Public Information Notice howrelativehumidityworksyajerk.org

Notice No. 100/RH · posted for the attention of all occupants

How relative
humidity works,
ya jerk

Issued in response to one passing remark that a building was freezing cold and also at 100 % humidity, as though these were two separate grievances. They are one grievance. Arguably zero.

Complaints received
1
Complainants
1
Original remark
One line. Typed once. In passing.
Severity as assessed by complainant
Mild. Conversational.
Measures taken
Domain registered. Notice drafted. Chart commissioned.
Proportionality review
Waived

Section 1 — Summary of findings

Relative humidity is a percentage, and you have forgotten what it is a percentage of.

The ceiling

Warm air can hold far more water vapour than cold air.

Not marginally more. Roughly double for every 10 °C. This ceiling is set by temperature alone and it moves whether you want it to or not.

The ratio

Relative humidity reports how full that ceiling is — not how much water is present.

100 % means "this air is holding everything it can at this temperature." In a cold building, everything it can is close to nothing.

Therefore

Cold at 100 % is a small glass, filled. Warm at 40 % is a large glass, sipped.

The large glass usually contains more water. Heating a room does not dry it out by removing moisture — it dries it out by enlarging the glass.

Section 2 — Demonstration

The chart your building engineer has been staring at this whole time.

Set the temperature and the humidity reading you are so upset about. The point plots itself on the psychrometric chart below. Then heat the air and watch the point travel horizontally — same water, rising ceiling, collapsing percentage.

Psychrometric chart · sea level Fig. 1
Saturated
condensing
Water actually present 9.4g/m³
Dew point 10.0°C
Reading after heating 49%
Determination

Section 3 — The part that ends the argument

A freezing room at 100 % is drier than a pleasant room at 30 %.

0 °C / 32 °F  at  100 % RH

4.8g/m³

"It is unbelievably humid in here."

21 °C / 70 °F  at  30 % RH

5.5g/m³

"It is so dry my lips are cracking."

Same building. Same air, even. The room everybody calls swampy contains measurably less water than the room everybody calls bone dry. The instrument was honest with you. You read it wrong.

Section 4 — In fairness to the complainant

You were wrong about the physics and right about the building.

All of this — the domain, the chart, the appendices — exists because one person mentioned once that they were cold. Honesty requires conceding that their complaint had something real buried in it. Splitting the difference:

Dismissed

That 100 % RH means the air is heavy with water.

In a cold building it means close to the opposite. There is very little vapour in that air; it simply has nowhere left to put more. Warm it up and the identical air reads 40 % or less. No water left the room. The ceiling rose.

Dismissed

That "cold" and "humid" are two independent problems.

They are one problem wearing two hats. The cold is why it reads 100 %. Fix the temperature and the humidity figure fixes itself — a deeply unsatisfying thing to be told while shivering, which is why this notice is annoying.

Upheld

That 100 % RH indoors is genuinely alarming.

It means the dew point has caught up with the air temperature, so every surface at or below room temperature is actively condensing. That is not a comfort complaint, it is a mould-and-rot complaint. A building sitting at saturation has moisture getting in, no ventilation, or both.

Upheld

That it feels awful.

Cold damp air pulls heat out of a person far faster than cold dry air, and perspiration has nowhere to evaporate to. "Cold and clammy" is a real sensation with real physics behind it. It is simply not the physics you cited.

The remedy, for the record, is heat and ventilation: warm the air so it can carry the moisture, then exchange it with outside air so the moisture actually leaves the building. A dehumidifier in a cold room is fighting uphill — it is trying to wring out a glass that was barely full to begin with.

Section 5 — Appendices

Receipts, for the pedants among you.

Every figure on this page is computed live from the Magnus–Tetens approximation for saturation vapour pressure over liquid water, accurate to a fraction of a percent between −40 and 50 °C. That comfortably covers your office.

Appendix A — The formulas
Saturation vapour pressure, hPa — this is "the ceiling"
es(T) = 6.112 · exp( 17.67·T / (T + 243.5) )

Actual vapour pressure, hPa — RH is literally this ratio
e = (RH / 100) · es(T)

Absolute humidity, grams of water per cubic metre of air
AH = 216.7 · e / (T + 273.15)

Dew point, °C
γ  = ln(RH/100) + 17.67·T / (T + 243.5)
Td = 243.5·γ / (17.67 − γ)

Heating the same air from T₁ to T₂ — e is unchanged, es climbs
RH₂ = RH₁ · es(T₁) / es(T₂)
Why heating collapses the percentage
Heating air adds no water and removes none, so e holds still while es runs away. Relative humidity is e/es. Numerator constant, denominator rising, percentage falling. On the chart above this is the horizontal arrow, and it is the entire trick.
Where 216.7 comes from
It is 100 / Rv, where Rv = 461.5 J·kg⁻¹·K⁻¹ is the specific gas constant for water vapour — the unit bookkeeping that converts a pressure in hectopascals into grams per cubic metre.
Appendix B — A correction to this notice itself

Section 1 told you that warm air "holds" more water, like a sponge. That is a lie told to schoolchildren, and this notice repeated it because it is a useful lie.

Air is not a container and nitrogen is doing you no favours. What actually sets the ceiling is water's own vapour pressure at that temperature — evaporation and condensation reaching equilibrium. You would measure the same numbers in a vacuum. Keep the sponge if it helps you argue in Slack; just don't specify an HVAC system with it.

Section 6 — Distribution

Deploy responsibly.

Best delivered in a thread, with no preamble, roughly four minutes after somebody says the thing. Do not explain it. Do not add a winking emoji. The domain is doing the work.