Psychrometric Calculator
Calculate psychrometric properties: humidity ratio, enthalpy, dew point, wet bulb temperature
Category: Hvac
Psychrometric Calculator Inputs
Psychrometric Calculator Formula
Equation
Psychrometric relationships for moist air properties
Excel Formula
=Psychrometricrelationshipsformoistairproperties
Variables
- Dry Bulb Temperature (°C) — Air temperature measured by standard thermometer
- Relative Humidity (%) — Percentage of water vapor in air relative to saturation
- Atmospheric Pressure (kPa) — Local atmospheric pressure (standard = 101.325 kPa)
How the Psychrometric Calculator Works
Psychrometrics is the study of thermodynamic properties of moist air and the processes involving water vapor in air. Understanding these properties is fundamental for HVAC design, including air conditioning, humidification, dehumidification, and ventilation systems. The psychrometric chart graphically represents these relationships, enabling engineers to analyze air conditioning processes.
The core relationship is Psychrometric relationships for moist air properties. Typical inputs include Dry Bulb Temperature, Relative Humidity, Atmospheric Pressure.
Enter your values in the psychrometric calculator above, review the step-by-step solution, and compare against the worked examples below so you can see how each input changes the result. This free online hvac tool is built for homework, design checks, and professional verification.
Psychrometric Calculator Theory & Explanation
Fundamental Properties
Moist air is a mixture of dry air and water vapor, characterized by several interdependent properties:
**Dry Bulb Temperature (DBT)**: The temperature measured by a standard thermometer, representing the sensible heat content of air.
**Wet Bulb Temperature (WBT)**: Temperature measured by a thermometer with wetted bulb, accounting for evaporative cooling. Always between DBT and dew point.
**Dew Point Temperature (DPT)**: Temperature at which water vapor begins to condense when air is cooled at constant pressure. Calculated using:
T_d = (b · γ(T,RH))/(a - γ(T,RH))
where γ(T,RH) = (a · T)/(b + T) + \ln(RH/100), with a = 17.27, b = 237.7°C
**Relative Humidity (RH)**: Ratio of actual water vapor pressure to saturation vapor pressure at given temperature:
RH = (P_v)/(P_vs) × 100\%
**Humidity Ratio (W)**: Mass of water vapor per unit mass of dry air (kg water/kg dry air):
W = 0.622 · (P_v)/(P - P_v)
where P is atmospheric pressure (typically 101.325 kPa) and P_v is water vapor pressure.
Vapor Pressure Relationships
Water vapor pressure is calculated using the Magnus-Tetens formula:
**Saturation Vapor Pressure**:
P_vs = 0.61078 · \exp((17.27 · T)/(T + 237.3))
where T is temperature in °C and P_vs is in kPa.
**Actual Vapor Pressure**:
P_v = (RH)/(100) · P_vs
This relationship enables conversion between relative humidity, temperature, and absolute moisture content.
Enthalpy of Moist Air
Enthalpy represents the total heat content of moist air (sensible + latent):
h = c_p · T + W · (h_fg + c_pv · T)
Simplified to:
h ≈ 1.006 · T + W · (2501 + 1.86 · T)
where: - h = enthalpy (kJ/kg dry air) - c_p = specific heat of dry air = 1.006 kJ/(kg·K) - W = humidity ratio (kg water/kg dry air) - h_fg = latent heat of vaporization = 2501 kJ/kg at 0°C - c_pv = specific heat of water vapor = 1.86 kJ/(kg·K) - T = dry bulb temperature (°C)
Enthalpy is crucial for calculating cooling/heating loads and energy transfer in HVAC processes.
Specific Volume
Specific volume is the volume of moist air per unit mass of dry air:
v = (R_a · (T + 273.15) · (1 + 1.608 · W))/(P)
where: - v = specific volume (m³/kg dry air) - R_a = gas constant for dry air = 0.287 kJ/(kg·K) - T = temperature (°C) - W = humidity ratio - P = atmospheric pressure (kPa)
Typically: v ≈ 0.83 to 0.90 m³/kg at standard conditions.
Wet Bulb Temperature Calculation
Wet bulb temperature calculation requires iterative solution of the psychrometric equation:
W_s(T_wb) - W = \fracc_p · (T - T_wb)h_fg
where W_s(T_wb) is humidity ratio at saturation at wet bulb temperature.
Approximate formula (accurate within ±0.5°C for typical conditions):
T_wb = T · \arctan[0.151977 · (RH + 8.313659)^0.5] + \arctan(T + RH) - \arctan(RH - 1.676331) + 0.00391838 · RH^1.5 · \arctan(0.023101 · RH) - 4.686035
Wet bulb temperature is essential for evaporative cooling calculations and comfort assessment.
