Psychrometric Calculator

The Psychrometric Calculator fixes the state of moist air from two known properties and reports everything else about it. You give it the dry-bulb temperature and one second property (relative humidity, wet-bulb temperature or dew point) together with the altitude, and it returns the humidity ratio, enthalpy, specific volume, density, vapour pressure, degree of saturation, and whichever of wet-bulb, dew point and relative humidity you did not supply.

It works in IP or SI units, and it accounts for altitude, which shifts every property that depends on barometric pressure.

Use it for HVAC load and process calculations, or to read a point off a psychrometric chart without the chart. It reports the state of air; it does not model equipment.

Purpose and model boundary

This model resolves a moist-air state from dry-bulb temperature, altitude, and one second property: relative humidity, thermodynamic wet-bulb temperature, or dew-point temperature. It reports barometric pressure, wet bulb, dew point, relative humidity, humidity ratio, degree of saturation, enthalpy, specific volume, moist-air density, and vapour-pressure quantities.

It is a single-state property calculator, not an HVAC process simulation or an authored psychrometric chart. It does not model mixing, coils, bypass factor, condensation mass, comfort, or equipment capacity.

Inputs and units

Unit_System selects IP or SI interpretation. Numeric inputs do not auto-convert when the selector changes. Dry bulb is entered in deg F or deg C; altitude in ft or m. The second value is % RH, wet-bulb temperature, or dew-point temperature according to Second_Property; the computed label and units follow that choice.

Internally, temperature is converted to deg C, altitude to metres, pressure to Pa, and humidity ratio to kg water/kg dry air. IP and SI outputs are converted from that common state, except enthalpy: IP enthalpy is referenced to 0 deg F while SI enthalpy is referenced to 0 deg C.

Governing relationships

Barometric pressure follows the ASHRAE standard-atmosphere relation

P = 101325 x (1 - 0.0000225577 x z)^5.2559

where z is altitude in metres. Saturation vapour pressure uses the Hyland-Wexler/ASHRAE logarithmic polynomial over ice below 0 deg C and the separate water polynomial at and above 0 deg C. Coefficients are stored on the Data sheet; the stated source ranges are 173.15–273.15 K over ice and 273.15–473.15 K over water.

For relative-humidity input, Pv = RH x Pws(Tdb). For dew-point input, Pv = Pws(Tdp). For wet-bulb input, humidity ratio is obtained from the ASHRAE rearrangement used in the workbook:

W = [ (2501 - 2.326 Twb) Ws(Twb) - 1.006 (Tdb - Twb) ] / [2501 + 1.86 Tdb - 4.186 Twb].

The shared moist-air relationships are

• W = 0.621945 Pv / (P - Pv);
• Ws = 0.621945 Pws / (P - Pws);
• RH = Pv / Pws;
• degree of saturation = W / Ws;
• h_SI = 1.006 Tdb + W (2501 + 1.86 Tdb) in kJ/kg dry air;
• h_IP = 0.24 Tdb + W (1061 + 0.444 Tdb) in Btu/lb dry air;
• v = Rda T_K (1 + 1.607858 W) / P;
• rho_moist = (1 + W) / v.

Dew point uses the ASHRAE correlations for vapour pressure below and above 0 deg C. When wet bulb is not the input, a Stull approximation supplies only the starting value; four explicit secant updates solve the workbook's thermodynamic wet-bulb equation without circular calculation.

Calculation sequence

1. Resolve unit system and second-property mode; convert dry bulb, altitude, and the second value to the internal SI basis.
2. Calculate barometric pressure and dry-bulb saturation pressure.
3. Resolve vapour pressure/humidity ratio from relative humidity, wet bulb, or dew point.
4. Calculate relative humidity, saturation humidity ratio, degree of saturation, enthalpy, volume, density, and dew point.
5. If necessary, solve wet bulb through the explicit secant chain.
6. Convert results to IP or SI display units and evaluate Model_Status in the order below.

Outputs and interpretation

Humidity ratio is mass of water vapour per mass of dry air; alternate units show grains/lb or g/kg. Relative humidity is vapour pressure divided by saturation pressure at dry bulb. Degree of saturation compares the actual humidity ratio with the saturated ratio. Enthalpy and specific volume are on a dry-air basis; moist-air density includes dry air plus vapour mass.

The reported dry bulb echoes the state input in the selected unit system. A blank dew point under perfectly dry conditions is intentional because the model does not assign a finite dew point to zero vapour pressure.

Validation and status logic

The workbook returns the first matching status.

Assumptions and limitations

The model treats moist air as an ideal-gas mixture and uses standard-atmosphere pressure rather than measured station pressure. Results inherit the stated temperature validity of the saturation-pressure correlations. The workbook has no separate altitude status range; extreme altitude that makes the standard-atmosphere expression or pressure relationships nonphysical should not be used merely because this calculator accepts a number.

The wet-bulb result is thermodynamic, not necessarily an aspirated-instrument reading. The Stull formula is only a seed; the final value comes from the ASHRAE relationship. IP and SI enthalpy values use different zero reference states and should not be converted by a single multiplier.

Restrictions and non-computing states

A valid state requires vapour pressure between zero and saturation and saturation pressure below total pressure. Dew point above dry bulb normally violates the saturation check. Relative-humidity input is interpreted as a percentage; the model's 1.0001 tolerance allows only a very small numerical margin above exactly saturated. Values outside the underlying correlation ranges are outside the documented model basis even when no separate input bound blocks them.

Errors and warnings

NOT VALID denotes a physically inconsistent or pressure-incompatible state. CHECK denotes the limiting dry-air state where most properties still compute but dew point is undefined. Rejected entries, wrong value types, and calculation-service failures occur outside this status formula.

The workbook derives its relations rather than reproducing any table, chart or figure from a handbook. The saturation-pressure formulation and the moist-air property relations are computed, and the wet-bulb inversion is solved iteratively.

• ASHRAE. Handbook: Fundamentals, Psychrometrics chapter, the source of the saturation-pressure equations and the 40°C dry-bulb / 20°C wet-bulb worked example used above for reconciliation. https://handbook.ashrae.org/Handbooks/F25/SI/F25_Ch01/F25_Ch01_si.aspx
• Wikipedia. Psychrometrics. https://en.wikipedia.org/wiki/Psychrometrics
• Wikipedia. Humidity, for the distinction between relative humidity, humidity ratio and dew point. https://en.wikipedia.org/wiki/Humidity

The ASHRAE Handbook is the authoritative source for psychrometric properties in United States practice; its equations are implemented here rather than its tables or charts being reproduced. No trademark or organisation name appearing in this tool implies endorsement by its owner.

Additional source notes migrated from Methodology

The workbook cites ASHRAE Handbook—Fundamentals Chapter 1 Eq.3, 5, 6, 20, 26, 30, 33, 37, and 38; Hyland and Wexler (1983) for saturation pressure; and Stull (2011) only for the wet-bulb seed. The secant iterations and all coefficients are visible in the workbook.