Relative humidity is the wrong unit for this job
Outdoor air at 20°F and 70 percent relative humidity sounds damp. It holds about 10.5 grains of water per pound of dry air. Indoor air at 70°F and 35 percent relative humidity sounds dry. It holds about 38 grains. Bring the first inside and warm it up and its relative humidity collapses to single digits, because warming air raises how much moisture it could hold without adding any. The 27 grain gap between those two numbers is the entire problem, and no calculation phrased in relative humidity can see it.
Grains per pound is the absolute measure: 7,000 grains to a pound, so 38 grains per pound is a little over half a percent of the air weight. The mass balance is then simple. Air comes in at the outdoor moisture content, leaves at the indoor content, and the difference has to be supplied by something. Multiply the air mass flow by the grain difference and you have pounds of water per hour, which divides by 8.34 into gallons.
Working the numbers through
A 2,000 square foot house with 8.5 foot ceilings holds 17,000 cubic feet. At 0.35 air changes per hour that is 99 CFM of exchange. Air weighs about 0.075 pounds per cubic foot at standard conditions, so 99 CFM is 446 pounds of air per hour. At 27.5 grains per pound of deficit, that is 12,265 grains, or 1.75 pounds of water an hour, which is 42 pounds a day, which is about 5 gallons.
Five gallons a day is a useful thing to know, because it puts the portable-humidifier route into perspective: a tabletop unit with a gallon tank is being asked to be refilled five times a day to do this, and that is why it never keeps up with a whole house. It also shows why the air change rate matters more than anything else on the page. Halve the leakage and you halve the water.
| Condition | Grains per lb | Comment |
|---|---|---|
| 0°F, 70% RH | about 4 | Deep winter air is almost bone dry in absolute terms |
| 20°F, 70% RH | about 10 | Typical cold-climate design condition |
| 40°F, 70% RH | about 25 | The humidification requirement mostly disappears |
| 70°F, 35% RH | about 38 | A common indoor winter target |
| 70°F, 50% RH | about 55 | Comfortable, but hard to hold without condensation in cold weather |
The condensation limit, which is what actually caps the target
The instinct is to set the humidistat where the house feels best and leave it. The reason that goes wrong is that indoor air meets cold surfaces, and where the surface is below the dew point of the air touching it, water appears. In a house, the coldest surface is nearly always window glass, followed by the frame perimeter and any thermal bridge in the wall. Condensation on glass is visible and annoying. Condensation inside a wall assembly is neither, and it is the failure mode that matters.
The practical consequence is that the sustainable indoor humidity is not a fixed number, it falls as the outdoor temperature falls. A house that can carry 40 percent comfortably at 35°F outside may fog its windows at 40 percent when it drops to 5°F. Outdoor-reset humidistats exist precisely to walk the setpoint down as the weather gets colder, and running a fixed high setpoint through a cold snap is the usual way people discover their window frames were rotting.
Better windows raise the limit by raising the coldest surface temperature, and so does anything that reduces thermal bridging. That connects the humidity question to the envelope: the insulation calculator and the home insulation guide cover that side, and the heat loss calculator shows what those same surfaces cost you in heat.
Where the moisture is already coming from
Houses generate water. Cooking, showering, laundry, dishwashing, houseplants and the occupants themselves all add moisture, and in a small tight house occupied by several people the total is not negligible against the requirement calculated here. The gain field exists so you can subtract what you already produce; if you have no figure for it, leave it at zero and treat the result as the upper bound.
The corollary runs the other way too. If a house is genuinely damp in winter rather than dry, adding a humidifier is the wrong direction and the question becomes where the water is entering: a wet crawlspace, an unvented dryer, a bathroom fan that does not reach outside. The dehumidifier sizing calculator covers the removal side, and the same grain arithmetic drives it.
Rated capacity, run time and the ventilation interaction
A duct-mounted humidifier only humidifies when air is moving past it, so on a system that cycles, the unit has a fraction of the day to deliver a full day of water. That is why the rated capacity has to exceed the daily requirement rather than match it, and why the run-time field on this page divides rather than being cosmetic. Bypass and flow-through designs also depend on the air temperature and airflow across the pad, so the plate rating is measured at conditions your installation may not reproduce.
One structural point: mechanical ventilation and humidification pull against each other in winter. Every cubic foot of outdoor air brought in deliberately by an ERV or HRV is a cubic foot that has to be re-humidified, which is one of the arguments for an ERV over an HRV in a cold dry climate, since an ERV returns some of the moisture from the outgoing stream. Include the mechanical rate in the ACH field here rather than counting infiltration alone; the air changes calculator converts between the two units if you have one and need the other.
Finally, the maintenance point that decides whether any of this works: humidifiers that sit wet grow things. Pads, reservoirs and sumps need the cleaning schedule the manufacturer specifies, and a unit that is not maintained becomes a distribution system for whatever is living in it rather than a solution to dry air.
Questions people ask
What size whole-house humidifier do I need?
It follows from the air exchange rate and the grain difference, not from square footage alone, though square footage is what most sizing charts use. Work out the volume, multiply by the air change rate to get CFM, convert to pounds of air per hour at 0.075 pounds per cubic foot, and multiply by the grain deficit divided by 7,000 for pounds of water per hour. A leaky 2,000 square foot house in a cold climate can genuinely need several gallons a day; a tight one of the same size needs a fraction of that. Two houses of identical area can differ by a factor of three, and the difference is the leakage.
Why does the calculation use grains instead of relative humidity?
Because relative humidity depends on temperature and the quantity of water does not. Air at 20°F and 70 percent RH and air at 70°F and 12 percent RH hold roughly the same amount of water; the relative figures differ by a factor of six because the temperatures do. A humidifier adds a quantity of water, so the sizing has to be in a quantity unit. Grains per pound of dry air is the standard one and it comes straight out of the psychrometrics: it is the humidity ratio multiplied by 7,000.
What indoor humidity should I aim for in winter?
Lower than feels ideal, and lower as it gets colder outside. The comfort range people quote sits somewhere in the 30s to 40s in percent, but the ceiling in cold weather is set by condensation on the coldest surface in the house rather than by comfort. If your windows fog at the current setting, the setting is above what the house can carry and the water is being deposited somewhere. Walk it down until the fogging stops, and expect the sustainable figure to move with the weather. Anything that raises the coldest surface temperature, notably better glazing, raises the limit with it.
Will a portable humidifier do the job?
For one room, sometimes. For a house, the arithmetic answers it: if the calculation says five gallons a day, a unit with a one gallon tank needs filling five times a day, every day, all winter. Portables also humidify the room they are in and rely on air movement to distribute the result, which in a house with closed doors means the bedroom gets damp and the rest does not. The case for a duct-mounted unit is that it uses the distribution system that already exists and connects to a water supply so nobody carries jugs.
Does mechanical ventilation change the answer?
Directly and substantially. Any outdoor air the ventilation system brings in has to be humidified along with the infiltration, so the ACH figure entered here should include both. That is one of the practical arguments for an energy recovery ventilator over a heat recovery ventilator in a cold dry climate: an ERV transfers some moisture from the outgoing air back into the incoming stream, which reduces the load on the humidifier. It does not eliminate it, and the transfer efficiency is a rated figure that falls away from the rating conditions like every other one.