Formula
Psychrometrics is the state of moist air. Dry-bulb is the air temperature. Wet-bulb is how far evaporation can cool a wetted sensor. Dew point is where the air you have would become saturated if you cooled it at constant pressure. Relative humidity is vapor pressure divided by the saturation pressure at the dry-bulb. This page uses that ratio directly. It does not apply an enhancement factor.
W = 0.621945 pw / (p − pw)
h = 1.006 t + W (2501 + 1.86 t)
v = 0.287042 (t + 273.15) (1 + 1.607858 W) / p
Saturation, dew point, and wet-bulb
Saturation pressure over liquid water is the Hyland–Wexler equation ASHRAE prints for SI: the log of pws, in pascals, is C1/T + C2 + C3 T + C4 T² + C5 T³ + C6 ln(T), with T in kelvin. The coefficients are −5.8002206×10³, 1.3914993, −4.8640239×10⁻², 4.1764768×10⁻⁵, −1.4452093×10⁻⁸, and 6.5459673. Dew point is the temperature where that pressure equals the actual vapor pressure. Wet-bulb solves the ASHRAE energy balance for t* between a cold floor and the dry-bulb:
W = [ (2501 − 2.326 t*) Ws(t*) − 1.006 (t − t*) ] / (2501 + 1.86 t − 4.186 t*)
Below 0 °C the page still uses the liquid coefficients and says so. Ice saturation is slightly different. A humidity ratio above saturation is clamped, and the note says it was clamped. Relative humidity is limited to 0–100%. Wet-bulb and dew point cannot sit above the dry-bulb.
Pressure, altitude, and the chart
Sea level is 101.325 kPa, which this page also calls 14.696 psia. Altitude uses p = 101.325 (1 − 2.25577×10⁻⁵ Z)^5.2559, Z in metres. A typed pressure replaces both. If pressure is not above the vapor pressure, there is no answer, and the page does not print NaN. IP enthalpy is 0.240 t + W (1061 + 0.444 t) Btu per pound of dry air, with t in °F. Specific volume in ft³/lb is the SI volume converted with 0.3048 m and 0.45359237 kg. The mass ratio itself does not change between kg/kg and lb/lb. Grains per pound are W × 7000.
A psychrometric chart draws the same relationships. This page reports one state point instead of the picture. It is not a substitute for a printed ASHRAE chart or for manufacturer software on a critical humidity process. Enthalpy is what a coil load cares about, because condensing water carries latent heat. Specific volume turns a volumetric fan rating back toward mass flow. Those are reasons to know the state. They are not a Manual J, and this page does not select equipment. The room BTU, tonnage, and duct calculators remain the rough estimates they already are.
Worked examples
25 °C dry-bulb, 50% RH, 101.325 kPa. Saturation pressure is 3.169 kPa. Vapor pressure is 1.585 kPa. Humidity ratio is 0.00988 kg/kg (9.9 g/kg). Enthalpy is 50.3 kJ/kg. Specific volume is 0.858 m³/kg. Dew point is 13.9 °C and wet-bulb is 17.9 °C.
The same state in IP, 77 °F and 50% RH. Humidity ratio is 69.2 gr/lb. Enthalpy is 29.3 Btu/lb. Dew point is 57.0 °F. Wet-bulb is 64.2 °F.
30 °C dry-bulb and 20 °C wet-bulb. W is 0.01052 kg/kg, relative humidity 39.7%, enthalpy 57.1 kJ/kg, dew point 14.8 °C, specific volume 0.873 m³/kg.
0 °C dry-bulb, 80% RH. W is 0.00302 kg/kg and enthalpy is 7.5 kJ/kg, from the liquid saturation equation. The page warns that ice coefficients differ.
Round trip. The wet-bulb or the dew point from the first example, entered with 25 °C, returns relative humidity within half a percentage point of 50% and humidity ratio within 0.00005 kg/kg of 0.00988.
