Mixing Ratio & Specific Humidity Calculator

Understanding the mixing ratio and specific humidity calculator — concept and principle

Relative humidity tells you how close air is to saturation, but not how much water vapour it actually holds. Mixing ratio and specific humidity do: they give grams of water vapour per kilogram of air. This calculator also gives the virtual temperature, used to account for the fact that moist air is lighter than dry air.

Vapour is only a thin slice of the pressure, yet it adds almost 14 g of water to each kilogram of air.

How it is calculated

Saturation vapour pressure (Magnus formula): e_s = 6.112 × exp(17.62 T / (243.12 + T)) hPa, with T in °C.
Actual vapour pressure: e = (RH / 100) × e_s.
Mixing ratio: w = 622 × e / (p − e) g/kg, where 622 comes from 0.622 (the ratio of the molar masses of water and dry air) × 1,000.
Specific humidity: q = 622 × e / (p − 0.378 e) g/kg.
Virtual temperature: T_v = T_K × (1 + 0.61 w), with w in kg/kg and T_K in kelvin, then converted back to °C.

The principle

By Dalton's law, the total pressure p is the sum of the dry-air pressure p − e and the vapour pressure e. In the ideal-gas law, the mass of each gas in a given volume is proportional to its partial pressure times its molar mass. Dividing the vapour mass by the dry-air mass gives w = ε e / (p − e), with ε = 18.015/28.96 ≈ 0.622. Specific humidity divides by the total mass instead, which leads to the p − 0.378e form. Because a water molecule is lighter than an average air molecule, adding vapour lowers the density; T_v is the temperature dry air would need to have the same density.

Worked example

Inputs: T = 25 °C, RH = 70%, p = 1013.25 hPa.
e_s = 6.112 × exp(17.62 × 25 / 268.12) = 31.6006 hPa.
e = 0.70 × 31.6006 = 22.1204 hPa.
w = 622 × 22.1204 / (1013.25 − 22.1204) = 13.88202692 g/kg.
q = 622 × 22.1204 / (1013.25 − 0.378 × 22.1204) = 13.69195484 g/kg.
T_v = 298.15 × (1 + 0.61 × 0.0138820) − 273.15 = 27.52474506 °C, about 2.5 °C above the actual temperature.

Each point is the calculator re-run with only “Temperature (°C)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Temperature (°C)	Mixing ratio (g/kg)
6.25	4.111558983
12.5	6.279412211
18.8	9.414228547
25	13.88202692
31.2	20.17391201
37.5	28.9539731
50	57.99401511

How to read the result

Mixing ratios near the surface range from below 1 g/kg in very cold, dry air to around 20 g/kg in humid tropical air. Around 14 g/kg, as here, feels muggy. Because w is conserved in unsaturated vertical motion, it is the quantity meteorologists use to track air masses.

Common mistakes

Comparing relative humidities at different temperatures; the same RH holds much more water in warm air.
Mixing up mixing ratio (per kg of dry air) and specific humidity (per kg of moist air).
Using T_v as the real air temperature; it is a density-equivalent temperature only.

Keep in mind: The Magnus formula is an approximation over liquid water, most accurate between about −45 °C and +60 °C. Below freezing, saturation over ice is lower. This calculator does not compute total precipitable water in a column, which requires a full humidity profile.

Frequently asked questions

What is a typical dew point for 14 g/kg?

At sea-level pressure, about 19 °C, consistent with 25 °C and 70% relative humidity.

Why does pressure matter?

The same vapour pressure is a larger share of the total at lower pressure, so the same e gives a higher mixing ratio at altitude.

Sources: World Meteorological Organization, Guide to Instruments and Methods of Observation (WMO-No. 8) · J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Introductory Survey, Academic Press

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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