Humidity Ratio Calculator

Calculate

Dry-bulb temperature of the air

Relative humidity of the air (0–100%)

Overview

Humidity ratio (W) — also called moisture content or mixing ratio — is the mass of water vapor per unit mass of dry air. It is the fundamental moisture variable in HVAC psychrometrics because it remains constant through any sensible heating or cooling process and changes only when moisture is added or removed.

Unlike relative humidity, which varies with temperature even when no moisture is added or removed, humidity ratio is an absolute measure of moisture content. Two air streams at different temperatures but the same humidity ratio contain exactly the same amount of water vapor per pound (or kilogram) of dry air. This makes W the correct variable for latent load calculations, mixing calculations, and dehumidification analysis.

This calculator derives humidity ratio from dry-bulb temperature combined with one of four moisture inputs: relative humidity, wet-bulb temperature, dew point temperature, or direct entry. It also computes the corresponding dew point temperature, partial vapor pressure, degree of saturation (μ), and saturation humidity ratio (W_sat) at the given dry-bulb temperature. All calculations use the Magnus approximation for saturation vapor pressure at standard atmospheric pressure, consistent with ASHRAE Handbook — Fundamentals psychrometric formulations.

How to Use This Calculator

  1. Enter dry-bulb temperature — in °C or °F.

  2. Select moisture input type — choose from Relative Humidity, Wet-Bulb Temperature, Dew Point Temperature, or Direct Entry.

  3. Enter relative humidity — in %.

  4. Enter wet-bulb temperature — in °C or °F.

  5. Enter dew point temperature — in °C or °F.

  6. Enter humidity ratio — in g/kg or gr/lb.

  7. Click "Calculate" — get humidity ratio, dew point, vapor pressure, saturation humidity ratio, and degree of saturation.

Use humidity ratio (ΔW) for latent load and dehumidification sizing; for altitude above ~2,000 ft, correct atmospheric pressure before using W.

Inputs & Outputs

Inputs

  • •Dry-Bulb Temperature (°C / °F)
  • •Moisture Input Type — Options: Relative Humidity (%), Wet-Bulb Temperature (°F), Dew Point Temperature (°F), Direct Entry (gr/lb)
  • •Relative Humidity (%)
  • •Wet-Bulb Temperature (°C / °F)
  • •Dew Point Temperature (°C / °F)
  • •Humidity Ratio (g/kg / gr/lb)

Outputs

  • •Humidity Ratio (W) (g/kg / gr/lb)
  • •Dew Point Temperature (°C / °F)
  • •Partial Vapor Pressure (kPa / psi)
  • •Saturation Humidity Ratio (W_sat) (g/kg / gr/lb)
  • •Degree of Saturation (μ) (%)
  • •Relative Humidity (when not entered) (%)

Formula

Calculator Formulas

All calculations assume standard atmospheric pressure:

  • Imperial: P_atm = 14.696 psi
  • Metric: P_atm = 101.325 kPa

Saturation Vapor Pressure (Magnus Approximation)

Metric:   P_sat = 0.61078 × exp(17.625 × T / (243.04 + T))   [kPa]
Imperial: P_sat = 0.08855 × exp(17.625 × Tc / (243.04 + Tc)) [psi]
          where Tc = (T_°F − 32) / 1.8

Humidity Ratio from Relative Humidity

Vapor pressure:

P_v = (RH / 100) × P_sat

Humidity ratio:

Imperial: W = 4350 × P_v / (P_atm − P_v)    [gr/lb]
Metric:   W = 621.945 × P_v / (P_atm − P_v) [g/kg]

The constant 621.945 = 1000 × (M_w / M_a) = 1000 × (18.015 / 28.966), converting the dimensionless ratio to g/kg. The Imperial constant 4350 = 7000 × (18.015 / 28.966), converting to gr/lb.

Humidity Ratio from Wet-Bulb Temperature

Imperial: W = W_sat(T_wb) − 0.3344 × (T_db − T_wb)   [gr/lb]
Metric:   W = W_sat(T_wb) − 0.622 × (T_db − T_wb)     [g/kg]

where W_sat(T_wb) is the saturation humidity ratio at the wet-bulb temperature.

Humidity Ratio from Dew Point Temperature

W = W_sat(T_dp)

The dew point is the temperature at which the air becomes saturated at its current moisture content, so W equals the saturation humidity ratio at the dew point.