Reference
Sea-level pressure, 101.325 kPa. Liquid-water saturation. Values are this page’s equations.
| State | Result |
|---|---|
| 25 °C, 50% RH | W 0.00988 · h 50.3 kJ/kg · v 0.858 · dp 13.9 °C · wb 17.9 °C |
| 77 °F, 50% RH | 69.2 gr/lb · h 29.3 Btu/lb · dp 57.0 °F · wb 64.2 °F |
| 30 °C DB, 20 °C WB | W 0.01052 · RH 39.7% · h 57.1 · dp 14.8 °C · v 0.873 |
| 0 °C, 80% RH | W 0.00302 · h 7.5 kJ/kg |
| 1,000 m | 89.875 kPa |
Questions
What is a psychrometric calculator?
It finds the rest of a moist-air state from two properties and the barometric pressure. Dry-bulb is the ordinary air temperature. From that plus relative humidity, wet-bulb, dew point, or humidity ratio, this page returns the others, plus enthalpy and specific volume. The equations are the perfect-gas relations in the style of ASHRAE Fundamentals, Chapter 1. The result is an engineering estimate, not a certified chart and not a load calculation.
What is the difference between dry-bulb and wet-bulb?
Dry-bulb is the air temperature. Wet-bulb is the temperature a wetted thermometer falls to as water evaporates into the air. They meet when the air is saturated. At 30 °C dry-bulb and 20 °C wet-bulb, sea level, the humidity ratio is about 0.01052 kg/kg and the relative humidity is about 39.7%.
How do you find dew point from temperature and humidity?
Relative humidity sets the vapor pressure: pw = RH × pws(dry-bulb). The dew point is the temperature where saturation pressure equals that pw. At 25 °C and 50% RH, pws is about 3.169 kPa, pw is about 1.585 kPa, and the dew point is about 13.9 °C. Feeding that dew point back with the same dry-bulb returns about 50% RH.
What is humidity ratio?
Humidity ratio W is kilograms of water vapor per kilogram of dry air. It is not relative humidity. At 25 °C and 50% RH, W is about 0.00988 kg/kg, or 9.9 g/kg, which is about 69.2 grains per pound. Degree of saturation is W divided by the saturation ratio at the same dry-bulb. Enthalpy, about 50.3 kJ/kg of dry air here, is what a cooling coil has to remove.
How does altitude change the numbers?
Lower pressure holds less vapor at the same relative humidity, and the humidity ratio changes. This page uses p = 101.325 (1 − 2.25577×10⁻⁵ Z)^5.2559 kPa, with Z in metres. At 1,000 m that is about 89.875 kPa, against 101.325 kPa at sea level. You can type a pressure instead. If the pressure is not above the vapor pressure, the page stops.
What is the difference between SI and IP on this page?
The state is computed in SI, then shown in the units you picked. °C and °F, kPa and psia, kJ/kg and Btu/lb, m³/kg and ft³/lb. The humidity ratio is a mass ratio, so kg/kg and lb/lb are the same number. Grains per pound are that ratio times 7,000. 101.325 kPa is 14.696 psia on this page.
Is this a substitute for a printed ASHRAE psychrometric chart?
No. A printed chart is a certified graphical tool with its own assumptions, and manufacturer software is what a process or a pharmaceutical spec will name. This page is one numeric state point from the published equations, including liquid-water saturation below freezing, where ice coefficients differ. It is not an ACCA Manual J, and it does not select equipment. Use the BTU, tonnage, and duct pages only as the rough sizing estimates they already claim to be.
Sources
- ASHRAE Handbook — Fundamentals, Chapter 1, Psychrometrics. Perfect-gas humidity ratio, enthalpy, specific volume, and the wet-bulb balance used here.
- Hyland and Wexler saturation formulations, as printed by ASHRAE for liquid water. The six SI coefficients are in the formula section. Below 0 °C this page does not switch to the ice set.
- The same relations are implemented in the open PsychroLib library. This page does not claim that library’s chart output. Numbers here are an engineering estimate.