Relative Humidity Calculator: From Temperature and Dew Point

Relative humidity (RH) is the number on your hygrometer and in the weather report: how much water vapor the air holds compared with the most it could hold at its temperature. The dew point is the other way to describe the same air, and it has one big advantage: it doesn’t change when the air warms up or cools down. This calculator converts between the two and shows what happens to the humidity when air changes temperature, which explains most of the dry-air and wet-window problems people have at home.

How the calculator works

It uses the inverse of the Magnus formula, with the coefficients recommended by Alduchov and Eskridge (1996), a = 17.625 and b = 243.04 °C:

RH = 100 × exp( a·Td ÷ (b + Td) − a·T ÷ (b + T) )

with the air temperature T and the dew point Td in °C (°F values are converted first). It is the exact algebraic reverse of our dew point calculator, so the two always agree.

For the “heat or cool this air” field, the calculator keeps the dew point fixed (the air holds the same amount of water) and recalculates RH at the new temperature. If the new temperature is below the dew point, the air can’t hold all its water and some condenses out.

Absolute humidity is the mass of water vapor per volume of air, from the ideal gas law: vapor pressure ÷ (461.52 J/(kg·K) × temperature in kelvin). The 461.52 is the gas constant for water vapor: NIST’s molar gas constant (8.314462618) divided by the molar mass of water (18.0153 g/mol). It’s shown in grams per cubic meter and in grains per cubic foot, the unit HVAC contractors use.

Worked examples

Air temperature	Dew point	Relative humidity
75 °F	55 °F	49.8%
70 °F	50 °F	49.1%
68 °F	40 °F	35.9%
72 °F	60 °F	65.9%

The first two match published calculators to within 0.05%. At 75 °F with a 55 °F dew point, the air holds about 10.8 g of water vapor per cubic meter (4.7 grains per cubic foot).

Why heated winter air is so dry

The dew point of outdoor air in winter is low because cold air holds little water. When that air leaks into your home and is heated, it keeps the same water, so its relative humidity falls sharply:

Outdoor air	Dew point	Heated to	Indoor RH
40 °F, 60%	27.2 °F	70 °F	20.1%
30 °F, 70%	21.4 °F	70 °F	15.8%
20 °F, 80%	14.8 °F	68 °F	12.7%
0 °F, 80%	−4.7 °F	70 °F	4.9%

That’s why a home with no moisture sources can drop well below the EPA’s 30% floor in a cold snap, and why our guide to the ideal indoor humidity suggests checking a hygrometer before you buy a humidifier. If you do need one, the humidifier size calculator shows how much water it has to add.

The reverse happens in summer: humid outdoor air at 90 °F and 60% has a dew point of about 74 °F. Cool it to 75 °F without removing water and it would sit at about 97.5%. Air conditioners avoid this by condensing water out on their cold coil; when that isn’t enough, see how to reduce humidity in the house.

Tip: Outdoor dew point is in most weather apps. Enter it with your thermostat temperature to estimate what indoor humidity you’d have with no humidifier and no moisture from cooking or showers.

How to read the result

• 30–50% is the EPA’s recommended range. Mayo Clinic notes that low humidity can cause dry skin; the humidifier guides cover the options.
• Above 50%, dust mites multiply faster; a long-running Ohio study saw mite counts fall sharply in homes kept below 51%.
• 60% or more is above the EPA’s limit; a University of Minnesota publication notes fungi increase at 60% or more.
• In cold weather, your windows may set a lower ceiling. Enter the glass temperature in the dew point calculator, or read why you get condensation on windows inside.

Limitations

The Magnus formula is accurate to about 0.4% for saturation vapor pressure between −40 °C and 50 °C (−40 °F to 122 °F). Below freezing it gives humidity relative to liquid water, not relative to ice. Home hygrometers are far less precise than the formula, so small differences between this result and your meter are normal.