Derived Properties

Partial vapor pressure from W:

Metric:   P_v = (W / 1000) × P_atm / (0.621945 + W / 1000)   [kPa]
Imperial: P_v = (W / 7000) × P_atm / (0.621945 + W / 7000)   [psi]

Dew point from vapor pressure:

α = ln(P_v / 0.61078)                [metric]
α = ln(P_v / 0.08855)              [imperial]
T_dp = 243.04 × α / (17.625 − α)    [°C]
T_dp(°F) = T_dp(°C) × 1.8 + 32

Degree of saturation:

μ = W / W_sat(T_db) × 100   [%]

Relative humidity (when not directly entered):

RH = P_v / P_sat(T_db) × 100   [%]

Variable Reference

Variable Meaning Units
T_db Dry-bulb temperature °F / °C
T_wb Wet-bulb temperature °F / °C
T_dp Dew point temperature °F / °C
RH Relative humidity %
W Humidity ratio gr/lb / g/kg
W_sat Saturation humidity ratio at T_db gr/lb / g/kg
P_v Partial vapor pressure psi / kPa
P_sat Saturation vapor pressure psi / kPa
μ Degree of saturation (W / W_sat) %
P_atm Standard atmospheric pressure 14.696 psi / 101.325 kPa

What Is Humidity Ratio?

Humidity ratio (W) is the mass of water vapor contained in a given mass of dry air. In Imperial units it is expressed in grains of moisture per pound of dry air (gr/lb), where 7,000 grains equals one pound. In SI units it is expressed in grams of moisture per kilogram of dry air (g/kg). The dimensionless form (lb/lb or kg/kg) is used in psychrometric equations.

Humidity ratio is an absolute moisture measurement — it does not change with temperature unless moisture is physically added or removed. This distinguishes it from relative humidity, which varies with temperature even when the actual moisture content stays constant.

Why Humidity Ratio Matters in HVAC

Humidity ratio is the basis for every latent load calculation in HVAC engineering. The latent cooling load on a coil equals the mass flow rate of air multiplied by the difference in humidity ratio between entering and leaving conditions, multiplied by the latent heat of vaporization:

Q_latent = ṁ × ΔW × h_fg

In Imperial units, the standard latent load formula is:

Q_latent = 0.68 × CFM × ΔW (gr/lb)

where 0.68 = 60 min/hr × 0.075 lb/ft³ × 1076 BTU/lb ÷ 7000 gr/lb.

Without accurate humidity ratio values, latent loads cannot be calculated, coil selections will be wrong, and dehumidification systems will be improperly sized.

Humidity Ratio vs. Relative Humidity

Relative humidity (RH) is the ratio of the actual vapor pressure to the saturation vapor pressure at the same temperature. It tells you how close the air is to saturation, but it does not tell you how much moisture the air actually contains.

For example, air at 75°F and 50% RH contains approximately 65 gr/lb of moisture. If that same air is cooled to 55°F without removing moisture, its relative humidity rises to approximately 100% — but the humidity ratio remains 65 gr/lb. The moisture content did not change; only the air's capacity to hold moisture changed.

This is why HVAC engineers use humidity ratio for load calculations and mixing problems, and use relative humidity primarily for comfort assessment and control setpoints.

Degree of Saturation vs. Relative Humidity

Degree of saturation (μ) is the ratio of the actual humidity ratio to the saturation humidity ratio at the same dry-bulb temperature: μ = W / W_sat. It is numerically close to relative humidity but not identical. The difference arises because RH is based on vapor pressures while μ is based on humidity ratios, and the relationship between vapor pressure and humidity ratio is not perfectly linear due to the (P_atm − P_v) term in the denominator. At typical HVAC conditions the difference is small (usually less than 2%), but at high humidity ratios the divergence becomes significant.

Key Facts

  • Humidity ratio remains constant through any sensible heating or cooling process. Only processes that add or remove moisture — such as dehumidification, humidification, or mixing with a different air stream — change the humidity ratio.
  • In Imperial units, 7,000 grains equals 1 pound. A humidity ratio of 70 gr/lb means the air contains 0.01 lb of water vapor per pound of dry air.
  • The standard Imperial latent load formula Q = 0.68 × CFM × ΔW requires ΔW in gr/lb. Using ΔW in lb/lb without the 7,000 multiplier produces a result that is 7,000 times too small.
  • At standard conditions (75°F, 50% RH, sea level), humidity ratio is approximately 65 gr/lb (9.3 g/kg). This is a useful benchmark for quick sanity checks.
  • Humidity ratio at saturation increases exponentially with temperature. At 60°F saturation W is about 77 gr/lb; at 90°F it is about 218 gr/lb — nearly three times higher for a 30°F increase.
  • The dew point temperature is the temperature at which the air's humidity ratio equals the saturation humidity ratio. Cooling air below its dew point causes condensation.

