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Thermofluid & HVAC Simulator

Dew Point and Relative Humidity Calculator — Magnus Approximation

Vary the dry-bulb temperature and relative humidity and the Magnus approximation immediately gives the dew point, wet-bulb temperature, vapor pressure and humidity ratio. Grasp where condensation starts and how much water the air actually carries.

Parameters
Dry-bulb temperature T
°C
Relative humidity RH
%
Atmospheric pressure p_atm
hPa
Display unit
0=SI/1=USCS

Magnus coefficients (a=17.62, b=243.12 °C) are the WMO-recommended values. The wet-bulb temperature uses the Stull approximation (accuracy about ±0.3 °C near 1013 hPa).

Results
—
Dew point T_d
—
Wet-bulb T_w
—
Vapor pressure e
—
Humidity ratio w (g/kg DA)
Saturation Curve and RH Iso-lines (e-T Diagram)

Cyan solid line = saturation vapor pressure e_s(T) / dashed = RH iso-lines (20/40/60/80 %) / red dot = current (T, e) / green cross = dew point location (T_d, e)

Theory & Key Formulas

The Magnus approximation expresses the saturation vapor pressure as a function of temperature only, with an error below 0.4 percent over the HVAC and meteorological range of minus 40 to plus 50 degrees Celsius.

Saturation vapor pressure e_s (T in °C, e_s in hPa):

$$e_s(T) = 6.112\,\exp\!\left(\dfrac{17.62\,T}{243.12 + T}\right)$$

Actual vapor pressure e and dew point T_d (γ is an auxiliary variable):

$$e = \dfrac{\mathrm{RH}}{100}\,e_s(T), \qquad T_d = \dfrac{243.12\,\gamma}{17.62 - \gamma}, \quad \gamma = \ln\!\dfrac{\mathrm{RH}}{100} + \dfrac{17.62\,T}{243.12 + T}$$

Humidity ratio w (mass of water vapor per kilogram of dry air, g/kg DA):

$$w = 622\,\dfrac{e}{p_\text{atm} - e}$$

Stull approximation for the wet-bulb T_w (near 1013 hPa, RH in %):

$$T_w \approx T\,\arctan\!\big(0.1520\sqrt{\mathrm{RH}+8.314}\big) + \arctan(T+\mathrm{RH}) - \arctan(\mathrm{RH}-1.676) + 0.00392\,\mathrm{RH}^{1.5}\arctan(0.0231\,\mathrm{RH}) - 4.686$$

Condensation starts on any surface whose temperature falls below the dew point T_d.

What is the Dew Point and Relative Humidity Calculator

🙋
In winter, water droplets form on the window glass — that is condensation, right? Under what conditions does it actually happen?
🎓
Roughly speaking, "when the surface temperature of the window drops below the dew point of the room air". Try setting T=25°C and RH=60% in the tool above. The dew-point card reads about 16.7°C. So the moment the window surface gets colder than 16.7°C, condensation begins. With single glazing, an outside temperature below freezing easily takes the inner pane down to that level.
🙋
So if I lower the humidity, condensation won't happen?
🎓
Exactly. Move the RH slider from 60% down to 40%. The dew point falls to about 10.5°C. Same room temperature, but dry air resists condensation. The reverse is also true — after a hot bath at RH 80%, the dew point climbs to around 21°C, and even slightly cool pipes drip wet. That is why humidity control is so strict in data centres and precision laboratories.
🙋
And what about the "wet-bulb temperature"? Is it different from the dew point?
🎓
Quite different. The dew point is "the temperature you reach by cooling alone". The wet-bulb is "the temperature you reach by adiabatic evaporative cooling with water". Sprinkling water to cool the streets, or the minimum outlet temperature of a cooling tower, is set by this wet-bulb. On a dry day (RH=30% at T=30°C), watch the wet-bulb card — it drops to around 19°C. That is the floor of evaporative cooling.
🙋
Between "humidity ratio" and "relative humidity", which one does the engineer use in design?
🎓
When you follow a heating or cooling process, you use the humidity ratio (g/kg DA). It is conserved as long as nothing is humidified or dehumidified, so it acts like a tracer. Outdoor air at 5°C and RH 60% holds about 3.3 g/kg; warming it indoors to 22°C plunges the RH below 20%, but the g/kg never changes. The required humidifier capacity is just "target g/kg minus outdoor g/kg". The humidity-ratio card in this tool is the starting point of design.

