How to use the indoor humidity from outdoor air calculator
- Pick Fahrenheit or Celsius and enter the outdoor temperature and outdoor relative humidity.
- Enter the indoor temperature, the temperature the outside air is warmed or cooled to.
- Optionally enter the humidity you want indoors. The page then finds the water to add per kilogram of dry air.
- In the advanced options add the room volume to turn that into a total amount of water for the room.
Formula
Saturation vapor pressure es(T) = 0.6112 x exp(17.62 T / (243.12 + T)) kPa, with T in degrees C
Indoor RH = outdoor RH x es(outdoor temperature) / es(indoor temperature)
Moisture = 0.622 x e / (101.325 - e) kg of water per kg of dry air
Water to add = moisture at the target - moisture in the air now
Heating air does not change how much water vapor it holds, so the vapor pressure stays the same. Warm air can hold more, so the relative humidity falls. The page uses standard sea level pressure.
A cold winter day
Outdoor air at 23 F (-5 C) and 80 percent humidity has a vapor pressure of 0.33775 kPa and holds 2.0803 g of water per kg of dry air. Warmed to 68 F (20 C), it has a relative humidity of only 14.479 percent, and its dew point is still 17.75 F.
To reach 40 percent at 68 F the air needs 3.7006 g more water per kg of dry air, which is 4.4411 g for each cubic meter of room air. A 1,000 cubic foot room needs about 125.76 g, or 4.252 fluid ounces. Air at 10 C and 70 percent warmed to 21 C reaches 34.593 percent, and 1.6163 g per kg would bring it to 45 percent.
Why winter air feels dry
Cold outdoor air holds very little water vapor even when it is damp. Once it leaks into a heated home and warms up, the same amount of vapor is spread over a much higher capacity, and the relative humidity drops. Cooking, bathing and breathing add water back, so real rooms are above the number shown here.
To find the temperature at which the water in the air would start to condense, use the dew point calculator. For how humid air feels when it is warm, see the heat index calculator.
Using the water figure
The water to add is the amount needed in the air that is already in the room. A home exchanges air with the outdoors, so a humidifier has to keep adding water as fresh dry air arrives. Treat the number as a starting point for sizing and compare it with the output rating of the humidifier you are considering. High indoor humidity in cold weather can cause condensation on windows, which is why the target is your own choice.
Assumptions and limits
- No water is added or removed, so the vapor pressure of the outdoor air is kept as the air is heated or cooled.
- The pressure is standard sea level pressure of 101.325 kPa, so the result is approximate at altitude.
- The Magnus form is used for saturation vapor pressure. It agrees with other forms within a fraction of a percent in this range.
- The room volume turns grams per kilogram into a total using the density of the dry air at the indoor temperature.
Frequently asked questions
Why is indoor air so dry in winter?
Cold air holds little water vapor. When it is heated indoors the vapor spreads over a much larger capacity, so the relative humidity falls. Air at 23 F and 80 percent warmed to 68 F is only about 14.5 percent.
How do I calculate indoor humidity from outdoor humidity?
Multiply the outdoor relative humidity by the saturation vapor pressure at the outdoor temperature and divide by the saturation vapor pressure at the indoor temperature.
How much water must I add to reach a target humidity?
Find the moisture in the air now and the moisture at the target, in grams of water per kilogram of dry air, and subtract. The page also converts it to grams per cubic meter and for a room.
What does 100 percent mean in the result?
It means the air would be saturated, so the extra water would condense as fog or on cold surfaces. That happens when moist air is cooled enough.