Relative Humidity Calculator

A window fogs before a room feels wet because relative humidity is about saturation, not just water vapor. This relative humidity calculator uses air temperature and dew point to estimate how close the air is to saturation, then places the result in a practical comfort range. Use it for weather logs, basements, greenhouses, archives, crawl spaces, and any place where condensation or mold risk depends on both moisture and temperature.

What the calculator is doing

Weather stations often report relative humidity with temperature and dew point because those three values describe the same moisture state from different angles. Dew point is the temperature at which the current water vapor would saturate the air. Relative humidity is the actual vapor pressure divided by the saturation vapor pressure at the current air temperature. If the air temperature falls toward the dew point overnight, the denominator shrinks and relative humidity rises; if the sun warms the same air mass during the afternoon, relative humidity falls even when the water vapor content has not changed.

The form accepts Celsius or Fahrenheit. When Fahrenheit is selected, the calculation converts both temperatures to Celsius, applies the Magnus-Tetens exponential approximation, multiplies the vapor-pressure ratio by 100, then clamps the display between 0 percent and 100 percent. It also rejects dew point above air temperature. The result is rounded to two decimals and labeled positive only when it falls from 30 percent through 60 percent, the comfort band used by this page and the form. For the reverse calculation, use the dew point calculator; for hot-weather stress, combine the result with the heat index calculator; for water loss from pools and ponds, compare it with the evaporation rate calculator.

Formula

The calculation applies the Magnus-Tetens relationship with constants 17.625 and 243.04 after any unit conversion to Celsius:

$RH = 100 \times \frac{\exp\left(\frac{17.625 \times T_{\text{d}}}{243.04 + T_{\text{d}}}\right)}{\exp\left(\frac{17.625 \times T}{243.04 + T}\right)}$

where:

• $RH$ is relative humidity in percent.
• $T$ is the air temperature in degrees Celsius.
• $T_{\text{d}}$ is the dew point temperature in degrees Celsius.
• $\exp$ is the natural exponential function.

The final displayed result is:

$RH_{\text{display}} = \min\left(100, \max\left(0, RH\right)\right)$

That clamp mainly protects the interface from rounding and unusual inputs; normal air-temperature and dew-point observations with dew point less than or equal to temperature already fall between 0 percent and 100 percent.

Worked example

Use the default values: air temperature 24 degrees Celsius and dew point 15 degrees Celsius.

For the dew point term, the exponent is 17.625 times 15 divided by 243.04 plus 15. That is 264.375 divided by 258.04, or about 1.02455, and its exponential is about 2.7858. For the air-temperature term, the exponent is 17.625 times 24 divided by 243.04 plus 24. That is 423 divided by 267.04, or about 1.58403, and its exponential is about 4.8745. The ratio is 2.7858 divided by 4.8745, then times 100, giving 57.15 percent after the calculator rounds to two decimals.

Because 57.15 percent is within 30 percent through 60 percent, the form marks it as a comfortable humidity range. If the dew point stayed 15 degrees Celsius while the air warmed to 30 degrees Celsius, the relative humidity would drop because warmer air has a higher saturation vapor pressure.

How to interpret the result

Outdoors, relative humidity is highest near the daily low temperature and lowest near the daily high temperature, so a single afternoon reading can hide how close the overnight air may get to saturation. Values above about 90 percent often accompany fog, dew, low clouds, or very slow drying, especially when winds are light. Very low values, often below 30 percent, speed evaporation from soil, skin, and wood, and they are common in heated winter buildings or dry air masses.

Indoors, the same percentage has practical consequences. The EPA emphasizes controlling moisture to prevent mold; high relative humidity plus cool surfaces can keep materials damp enough for growth. A basement at 65 percent relative humidity may feel merely cool, but a cold wall or pipe can sit below the dew point and collect water. Conversely, a room at 25 percent can feel dry even when the outdoor air is not especially arid. For personal comfort planning, compare moisture with the water intake calculator during heat and with wind chill during cold, dry winter weather.

Edge cases and common mistakes

Do not enter a dew point from a different time or location than the temperature. The formula assumes both describe the same parcel of air. Do not compare two relative humidity readings without noting temperature; 60 percent at 10 degrees Celsius contains much less water vapor than 60 percent at 30 degrees Celsius. Also avoid using the value as a direct mold diagnosis. Mold risk depends on surface temperature, wetting duration, leaks, ventilation, and materials, not the room-air percentage alone.

The calculator uses constants chosen for ordinary meteorological temperatures. Very extreme values near the mathematical denominator limit are outside normal weather use. The form also reports comfort using a simple 30 percent to 60 percent band; museums, greenhouses, musical instruments, and industrial processes may require narrower ranges.

Sources

• National Weather Service Louisville, Relative Humidity — definitions and weather context for relative humidity and dew point.
• National Weather Service, Dry bulb, wet bulb, and dew point temperature — humidity terminology used in weather observations.
• EPA, A Brief Guide to Mold, Moisture and Your Home — practical moisture-control guidance for buildings.