Frequently Asked Questions

These are the WMO-recommended (2008) Magnus coefficients for the saturation vapor pressure over water. Based on the fits by Sonntag and Alduchov-Eskridge against measurements, they achieve an error below 0.4 percent from minus 40 to plus 50 degrees Celsius. Over ice, a different pair (22.46, 272.62) is commonly used; this tool targets HVAC and meteorological use and adopts only the over-water coefficients.
The saturation vapor pressure e_s and the dew point T_d are almost independent of atmospheric pressure (the Magnus formula is a function of temperature only). The humidity ratio w = 622·e/(p_atm − e), however, does depend on pressure. At high altitude (about 800 hPa), the same vapor pressure gives a w about 1.3 times larger, so HVAC design on Mount Fuji or in aircraft cabins must include the pressure correction. Move the slider and only the w card changes.
Stull (2011) gives an analytical approximation that, near 1013 hPa and over dry-bulb minus 20 to 50 degrees Celsius and RH 5 to 99 percent, agrees with the exact solution (iterative saturation enthalpy balance) within an average error of ±0.3 degrees Celsius. For precision air conditioning and humidity control the exact solution should be used, but for design estimates, on-site checks and educational use the accuracy is more than enough. Note that the error grows at very low RH (below about 5 percent).
Setting the display-unit slider to 1 changes temperatures from °C to °F, vapor pressure from hPa to inHg, and humidity ratio from g/kg to gr/lb (grains per pound, where 1 g/kg ≈ 7 gr/lb). This makes it easy to read US ASHRAE references or imported chiller nameplates. Input sliders remain in SI, so you can keep the feel of the inputs while converting only the outputs.

Real-World Applications

Building condensation and mould prevention: The basic principle is to keep the surface temperature of windows and north-facing exterior walls above the dew point of the indoor air. Check the dew point here, then decide the required insulation level (double glazing, inner windows, external insulation). Persistent condensation breeds mould and triggers sick-building syndrome and allergies.

Precision air conditioning for data centres and server rooms: The ASHRAE TC9.9 recommended envelope for server spaces is a dew point of 5.5 to 15 °C with RH below 60 percent. Too low and electrostatic discharge destroys ICs; too high and the server chassis sweats and short-circuits. Using this tool to read the dew point of the operating air immediately tells you whether the humidifier and dehumidifier setpoints are sound.

Evaporative cooling towers, water sprinkling and direct evaporative humidifiers: The lower limit of all these devices is the wet-bulb temperature T_w. On a midsummer rooftop at dry-bulb 35 °C and RH 30 percent, the wet-bulb of about 22 °C sets the floor of the cooling-tower outlet, enabling large energy savings against air-cooled chillers. The wet-bulb card lets you size the evaporative cooling potential of a site and a season.

Food, pharmaceutical and warehouse quality control: Chocolate fat bloom, pharmaceutical tablet deliquescence, and the dimensional change of paper and timber all stem from the relation between the storage air dew point and the surface temperature of the goods. Read the dew point here, then design the temperature control and insulation so that all surfaces stay safely above it.

Common Misconceptions and Cautions

The most common misconception is the belief that "if the relative humidity is low, condensation will not occur". Set T=22 °C and RH=40 percent in this tool and the dew point reads about 8 °C. The air looks dry, but as soon as a window sash chilled by winter weather drops below 8 °C, condensation begins anyway. What matters is not the relative humidity, but the gap between the dew point and the surface temperature. Make a habit of reading the dew-point card first.

Next is the misunderstanding that "raising the temperature lowers the humidity, so the room feels comfortable". The RH slider does fall, but look at the humidity-ratio card w in this tool — it does not change. The actual water content of the air is the same; the dryness your skin feels depends on how fast moisture evaporates from your breath and skin, which is governed by the humidity ratio. Winter heating dries the throat and skin because w stays low. Judge the need for humidification from w, not from RH.

Finally, do not assume "the Magnus formula is universal". The over-water coefficients used here are accurate from minus 40 to plus 50 degrees Celsius, but extremely low temperatures (saturation over ice), high-pressure steam above 150 °C, and the salinity effect of seawater require different models. For everyday-scale HVAC, buildings, agriculture and weather it is amply practical, but for fuel cells, steam turbines, spacesuits and other special environments use the strict IAPWS-IF97 model.

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