Air Enthalpy Calculator: Temperature and Humidity

An air enthalpy calculator uses dry-bulb temperature, relative humidity, and usually air pressure to estimate the enthalpy of moist air. Enter those conditions to get energy per kilogram of dry air; the result helps compare heating, cooling, and humidification loads.

Formula

The calculator uses the common moist-air psychrometric approximation:

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

w = 0.62198p_v / (p − p_v), where p_v = (RH/100)p_ws and p_ws = 0.61121 exp[(18.678 − t/234.5)(t/(257.14 + t))].

• h is moist-air enthalpy in kJ per kg of dry air.
• t is dry-bulb temperature in °C.
• w is humidity ratio, kg of water vapor per kg of dry air.
• RH is relative humidity in percent, entered from 0 to 100.
• p is total air pressure in kPa; the default, 101.325 kPa, is standard atmospheric pressure.
• p_v is water-vapor partial pressure in kPa, and p_ws is saturation vapor pressure in kPa.

The coefficients are conventional engineering approximations. The enthalpy reference is approximately dry air and liquid water at 0 °C; enthalpy values depend on the chosen reference, so comparisons should use the same convention.

Worked Example

Using the defaults—25 °C, 50% relative humidity, and 101.325 kPa—first estimate saturation vapor pressure:

p_ws = 0.61121 exp[(18.678 − 25/234.5)(25/(257.14 + 25))] ≈ 3.1685 kPa.

Then calculate vapor pressure: p_v = (50/100) × 3.1685 ≈ 1.5843 kPa.

The humidity ratio is w = 0.62198 × 1.5843 / (101.325 − 1.5843) ≈ 0.009881 kg/kg dry air.

Finally, h = 1.006 × 25 + 0.009881 × (2501 + 1.86 × 25) ≈ 50.32 kJ/kg dry air. Rounded to the calculator’s two decimal places, the displayed result is 50.32 kJ/kg dry air.

Assumptions

• The air is treated as a moist-air mixture at a single, uniform temperature and pressure.
• The saturation-pressure equation is an engineering approximation, not a high-precision equation for every temperature range or unusual gas mixture.
• Relative humidity describes water vapor relative to saturation at the entered dry-bulb temperature.
• The result is per kilogram of dry air, not per kilogram of the combined moist-air mixture and not total energy in a room or duct.

What Temperature and Humidity Tell You

Temperature alone does not describe how much water vapor air contains. At the same dry-bulb temperature, air at higher relative humidity generally has a larger humidity ratio and higher enthalpy. Conversely, relative humidity can change when air is heated or cooled even if its water-vapor content stays constant: warming unsaturated air lowers its relative humidity, while cooling it raises relative humidity.

That distinction matters in comfort and building calculations. A room at 25 °C and 50% RH has about 0.0099 kg of water vapor per kilogram of dry air under the assumptions above. Heating that air without adding moisture changes its relative humidity and enthalpy; adding moisture also changes the latent-energy contribution represented by the humidity-ratio term.

When to Use the Result

Air enthalpy is useful for comparing two air states and estimating the energy change associated with conditioning air. For a process involving a known dry-air mass flow, the approximate heat-transfer rate is often calculated from the enthalpy difference:

Heat-transfer rate ≈ dry-air mass flow rate × (h_out − h_in)

Use consistent units: if enthalpy is in kJ/kg and dry-air flow is in kg/s, the product is kJ/s, or kW. This is a state comparison, not a complete equipment-sizing calculation. Real systems may also require fan heat, heat losses, condensate removal, changing pressure, and equipment efficiency.

• Use dry-bulb temperature, not wet-bulb temperature or a temperature measured on a surface.
• Enter relative humidity as a percentage: enter 50 for 50%, not 0.50.
• Use the local or process pressure when it differs materially from standard atmospheric pressure, such as at elevation or in a pressurized system.

Reading the Calculator and Common Errors

The first output is enthalpy in kJ/kg of dry air. The humidity-ratio output offers a useful cross-check: a larger value means more water vapor per unit mass of dry air. Water-vapor partial pressure is also reported in kPa. These outputs describe the same air state in different ways; they are not interchangeable units.

A frequent misconception is that relative humidity alone measures the amount of moisture in air. It does not: RH depends on temperature as well as vapor content. Another common mistake is to interpret 50.32 kJ/kg as the energy required to heat an entire room. To estimate total energy, a dry-air mass or flow and a change between initial and final states are needed, along with a defined process boundary.

Results are approximate and rounded. Small differences from a psychrometric chart or another calculator can arise from its saturation-pressure equation, enthalpy reference, pressure setting, and rounding. The equation shown here is most appropriate for ordinary air-conditioning conditions; it should not be treated as a specialist property model for very low temperatures, high pressures, or non-air gas mixtures.

Frequently Asked Questions

What is the formula for air enthalpy from temperature and humidity?
First use temperature, relative humidity, and pressure to estimate water-vapor pressure and humidity ratio. Then use h = 1.006t + w(2501 + 1.86t), with t in °C and h in kJ/kg dry air.

Can I calculate enthalpy with temperature and relative humidity only?
You can make an estimate if you assume a pressure. This calculator defaults to 101.325 kPa, but actual pressure should be entered when known, particularly at elevation or in a pressurized process.

Is moist-air enthalpy measured per kilogram of air or water?
The result is per kilogram of dry air. It includes the sensible and water-vapor contributions, but its denominator is dry-air mass—not the total mass of moist air.

Does higher relative humidity always mean higher enthalpy?
At the same temperature and pressure, higher RH means a higher humidity ratio and generally higher enthalpy. Across different temperatures, RH alone cannot determine which air state has greater enthalpy.

Why does my psychrometric chart show a slightly different value?
Charts and calculators can use different saturation-pressure correlations, reference states, and rounding. Confirm that temperature, RH, pressure, and the dry-air basis match before comparing results.

Related

• Outdoor Air Enthalpy Calculator: HVAC Moist-Air Values
• Temperature to Enthalpy Calculator: What You Need
• Gibbs Free Energy Calculator and Formula

in t | Dry-bulb temperature | °C | 25 | -50 | 100
in rh | Relative humidity | % | 50 | 0 | 100
in p | Air pressure | kPa | 101.325 | 0.01
out h | Moist-air enthalpy | kJ/kg dry air | 1.006 * t + (rh / 100 * 0.61121 * exp((18.678 - t / 234.5) * (t / (257.14 + t))) * 0.62198 / (p - rh / 100 * 0.61121 * exp((18.678 - t / 234.5) * (t / (257.14 + t))))) * (2501 + 1.86 * t) | 2
out w | Humidity ratio | kg water/kg dry air | 0.62198 * (rh / 100 * 0.61121 * exp((18.678 - t / 234.5) * (t / (257.14 + t)))) / (p - rh / 100 * 0.61121 * exp((18.678 - t / 234.5) * (t / (257.14 + t)))) | 4
out pv | Water-vapor partial pressure | kPa | rh / 100 * 0.61121 * exp((18.678 - t / 234.5) * (t / (257.14 + t))) | 3