Applications

  • Latent cooling load calculation — Q_latent = 0.68 × CFM × ΔW (Imperial) or ṁ × ΔW × h_fg (Metric)
  • Dehumidification system sizing — required moisture removal rate in lb/hr or kg/hr from airflow × ΔW
  • Air mixing calculations — mixed air W = (W₁ × ṁ₁ + W₂ × ṁ₂) / (ṁ₁ + ṁ₂)
  • Cooling coil apparatus dew point estimation — the coil surface temperature at which the supply air humidity ratio is achieved
  • Energy recovery ventilation latent effectiveness — η_latent = ΔW_actual / ΔW_max
  • Indoor air quality assessment — verifying that indoor humidity ratio stays within ASHRAE 55 comfort limits
  • Desiccant wheel sizing — moisture removal capacity depends on the humidity ratio difference across the wheel
  • Condensation risk analysis — comparing surface temperature to dew point derived from humidity ratio

Example Calculation

Imperial Example

Given: T_db = 75°F, RH = 50%

Step 1 — Saturation Pressure:

Tc = (75 − 32) / 1.8 = 23.89°C
P_sat = 0.08855 × exp(17.625 × 23.89 / (243.04 + 23.89))
P_sat = 0.08855 × exp(1.578) = 0.08855 × 4.846 = 0.4291 psi

Step 2 — Vapor Pressure:

P_v = 0.50 × 0.4291 = 0.2146 psi

Step 3 — Humidity Ratio:

W = 4350 × 0.2146 / (14.696 − 0.2146)
W = 933.5 / 14.481 = 64.5 gr/lb
W = 64.5 / 7000 = 0.00921 lb/lb

Step 4 — Dew Point:

α = ln(0.2146 / 0.08855) = ln(2.423) = 0.886
T_dp(°C) = 243.04 × 0.886 / (17.625 − 0.886) = 215.3 / 16.739 = 12.86°C
T_dp(°F) = 12.86 × 1.8 + 32 = 55.1°F

Step 5 — Saturation Humidity Ratio at T_db:

W_sat = 4350 × 0.4291 / (14.696 − 0.4291) = 1866.6 / 14.267 = 130.8 gr/lb

Step 6 — Degree of Saturation:

μ = 64.5 / 130.8 × 100 = 49.3%

Metric Example

Given: T_db = 24°C, RH = 50%

Step 1 — Saturation Pressure:

P_sat = 0.61078 × exp(17.625 × 24 / (243.04 + 24))
P_sat = 0.61078 × exp(1.584) = 0.61078 × 4.874 = 2.978 kPa

Step 2 — Vapor Pressure:

P_v = 0.50 × 2.978 = 1.489 kPa

Step 3 — Humidity Ratio:

W = 621.945 × 1.489 / (101.325 − 1.489)
W = 926.1 / 99.84 = 9.28 g/kg
W = 9.28 / 1000 = 0.00928 kg/kg

Step 4 — Dew Point:

α = ln(1.489 / 0.61078) = ln(2.438) = 0.891
T_dp = 243.04 × 0.891 / (17.625 − 0.891) = 216.55 / 16.734 = 12.94°C

Step 5 — Saturation Humidity Ratio at T_db:

W_sat = 621.945 × 2.978 / (101.325 − 2.978) = 1852.2 / 98.35 = 18.83 g/kg

Step 6 — Degree of Saturation:

μ = 9.28 / 18.83 × 100 = 49.3%

Standards & References

  • ASHRAE Handbook — Fundamentals (2021), Ch. 1 Psychrometrics — Primary reference for psychrometric definitions, humidity ratio formulations, and moist-air property calculations
  • ASHRAE Standard 55-2023: Thermal Environmental Conditions for Human Occupancy — Defines acceptable humidity limits for comfort (upper limit approximately 0.012 kg/kg or 84 gr/lb)
  • ASHRAE Standard 62.1-2022: Ventilation and Acceptable Indoor Air Quality — Outdoor air humidity ratio affects ventilation latent loads
  • Magnus Formula (Alduchov & Eskridge, 1996) — Saturation vapor pressure approximation: P_sat = 0.61078 × exp(17.625T / (243.04 + T))
  • ASHRAE Handbook — HVAC Systems and Equipment (2020), Chapter 23 — Dehumidification system sizing based on humidity ratio difference

