Calculator
Pick pressure or altitude mode, enter temperature, and compute the saturated (moist) lapse rate. Use advanced constants when you need specialized assumptions.
Formula used
The moist adiabatic lapse rate estimates how temperature changes with height for saturated rising air, where condensation releases heat and reduces the cooling rate.
- T is temperature in kelvin.
- r is mixing ratio (kg/kg). For saturation, r uses e = es(T).
- es is saturation vapor pressure from temperature (hPa).
- Γd = g/cp is also shown for comparison.
How to use this calculator
- Select I know pressure or I know altitude.
- Enter temperature and your chosen unit.
- Provide pressure, or altitude for a standard-atmosphere estimate.
- Keep saturated ascent checked for true moist adiabatic results.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for reporting.
Example data table
| Temperature (°C) | Pressure (hPa) | Assumption | Γm (K/km) | Γd (K/km) |
|---|---|---|---|---|
| 20 | 1000 | Saturation | ≈ 4.0–5.0 | ≈ 9.77 |
| 10 | 850 | Saturation | ≈ 5.0–6.5 | ≈ 9.77 |
| -5 | 700 | Saturation | ≈ 6.5–8.0 | ≈ 9.77 |
Values are typical ranges; your computed result depends on moisture and pressure.
Article
1) Why the moist lapse rate matters
The moist adiabatic lapse rate describes how quickly a saturated air parcel cools as it rises. Because condensation releases latent heat, the cooling is slower than the dry rate. This difference shapes cloud depth, thunderstorm potential, and the stability of humid layers near fronts and sea breezes.
2) Dry versus moist cooling
For dry ascent, temperature typically decreases near 9.8 K per kilometer, set mainly by gravity and heat capacity. In saturated ascent, typical values can fall to about 4–7 K per kilometer, depending on temperature and pressure. Warmer air holds more vapor, so latent heating is stronger.
3) Temperature and pressure sensitivity
The calculator shows that Γm changes with environmental state. At higher temperatures, saturation vapor pressure increases rapidly, raising the mixing ratio and reducing Γm. At lower pressures aloft, the same moisture produces different thermodynamic leverage, often pushing Γm upward toward the dry rate.
4) Role of mixing ratio and humidity
Mixing ratio r (kg of water vapor per kg of dry air) is the key moisture variable inside the formula. When the “saturated ascent” option is enabled, r is computed from saturation vapor pressure. If you uncheck it, the tool scales vapor pressure by RH as a practical approximation.
5) Using altitude mode responsibly
Altitude mode estimates pressure using a standard tropospheric profile. This is useful for quick studies and classroom problems, but it will not capture local pressure anomalies, strong inversions, or nonstandard temperature structures. For best accuracy in field work, enter observed pressure directly.
6) Interpreting stability from results
Compare your environmental lapse rate to Γm and Γd. If the environment cools faster than the dry rate, the layer is strongly unstable. If it cools between moist and dry rates, saturated parcels can accelerate upward while unsaturated parcels may remain stable until they reach saturation.
7) Typical ranges you may observe
Near 20 °C and around 1000 hPa, Γm often falls near 4–5 K/km. Around 10 °C at 850 hPa, values frequently rise into the 5–6.5 K/km range. Colder midlevel conditions can yield 6.5–8 K/km, approaching the dry value as moisture declines.
8) Practical workflow for reports
Start with measured temperature and pressure, keep saturation enabled for cloud-layer analysis, then export CSV or PDF for documentation. Include the displayed vapor pressures and mixing ratio to justify your assumptions. When comparing scenarios, adjust temperature or altitude to see how Γm changes with synoptic setting.
FAQs
1) What does this calculator output?
It outputs the moist adiabatic lapse rate Γm and the dry adiabatic lapse rate Γd, plus supporting values like saturation vapor pressure, vapor pressure, and mixing ratio for transparency.
2) When should I keep “saturated ascent” enabled?
Use it when analyzing cloudy or nearly saturated layers, parcel lifting after condensation begins, or any situation where latent heat release is expected to be important throughout the ascent.
3) Why does Γm change with temperature?
Warmer air can hold more water vapor at saturation, so condensation releases more latent heat as the parcel rises. That extra heating offsets cooling and reduces Γm.
4) Is the RH-based option a true moist adiabat?
No. Moist adiabatic lapse rate is defined for saturated ascent. The RH option is a convenient approximation that uses reduced vapor pressure to explore sensitivity in partly humid air.
5) How accurate is altitude mode?
It is suitable for quick estimates in the troposphere using a standard pressure profile. Accuracy decreases when local pressure deviates from standard conditions or when temperature profiles are unusual.
6) Which units should I use for best consistency?
Any supported units work because the tool converts internally. For meteorology datasets, °C and hPa are common. For engineering contexts, K and Pa may integrate better with other calculations.
7) What should I cite in a lab report?
Report the input temperature, pressure (or altitude), whether saturation was assumed, and the resulting Γm and Γd. Include mixing ratio and vapor pressures if you discuss moisture impacts.