Psychrometric Calculator Worked Examples
Worked Example
Inputs
- dryBulbTemp: 25
- relativeHumidity: 60
- pressure: 101.325
Result: Humidity Ratio: 12.03 g/kg | Enthalpy: 55.6 kJ/kg | Dew Point: 16.7°C | Wet Bulb: 19.8°C
Explanation
For air at 25°C dry bulb temperature with 60% relative humidity:
**Step 1: Calculate Saturation Vapor Pressure** Using Magnus-Tetens formula: P_vs = 0.61078 · \exp(17.27 · 25 / (25 + 237.3)) = 3.169 kPa
**Step 2: Calculate Actual Vapor Pressure** P_v = (60/100) · 3.169 = 1.901 kPa
**Step 3: Calculate Humidity Ratio** W = 0.622 · 1.901 / (101.325 - 1.901) = 0.01203 kg/kg = 12.03 g/kg
**Step 4: Calculate Enthalpy** h = 1.006 · 25 + 0.01203 · (2501 + 1.86 · 25) = 55.6 kJ/kg
**Step 5: Calculate Dew Point** Using inverse Magnus formula: T_d = 16.7°C
**Step 6: Calculate Wet Bulb Temperature** Using iterative psychrometric equation: T_wb = 19.8°C
This represents typical comfortable indoor conditions.
Second Scenario
Inputs
- dryBulbTemp: 32.25
- relativeHumidity: 60
- pressure: 101.325
Result: Humidity Ratio: 12.03 g/kg | Enthalpy: 55.6 kJ/kg | Dew Point: 16.7°C | Wet Bulb: 19.8°C
Explanation
This scenario uses different inputs (dryBulbTemp = 32.25, relativeHumidity = 60, pressure = 101.325) to show how changing one variable affects the psychrometric result. Run the calculator above with these values to get the exact updated output with step-by-step work.
Common Psychrometric Calculator Use Cases
- HVAC load and equipment sizing
- Comfort and indoor air quality analysis
- Energy audit support
- Humidity ratio
- Enthalpy
Psychrometric Calculator FAQs
What is the difference between absolute and relative humidity?
Absolute humidity (humidity ratio) is the actual mass of water vapor per unit mass of dry air (g/kg or lb/lb), independent of temperature. Relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at a given temperature, expressed as a percentage. RH varies with temperature even if absolute moisture content remains constant. For example, air with 10 g/kg moisture at 25°C has 50% RH, but the same air cooled to 15°C would have approximately 80% RH without adding or removing moisture.
How do I use psychrometric properties for HVAC calculations?
Psychrometric properties enable energy and mass balance calculations for HVAC processes: 1) Cooling/Heating Load: Q = \dotm · Δ h where mass flow rate times enthalpy change gives cooling/heating load in kW. 2) Dehumidification: Track humidity ratio change to calculate moisture removal. 3) Mixing: Use mass-weighted averages of properties. 4) Evaporative Cooling: Follow constant wet bulb lines. 5) Sensible Cooling: Horizontal line (constant W) on psychrometric chart. 6) Humidification: Vertical line (constant DBT) or adiabatic saturation line depending on process.
Why is wet bulb temperature important?
Wet bulb temperature is crucial for several reasons: 1) Cooling Tower Design: Determines minimum achievable water temperature in evaporative cooling systems. 2) Human Comfort: Combined with dry bulb, indicates thermal stress. Wet bulb above 35°C is dangerous even for healthy humans. 3) Evaporative Cooling Potential: Difference between dry bulb and wet bulb (wet bulb depression) indicates evaporative cooling effectiveness. 4) Adiabatic Saturation: Represents temperature achieved through adiabatic humidification process. 5) HVAC Equipment Selection: Used in psychrometric calculations for air washers, cooling towers, and evaporative coolers.
How does altitude affect psychrometric calculations?
Altitude significantly affects psychrometric properties through reduced atmospheric pressure. At higher elevations: 1) Saturation humidity ratio increases for same temperature (W = 0.622 × Pv/(P-Pv) where P decreases with altitude). 2) Specific volume increases (less dense air). 3) Boiling point decreases, affecting water evaporation rates. 4) Enthalpy calculations require pressure correction. For example, at 2000m elevation (P ≈ 80 kPa), air holds about 25% more moisture at saturation than at sea level. Always use local atmospheric pressure in calculations. Standard pressure (101.325 kPa) is only valid at sea level.
What does the Psychrometric Calculator calculate?
It applies the formula on this page to your inputs and returns the primary result plus any supporting values shown in the output panel.