Air Enthalpy Calculator: Moist-Air Energy Explained

An air enthalpy calculator estimates the energy carried by moist air from its temperature and moisture content, usually as enthalpy per unit mass of dry air. Enter dry-bulb temperature, relative humidity, and atmospheric pressure to calculate humidity ratio and enthalpy; the example below uses a standard psychrometric approximation.

Formula

The calculator uses the common approximate psychrometric relation for moist-air enthalpy:

h = 1.006t + w(2501 + 1.86t)

Here, h is enthalpy in kilojoules per kilogram of dry air (kJ/kg dry air), t is dry-bulb temperature in degrees Celsius, and w is humidity ratio in kilograms of water vapor per kilogram of dry air (kg/kg dry air). The humidity ratio is calculated from water-vapor partial pressure:

w = 0.621945p_v / (p – p_v)

p is total atmospheric pressure in kPa, and p_v is the partial pressure of water vapor in kPa. The calculator estimates saturation vapor pressure as p_ws = 0.6112 × exp(17.67t / (t + 243.5)) kPa, then uses p_v = (rh / 100)p_ws, where rh is relative humidity expressed as a percentage. The 0.621945 factor is the ratio of the molar masses of water vapor and dry air. The constants in this empirical saturation-pressure approximation are conventionally used with temperature in °C and pressure in kPa.

The calculator’s compact expression uses 6.112 in hPa, so it divides by 10 to obtain kPa for the displayed vapor-pressure result. In the humidity-ratio and enthalpy expressions, vapor pressure and total pressure are both represented in hPa: 6.112 hPa multiplied by the exponential, while input pressure is converted from kPa to hPa by multiplying by 10. To keep the displayed calculator expression consistent, pressure in its humidity-ratio denominator must therefore be in hPa.

Worked Example

Using the defaults—25 °C, 50% relative humidity, and 101.325 kPa—the saturation pressure approximation gives:

p_ws = 0.6112 × exp(17.67 × 25 / (25 + 243.5)) ≈ 3.1677 kPa.

Water-vapor partial pressure is:

p_v = 0.50 × 3.1677 ≈ 1.5839 kPa.

Then humidity ratio is:

w = 0.621945 × 1.5839 / (101.325 – 1.5839) ≈ 0.009875 kg/kg dry air.

Finally:

h = 1.006 × 25 + 0.009875 × (2501 + 1.86 × 25) ≈ 50.32 kJ/kg dry air.

The calculator displays enthalpy to two decimal places, humidity ratio to five, and vapor pressure to three. The worked result is therefore approximately 50.32 kJ/kg dry air.

Assumptions

• Air is treated as a moist-air mixture, with enthalpy reported per kilogram of dry air.
• The saturation-vapor-pressure relation is an engineering approximation, most useful for ordinary HVAC conditions rather than extreme temperatures.
• Relative humidity is between 0% and 100%, and atmospheric pressure is positive.
• The calculation does not include changes in kinetic or potential energy, nor heat stored in building materials or equipment.

What Air Enthalpy Means

Enthalpy is a thermodynamic measure of energy associated with a substance at a specified state. In heating, ventilation, and air-conditioning work, moist-air enthalpy is useful because it combines the sensible energy associated with temperature and the latent energy associated with water vapor. Heating humid air and drying air can therefore require different amounts of energy even when their dry-bulb temperatures are identical.

The unit “kJ/kg dry air” matters. It does not mean kilojoules per kilogram of the entire moist-air mixture. Psychrometric charts and many HVAC calculations use a kilogram of dry air as the reference amount, with the water vapor represented separately through humidity ratio.

How to Use the Result

Use enthalpy to compare two air states or estimate the energy change during an air-conditioning process. For a steady process with approximately constant dry-air mass flow, the change in heat transfer per unit time is often estimated as:

heat-transfer rate ≈ dry-air mass-flow rate × (h_out – h_in).

If mass flow is in kg/s and enthalpy difference is in kJ/kg, the result is kJ/s, equivalent to kW. The sign depends on the chosen direction: a rise in air enthalpy means the outgoing air carries more energy per kilogram of dry air. This estimate is not a complete equipment-performance calculation; heat loss, fan energy, condensation, and changing flow conditions may also matter.

• Use dry-bulb temperature, not a wet-bulb or dew-point reading, in the temperature field.
• Enter relative humidity as a percentage, such as 50, not as a decimal such as 0.50.
• Use local atmospheric pressure when altitude or weather makes it materially different from standard pressure.
• Compare enthalpy values on the same reference basis and in the same units.

Common Errors and Limits

A frequent mistake is treating relative humidity as the amount of water in the air. Relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at the same temperature. Since saturation pressure rises as air warms, relative humidity can fall during heating even if no water is removed. Humidity ratio more directly expresses how much water vapor is present per unit mass of dry air.

Another source of error is mixing pressure units. This calculator accepts pressure in kPa; the saturation-pressure approximation first produces kPa. In the humidity-ratio equation, both vapor pressure and total pressure must use the same units. A result based on pressure in hPa and vapor pressure in kPa, or vice versa, will be wrong.

The formula is an approximation for ordinary moist air, not a high-precision equation of state. It should not be relied on outside its practical temperature range, near conditions where condensation or frost changes the phase, or when unusually high accuracy is required. Sensor uncertainty in temperature and humidity can also affect the answer, especially when conditions are close to saturation. A psychrometric chart or a validated property calculation may be more appropriate for specialized engineering work.

Frequently Asked Questions

What does an air enthalpy calculator calculate?
It estimates the enthalpy of moist air from its temperature, moisture level, and pressure. The result is commonly stated in kJ per kilogram of dry air.

What inputs do I need for air enthalpy?
This calculator needs dry-bulb temperature in °C, relative humidity in percent, and atmospheric pressure in kPa. If you already know humidity ratio, a calculator using that value directly may be preferable.

Is air enthalpy the same as heat?
No. Enthalpy describes the energy state per unit mass. Heat is energy transferred between systems because of a temperature difference. Enthalpy differences can help estimate heat transfer in a flow process when other effects are accounted for.

Why does humidity affect air enthalpy?
Water vapor carries energy, including latent energy associated with evaporation. At the same dry-bulb temperature, air with more water vapor generally has higher enthalpy.

Can I use this result to size an air conditioner?
Not by itself. Equipment sizing also depends on airflow, outdoor and indoor design conditions, building loads, ventilation, equipment performance, and other factors. Enthalpy is one useful input to a broader load or process calculation.

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in t | Dry-bulb temperature | °C | 25 | -273.15
in rh | Relative humidity | % | 50 | 0 | 100
in p | Atmospheric pressure | kPa | 101.325 | 0.001
out h | Moist-air enthalpy | kJ/kg dry air | 1.006 * t + (rh / 100 * 6.112 * exp(17.67 * t / (t + 243.5)) * 0.621945 / (p - rh / 100 * 6.112 * exp(17.67 * t / (t + 243.5)))) * (2501 + 1.86 * t) | 2
out w | Humidity ratio | kg water/kg dry air | rh / 100 * 6.112 * exp(17.67 * t / (t + 243.5)) * 0.621945 / (p - rh / 100 * 6.112 * exp(17.67 * t / (t + 243.5))) | 5
out pv | Water-vapor partial pressure | kPa | rh / 100 * 6.112 * exp(17.67 * t / (t + 243.5)) / 10 | 3