Actual Mixing Ratio Calculator: Convert and Measure

An actual mixing ratio calculator finds the mass of water vapor per mass of dry air, usually expressed in grams of water vapor per kilogram of dry air (g/kg). Enter the water-vapor partial pressure and total air pressure; the calculator returns the actual mixing ratio and vapor density, with all pressures in the same units.

Formula

For moist air, the actual mixing ratio is the mass of water vapor divided by the mass of dry air. Using partial pressure, the standard approximation is:

r = 0.622 × e / (p − e)

• r is the actual mixing ratio in kilograms of water vapor per kilogram of dry air. The calculator multiplies this value by 1,000 to display g/kg.
• e is the actual water-vapor partial pressure, in hPa in this calculator. It can also be entered in kPa or another pressure unit if both inputs use that same unit.
• p is total atmospheric pressure, in the same unit as e.
• 0.622 is the approximate ratio of the molar mass of water vapor to that of dry air.

The calculator’s first output therefore uses 621.97 × e / (p − e) to give g/kg. Its second output estimates water-vapor density using ρᵥ = 216.7 × e / T, where ρᵥ is in g/m³, e is in hPa, and T is absolute temperature in kelvins. For this additional density estimate, the calculator assumes 20°C (293.15 K); density changes with temperature, while the mixing-ratio calculation does not require temperature when e and p are known.

Worked Example

With the default inputs, water-vapor partial pressure is 10 hPa and total pressure is 1,000 hPa. First find the dry-air partial pressure: 1,000 − 10 = 990 hPa. Then calculate:

r = 621.97 × 10 / 990 = 6.2825… g/kg

Rounded to two decimal places, the actual mixing ratio is 6.28 g/kg. For the density output, the assumed temperature is 20°C, or 293.15 K:

ρᵥ = 216.7 × 10 / 293.15 = 7.392… g/m³

Rounded to two decimal places, the estimated water-vapor density is 7.39 g/m³.

What Actual Mixing Ratio Means

In atmospheric science, mixing ratio describes how much of one gas is present relative to another by mass. The actual mixing ratio refers to the water vapor present in a particular air sample, not the maximum amount the air could hold before saturation. It is commonly written r or w. A value of 6.28 g/kg means there are about 6.28 grams of water vapor for each kilogram of dry air.

Mixing ratio is not the same as specific humidity. Mixing ratio divides water-vapor mass by dry-air mass; specific humidity divides water-vapor mass by the total mass of moist air. Their values are close when the air is not especially humid, but the definitions and denominators differ. Nor is mixing ratio the same as relative humidity, which compares actual vapor pressure with saturation vapor pressure at a given temperature.

When to Use This Calculator

This calculation is useful in meteorology, atmospheric measurements, and other work that describes moisture in air. It helps compare water-vapor content across samples when temperature alone would be misleading. The key inputs are actual vapor pressure and total air pressure. Vapor pressure may be measured or derived from suitable humidity and temperature data; a relative-humidity reading by itself is not enough.

For example, if a weather observation provides actual vapor pressure of 10 hPa and atmospheric pressure of 1,000 hPa, the result is 6.28 g/kg. If pressure is supplied in kilopascals instead, enter both pressures in kPa: 1.0 kPa and 100 kPa produce the same ratio. Do not enter one pressure in hPa and the other in kPa.

How to Get and Check the Inputs

• Use actual water-vapor partial pressure, not total atmospheric pressure or saturation vapor pressure.
• Use total pressure for the same air sample, and keep the units consistent between both entries.
• Check that e is positive and less than p. If e equals or exceeds p, the dry-air pressure in the denominator is zero or negative, so the result is not physically valid for this formula.
• Keep adequate precision in measured or converted pressures. Rounding inputs too early can noticeably affect a result when e is close to p.

If you only have temperature and relative humidity, first determine actual vapor pressure using an appropriate saturation-vapor-pressure relationship, then use that e with total pressure. The result depends on the quality and convention of those source measurements.

Common Mistakes and Limitations

A frequent mistake is treating relative humidity as though it were actual vapor pressure. Relative humidity is a percentage; e is a pressure. Another is using saturation vapor pressure in place of actual vapor pressure. Saturation pressure represents equilibrium at a stated temperature and will generally exceed actual vapor pressure when the air is unsaturated.

The equation assumes air can be treated as a mixture of dry air and water vapor and uses a rounded molecular-mass constant. It is a standard practical relationship for ordinary atmospheric calculations, not a substitute for a specialized equation of state under unusual, high-pressure conditions. The displayed precision is rounding, not a claim that the inputs or atmosphere are known to that precision.

Units can also be confused: g/kg is a mass ratio, not grams per cubic metre. The latter is vapor density, which depends on temperature as well as vapor pressure. The calculator’s density output is explicitly based on 20°C; use a different temperature only by applying the density formula with that temperature converted to kelvins.

Frequently Asked Questions

What is the formula for actual mixing ratio?
Use r = 0.622e/(p − e), where e is actual water-vapor partial pressure and p is total pressure in matching units. Multiply the result by 1,000 to express it in g/kg.

What units should I use?
Use any consistent pressure unit for both inputs, such as hPa, Pa, or kPa. The displayed mixing ratio is in g/kg. The density estimate is in g/m³ and uses the calculator’s stated 20°C assumption.

Can I calculate mixing ratio from relative humidity alone?
No. You also need temperature to obtain saturation vapor pressure and then actual vapor pressure, as well as total pressure for the mixing-ratio formula.

Does actual mixing ratio change with temperature?
At fixed actual vapor pressure and total pressure, this formula gives the same mixing ratio regardless of temperature. In real air, temperature changes can affect vapor pressure and moisture conditions, so the measured inputs may change.

Why is my result invalid or unusually large?
Check for mismatched pressure units and confirm that actual vapor pressure is less than total pressure. When e approaches p, the dry-air pressure p − e becomes very small and the calculated ratio rises sharply.

Related

• Calculate the Hypotenuse of a Triangle
• Absolute Uncertainty Calculator Formula and Examples
• Absolute Risk Reduction Calculator: Formula and Example

in e | Water-vapor partial pressure | hPa | 10 | 0
in p | Total air pressure | hPa | 1000 | 0
out r | Actual mixing ratio | g/kg | 621.97 * e / (p - e) | 2
out rho | Water-vapor density | g/m^3 | 216.7 * e / (273.15 + 20) | 2