Limitations

  • All calculations assume standard atmospheric pressure: 14.696 psi (101.325 kPa). At 5,000 ft elevation, atmospheric pressure drops to approximately 12.23 psi, increasing humidity ratio by roughly 20% for the same vapor pressure.
  • The wet-bulb to humidity ratio conversion uses a simplified psychrometric constant (0.3344 for Imperial, 0.622 for Metric). This approximation is accurate within the normal HVAC range but may introduce small errors at extreme temperatures or very high humidity.
  • The Magnus approximation for saturation vapor pressure is accurate to within ±0.4% over the range −40°C to 50°C. Outside this range, use the more precise Hyland-Wexler or IAPWS-IF97 formulations.
  • This calculator does not account for the effect of dissolved salts or contaminants on vapor pressure. For industrial processes involving hygroscopic materials, additional corrections may be needed.
  • Degree of saturation (μ) and relative humidity (RH) diverge at high humidity ratios. At W > 100 g/kg, the difference can exceed 5%.

Common Mistakes to Avoid

  • Confusing humidity ratio units: gr/lb vs. lb/lb. The ASHRAE enthalpy formula uses lb/lb (W / 7000), while the latent load formula 0.68 × CFM × ΔW uses gr/lb directly. Mixing these up produces errors of 7,000×.
  • Using relative humidity instead of humidity ratio for latent load calculations. RH changes with temperature; W does not. Latent load depends on the actual moisture difference (ΔW), not the RH difference.
  • Assuming humidity ratio and specific humidity are identical. Specific humidity is the mass of vapor per unit mass of moist air (W / (1 + W)), while humidity ratio is per unit mass of dry air. The difference is small at low moisture levels but grows at high humidity.
  • Forgetting that the wet-bulb depression formula is an approximation. The simplified W = W_sat(T_wb) − C × (T_db − T_wb) uses a constant C that varies slightly with conditions. For highest accuracy, use measured RH or dew point.
  • Applying sea-level formulas at high altitude without correction. At 5,000 ft elevation, atmospheric pressure is approximately 12.23 psi instead of 14.696 psi, which increases humidity ratio by roughly 20% for the same vapor pressure.

Frequently Asked Questions

What is the difference between humidity ratio and specific humidity?
Humidity ratio (W) is the mass of water vapor per unit mass of dry air: W = m_v / m_a. Specific humidity (q) is the mass of water vapor per unit mass of moist air: q = m_v / (m_a + m_v) = W / (1 + W). At typical HVAC conditions where W is small (e.g., 0.01 kg/kg), the difference is less than 1%. At very high moisture levels the distinction becomes significant. ASHRAE psychrometric formulas use humidity ratio, not specific humidity.
How do I convert between gr/lb and g/kg?
Multiply gr/lb by 1/7 to get g/kg (approximately). The exact conversion is: g/kg = gr/lb × (1 lb / 7000 gr) × (1000 g / 1 kg) × (1 kg / 2.20462 lb) × (2.20462 lb / 1 kg) ≈ gr/lb / 7.0. More precisely, since both are mass ratios: W(g/kg) = W(gr/lb) × (1000/7000) × (1 lb / 0.45359 kg) × (0.45359 kg / 1 lb) = W(gr/lb) / 7.0. For practical purposes, divide gr/lb by 7 to get g/kg.
Why does humidity ratio stay constant during sensible heating?
Sensible heating adds energy to the air without adding or removing moisture. Since no water vapor is added or removed, the mass of vapor per mass of dry air (W) remains unchanged. The relative humidity decreases because the saturation capacity increases with temperature, but the absolute moisture content stays the same.
What humidity ratio corresponds to comfortable indoor conditions?
ASHRAE Standard 55 recommends an upper humidity limit of approximately 0.012 kg/kg (12 g/kg or 84 gr/lb) for thermal comfort. There is no explicit lower limit in the standard, but humidity ratios below about 0.004 kg/kg (4 g/kg or 28 gr/lb) are often associated with dry skin, static electricity, and respiratory discomfort. Typical comfortable indoor conditions at 72–75°F (22–24°C) and 40–60% RH correspond to approximately 47–82 gr/lb (6.7–11.7 g/kg).
How does altitude affect humidity ratio calculations?
At higher altitudes, atmospheric pressure is lower. Since W = 0.621945 × P_v / (P_atm − P_v), a lower P_atm increases the denominator's reduction, resulting in a higher humidity ratio for the same vapor pressure. At 5,000 ft (1,524 m), P_atm ≈ 12.23 psi (84.3 kPa), and humidity ratio is approximately 20% higher than at sea level for the same temperature and relative humidity.
Can humidity ratio be negative?
No. Humidity ratio is a mass ratio and cannot be physically negative. If a calculation produces a negative value — typically from the wet-bulb approximation when T_wb > T_db — the result is clamped to zero. A negative intermediate value indicates an invalid input combination.

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