Psychrometric calculator
Psychrometrics is the study of moist air: how much water vapor it holds, how close it is to saturation, and the temperature at which that vapor would condense. This calculator takes two everyday measurements, the air temperature in degrees Celsius and the relative humidity as a percentage, and returns three key properties. First it computes the saturation vapor pressure, the maximum pressure water vapor can exert at that temperature, using the well established Magnus formula. Then it multiplies by the relative humidity to get the actual vapor pressure present in the air. Finally it inverts the relationship to find the dew point, the temperature to which the air must cool, at constant pressure, for that vapor to begin condensing into dew, fog or mist. These quantities underpin air conditioning design, weather forecasting, condensation control in vehicles and buildings, and human comfort calculations. Enter your own temperature and humidity to study a specific condition or to check a textbook problem. The results update as you type. Every figure here is computed deterministically from the Magnus equation, the standard approximation used across meteorology and HVAC engineering, with a worked example below that reconciles exactly to the calculator so you can follow each step of the arithmetic from start to finish.
Saturation vapor pressure follows the Magnus formula es = 6.112 x exp(17.625 T / (243.04 + T)), and dew point inverts it. At 25 degrees C and 60% relative humidity, es is 31.63 hPa, the actual vapor pressure is 18.98 hPa and the dew point is 16.70 degrees C.
Magnus psychrometric formulas
es = 6.112 x exp( 17.625 T / (243.04 + T) ) [hPa]
e = (RH / 100) x es
gamma = ln(RH/100) + 17.625 T / (243.04 + T)
dew point Td = 243.04 x gamma / (17.625 - gamma)
T = air temperature in degrees C, RH = relative humidity (%)
The saturation vapor pressure es rises sharply with temperature. The actual vapor pressure e is the fraction of es set by the relative humidity. The dew point Td is the temperature at which that actual vapor pressure would itself be the saturation value, so the air would be fully saturated.
Worked example
Air is at 25 degrees C with 60% relative humidity. Find the vapor pressures and the dew point.
- 17.625 x 25 / (243.04 + 25) = 440.625 / 268.04 = 1.643890
- es = 6.112 x exp(1.643890) = 6.112 x 5.17552 = 31.63 hPa
- e = 0.60 x 31.63 = 18.98 hPa
- gamma = ln(0.60) + 1.643890 = -0.510826 + 1.643890 = 1.133064
- Td = 243.04 x 1.133064 / (17.625 - 1.133064) = 275.385 / 16.491936 = 16.70 degrees C
The dew point is 16.70 degrees C, so cooling this air below that temperature would cause condensation. These are the calculator's default inputs, so the results above match the widget exactly.
Dew point at 60% relative humidity
| Air temp (deg C) | es (hPa) | Dew point (deg C) |
|---|---|---|
| 15 | 17.06 | 7.30 |
| 20 | 23.39 | 12.00 |
| 25 | 31.63 | 16.70 |
| 30 | 42.47 | 21.39 |
Computed with the Magnus coefficients a = 17.625, b = 243.04 degrees C.
Psychrometric calculator: frequently asked questions
What is the dew point?
The dew point is the temperature to which air must be cooled, at constant pressure and water content, for it to become saturated so that water vapor starts to condense. A higher dew point means more moisture in the air and a muggier feel. When a surface is colder than the dew point, condensation forms on it, which is why windows fog and cold pipes sweat.
What is the Magnus formula?
The Magnus formula is the standard approximation for the saturation vapor pressure of water over a liquid surface: es = 6.112 times the exponential of 17.625 T divided by (243.04 + T), in hectopascals, with T in degrees Celsius. It is accurate to a fraction of a percent across the normal range of weather temperatures and is widely used in meteorology and HVAC engineering.
What is the difference between relative humidity and dew point?
Relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure at the current temperature, so it changes as the air warms or cools even when the moisture content is fixed. The dew point measures the absolute moisture content directly and does not change unless water is added or removed, which makes it a more stable indicator of how humid the air really is.
What units does this calculator use?
Temperature and dew point are in degrees Celsius, relative humidity is a percentage between 0 and 100, and the vapor pressures are given in hectopascals (hPa), which are numerically identical to millibars. One hectopascal equals 100 pascals. To convert to kilopascals, divide the hectopascal value by 10.
Is the result exact?
The Magnus formula is an empirical fit, so it carries a small approximation error of well under one percent over normal weather temperatures, which is more than precise enough for design and forecasting. The arithmetic on this page is deterministic and reproducible, and the worked example reconciles exactly to the calculator output.
Official sources
- Vehicle climate and atmospheric measurement context: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.