How much output does a humidifier need? Litres per day.

Short answer

A 15 x 12 ft room with an 8 ft ceiling held at 21 C and 40% relative humidity, with air leaking at 0.5 air changes per hour while it is -10 C and 70% outside, needs about 2.8 litres (0.73 US gallons, 5.9 pints) of water evaporated per day. This is an estimate: there is no published sizing standard, so the leakage rate is your assumption.

How it works, with a worked example

Leaking air carries your indoor water vapour out, and cold outdoor air brings in very little. The humidifier has to replace the difference. The tool computes the vapour content of indoor and outdoor air in kilograms per cubic metre, then: water per day = room volume x air changes per hour x 24 x (indoor vapour density - outdoor vapour density). One kilogram of water is one litre. Vapour pressure uses the National Weather Service form e = RH x 6.112 x exp[17.67T / (T + 243.5)] hPa, and vapour density is e / (R_v x T) with R_v = 461.495 J/(kg K).

Worked example. A 15 x 12 x 8 ft room is 1,440 ft3 (40.8 m3). At 21 C and 40% the air holds 7.32 g/m3 of vapour. Outdoors at -10 C and 70% it holds 1.65 g/m3. The difference is 5.67 g/m3. With 0.5 air changes per hour: 40.8 m3 x 0.5 x 24 x 5.67 g/m3 = about 2,775 g, or 2.8 litres per day (0.73 US gallons, 5.9 pints), about 116 mL per hour.

Limits. The result covers only the air leaking out of the room. Moisture absorbed by furniture and walls the first days, adjoining rooms and people or cooking adding vapour all shift the real figure. Humidifier labels quote output at test conditions. Pick a unit with some margin, and watch the windows: if they fog or drip, lower the target (see the window condensation tool).