Quick answer
Relative humidity can be computed from air temperature and dew point: RH = 100 × exp(aTd ÷ (b + Td) − aT ÷ (b + T)) with a = 17.625 and b = 243.04 °C. Air at 25 °C with a dew point of 15 °C has a relative humidity of 53.83%.
Enter the air temperature and the dew point. The calculator returns the relative humidity.
Related tools: Absolute Humidity Calculator: Water vapor content of air in grams per cubic meter. Wet Bulb Temperature Calculator: Wet-bulb temperature from air temperature and relative humidity (Stull's formula). Air Density Calculator: Density of moist air from pressure, temperature and humidity.
How to use the Relative Humidity Calculator
- Enter air temperature (°C) (between -45 and 60).
- Enter dew point (°C) (between -45 and 60).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Air temperature | A number, in °C | ≥ -45, ≤ 60 |
| Dew point | A number, in °C | ≥ -45, ≤ 60 |
Formula and method
Formula
RH = 100 × exp(aTd ÷ (b + Td) − aT ÷ (b + T)), a = 17.625, b = 243.04 °C
IEEE-754 double precision; shown to the decimals indicated.
Magnus formula; the dew point cannot exceed the air temperature.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Air temperature = 25; Dew point = 15.
| Result | Value |
|---|---|
| Relative humidity | 53.83% |
Example 2
Inputs: Air temperature = 30; Dew point = 30.
| Result | Value |
|---|---|
| Relative humidity | 100% |
Example 3
Inputs: Air temperature = 10; Dew point = -2.
| Result | Value |
|---|---|
| Relative humidity | 43.05% |
The first line is the headline result (relative humidity). IEEE-754 double precision; shown to the decimals indicated.
The ratio behind it
RH is the vapour pressure divided by the saturation vapour pressure at the air temperature. At 25 °C saturation is 31.7 hPa, and the vapour pressure at the 15 °C dew point is 17.1 hPa, so RH = 17.1 ÷ 31.7 = 54%.
Why dew point is better
Dew point measures the actual moisture in the air and doesn't change when the temperature rises, unlike RH. The dew point can't exceed the air temperature; at equality RH is 100%.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Dew point: entering "20" shows "The dew point cannot be above the air temperature." beside that field and no result.
- Air temperature: left empty shows "Enter air temperature." beside that field and no result.
Choosing between the Relative Humidity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Absolute Humidity Calculator](/science/absolute-humidity/) | temperature and relative humidity | Absolute humidity |
| [Wet Bulb Temperature Calculator](/science/wet-bulb/) | air temperature and relative humidity | Wet-bulb temperature |
| [Air Density Calculator](/science/air-density/) | pressure, temperature and relative humidity | Air density |
| [Relative Frequency Calculator](/statistics/relative-frequency/) | counts | Relative frequencies |
| [Relative Risk Calculator](/statistics/relative-risk-calculator/) | exposed with outcome, exposed without outcome and unexposed with outcome | Relative risk |
Background: environment and acoustics
Decibels are a logarithmic scale, so sound levels cannot be added arithmetically: two equal sources raise the level by about 3 dB, not double it. Environmental and emissions results depend on the factors behind them (for example the US EPA's equivalency factors), which are averages for a country, fuel and year.
Use the result to compare scenarios rather than as a measured value.
Assumptions and limitations
- Dew point must not exceed temperature
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for dew point and air temperature to confirm this.
Frequently asked questions
What RH is comfortable indoors?
Indoor relative humidity of about 30 to 50% is comfortable; above 60% invites mould and below 25% dries skin.
Does RH change when air is heated?
Yes. Heating air without adding moisture lowers relative humidity, because warmer air can hold more water vapour.
What is the dew point?
The temperature where air becomes saturated.
What does the Relative Humidity Calculator calculate?
Relative humidity from air temperature and dew point. It returns Relative humidity.
What formula does the Relative Humidity Calculator use?
RH = 100 × exp(aTd ÷ (b + Td) − aT ÷ (b + T)), a = 17.625, b = 243.04 °C. Magnus formula; the dew point cannot exceed the air temperature.
What do I need to enter in the relative Humidity Calculator?
You enter Air temperature (°C) and Dew point (°C).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Dew point must not exceed temperature.
What is an example of a relative Humidity result?
With air temperature 25 and dew point 15, the relative humidity is 53.83%.
Where does the method come from?
The method follows: Alduchov & Eskridge, J. Appl. Meteor. 35 (1996) 601.
Related calculators
- Absolute Humidity Calculator — Water vapor content of air in grams per cubic meter.
- Wet Bulb Temperature Calculator — Wet-bulb temperature from air temperature and relative humidity (Stull's formula).
- Air Density Calculator — Density of moist air from pressure, temperature and humidity.
- Relative Frequency Calculator — Relative frequencies and percentages from counts.
- Relative Risk Calculator — Relative risk from a 2×2 table.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
Sources
- Alduchov & Eskridge, J. Appl. Meteor. 35 (1996) 601
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.