Calculator Inputs
Calculation Results
Values are based on saturation over liquid water using a Tetens approximation.
| Input Temperature | Temperature (°C) | Pressure (hPa) | Saturation Vapor Pressure es (hPa) | ws (kg/kg) | ws (g/kg) |
|---|---|---|---|---|---|
| Enter temperature and pressure, then press Calculate to see results. | |||||
Example Saturation Mixing Ratios
The following table shows typical saturation mixing ratios at sea-level pressure (1013 hPa) for common temperatures.
| Temperature (°C) | Pressure (hPa) | Saturation Vapor Pressure (hPa) | Saturation Mixing Ratio (g/kg) |
|---|---|---|---|
| 0 | 1013 | 6.11 | 3.8 |
| 10 | 1013 | 12.27 | 7.6 |
| 20 | 1013 | 23.37 | 14.7 |
| 30 | 1013 | 42.43 | 27.0 |
| 35 | 1013 | 56.20 | 36.7 |
Formula Used
The calculator first converts the input temperature to degrees Celsius if necessary. It then estimates the saturation vapor pressure es (hPa) using a Tetens-type relationship:
e_s = 6.112 × exp(17.67 × T_C / (T_C + 243.5))
Here TC is temperature in degrees Celsius. The saturation mixing ratio ws (kg/kg) is then obtained from:
w_s = 0.622 × e_s / (p − e_s)
where p is the total air pressure in the same units as es. The result is also reported as grams of water per kilogram of dry air.
How to Use This Calculator
- Enter the air temperature and select the appropriate temperature unit.
- Provide the total ambient pressure in hectopascals, typically near 1013 hPa at sea level.
- Click Calculate to compute saturation vapor pressure and saturation mixing ratio.
- Review the resulting ratios in both kg/kg and g/kg formats.
- Use the CSV or PDF download buttons to archive your calculations or attach them to technical reports.
Understanding Saturation Mixing Ratio
Saturation mixing ratio expresses the maximum mass of water vapor that air can hold at a given temperature and pressure. It is usually reported as grams of water per kilogram of dry air. Because it is a ratio of masses, it remains independent of volume changes. This makes comparisons straightforward.
Physical Meaning in Atmospheric Science
When air is saturated, any further cooling or addition of water vapor produces condensation. The saturation mixing ratio therefore marks the threshold separating unsaturated and saturated conditions. Comparing actual and saturation values reveals relative humidity, cloud formation potential, and the likelihood of fog or dew near the surface.
Core Formula Behind the Calculator
This calculator uses the common meteorological relationship ws = 0.622 es / (p − es). Here ws is saturation mixing ratio, es is saturation vapor pressure, and p is total air pressure. Saturation vapor pressure is estimated from temperature using an exponential Tetens-type formula valid for typical tropospheric conditions.
Unit Conventions and Assumptions
Inputs accept temperature in degrees Celsius or Kelvin and pressure in hectopascals. Internally the calculation treats pressure in the same units as saturation vapor pressure. Results are displayed both as kilograms of water per kilogram of dry air and as the more intuitive grams of water per kilogram of dry air.
Applications in Weather and Climate Work
Forecasters use saturation mixing ratio to track moisture transport, frontal boundaries, and vertical stability. It supports diagnosing convective potential and cloud base heights when combined with actual mixing ratio and temperature profiles. Climate scientists analyze long records of saturation values to study changing moisture capacity under warming trends. Aviation meteorologists, air quality analysts, and hydrologists also rely on saturation metrics when assessing icing risk, pollutant dispersion, and watershed evaporation.
Integrating with Other Engineering Calculators
Building engineers often couple moisture calculations with airflow tools. After estimating humidity with this calculator, you can size ventilation ducts using the Duct Sizing by Friction Calculator. Bathroom or laboratory designs may reference the Restroom Exhaust Sizing Calculator to maintain safe, comfortable indoor environments.
Limitations, Good Practices, and Next Steps
The formulas assume standard atmospheric composition, well-mixed air, and liquid water, not ice. Extremely high temperatures, very low pressures, or strong chemical contaminants may require more specialized thermodynamic models. Always check units, compare against benchmark cases, and document assumptions. When precision is critical, validate important values against laboratory data or trusted psychrometric charts. Use exported CSV or PDF results to archive calculations and share them within reports.
Frequently Asked Questions
What does saturation mixing ratio represent?
Saturation mixing ratio is the maximum mass of water vapor that air can hold at a given temperature and pressure, expressed as mass of vapor per mass of dry air.
How is saturation mixing ratio different from specific humidity?
Specific humidity uses the total moist air mass in the denominator, while saturation mixing ratio uses only the dry air mass. For small vapor contents the values are similar but not identical.
Can I use this calculator for very low pressures?
The formula works best for typical tropospheric pressures. At extremely low pressures, such as in high-altitude laboratory chambers, more specialized thermodynamic models or experimental data may be required for reliable results.
Does the calculator account for ice instead of liquid water?
No, the Tetens approximation implemented here assumes saturation over liquid water. For conditions well below freezing, use an ice-saturation formulation or dedicated cold-cloud microphysics tools.
Why do I get unrealistic or extremely large mixing ratios?
Unrealistic results usually indicate that pressure is too low, or that it is close to the computed saturation vapor pressure. Verify units, recheck inputs, and ensure that pressure comfortably exceeds e_s.
Can I combine this calculator with other design tools?
Yes. You can compute moisture levels here and then use airflow or ventilation sizing calculators to design ducts, fans, and exhaust systems that maintain appropriate humidity in indoor or process environments.