidity, and neither tells you what you actually want to know: how much water is in the air. One compact 19th-century formula bridges the gap — the Magnus formula. It fits on a sticky note, and it is the quiet engine behind every good ventilation decision.
What the formula computes
Warm air can hold far more water vapour than cold air, and the relationship is steeply nonlinear — capacity roughly doubles for every 10 °C or so of warming. The Magnus formula captures that curve. It gives you, for any temperature, the saturation vapour pressure: the maximum pressure water vapour can contribute before it starts condensing.
Why care about a pressure? Because relative humidity is defined against it. “60% RH” literally means: the actual vapour pressure is 60% of the saturation value at the current temperature. So once Magnus gives you the ceiling, RH tells you where under that ceiling you are — and from there, real water content is one step away.
The formula itself
Saturation vapour pressure in hectopascals, with temperature T in °C:
e_s(T) = 6.112 · exp( 17.62 · T / (243.12 + T) )It is an empirical fit — measured behaviour of water vapour compressed into one exponential — accurate to a fraction of a percent across everyday temperatures. Two more lines finish the job:
e = RH/100 · e_s(T) (actual vapour pressure, hPa)
AH = 216.68 · e / (T + 273.15) (absolute humidity, g/m³)The last line is the ideal gas law wearing work clothes: pressure divided by absolute temperature, scaled by a constant that rolls up the gas constant and the molar mass of water. Out comes the number that matters — grams of water per cubic metre of air.
One example, two air masses
Say it is a summer afternoon, 30 °C and 40% RH outside — “dry”, says the weather app. Meanwhile your cool cellar-facing room sits at 15 °C, and yesterday’s damp air in it reads 90% RH — “very humid”, says the hygrometer. Run both through Magnus:
| Air | T | RH | e_s | AH |
|---|---|---|---|---|
| Outside, afternoon | 30 °C | 40% | ~42.4 hPa | ~12.1 g/m³ |
| Cool room | 15 °C | 90% | ~17.0 hPa | ~11.5 g/m³ |
The “dry” afternoon air carries more water than the “very humid” cool room. Open the windows on the strength of that 40% and you import both heat and moisture. This is the afternoon dry-air trap in numeric form, and the reason relative humidity alone should never drive ventilation decisions.
What the formula unlocks
Once you can turn (T, RH) into g/m³, three practical tools fall out of it:
- A fair comparison. Indoor air versus outdoor air, in the same physical unit. Open when outside is cooler and holds less water; keep shut otherwise.
- The dew point. Run Magnus backwards — find the temperature whose saturation pressure equals the current vapour pressure — and you get the temperature at which this air’s water condenses. That single number explains misted windows and mouldy corners; see dew point, explained simply.
- Honest forecasts. Every hourly forecast of temperature and RH becomes an hourly forecast of water content, so you can spot tonight’s genuinely dry window before it arrives.
None of this requires a lab — just the three lines above and a weather feed.
Let the app watch for you
You could keep a spreadsheet of exponentials next to the window. Or let Open/Shut run the Magnus formula continuously on your local forecast and your home’s own readings, and simply tell you when the air outside is genuinely worth letting in.