Compute the dry adiabatic lapse rate instantly. Predict parcel temperature with altitude or pressure steps. Save tables for reports and verify inputs on-site today.
The dry adiabatic lapse rate is the temperature decrease of an unsaturated air parcel rising adiabatically: Γd = g / cp. Here, g is gravitational acceleration and cp is the specific heat at constant pressure. The altitude method uses T₂ = T₁ − Γd·Δz.
The optional pressure method uses the Poisson relation for a dry ideal-gas parcel: T₂ = T₁ (p₂/p₁)^(R/cp), with R as the gas constant.
| Scenario | g (m/s²) | cp (J/kg·K) | T₁ (°C) | Δz | Γd (K/km) | T₂ (°C) |
|---|---|---|---|---|---|---|
| Standard dry air rise | 9.80665 | 1004 | 20 | 1000 m | 9.77 | 10.23 |
| Moderate hill climb | 9.80665 | 1004 | 30 | 500 m | 9.77 | 25.12 |
| Custom cp sensitivity | 9.81 | 1015 | 25 | 1500 m | 9.66 | 10.51 |
The dry adiabatic lapse rate (DALR) describes how an unsaturated air parcel’s temperature changes as it moves vertically without exchanging heat with its environment. Under ideal dry conditions, the rate depends mainly on gravity and the parcel’s heat capacity. A common reference value is about 9.8 K per kilometer, which helps meteorologists estimate stability and buoyancy.
For near-surface dry air, many texts use g ≈ 9.80665 m/s² and cp ≈ 1004 J/kg·K. These numbers produce Γd ≈ 0.00977 K/m, or 9.77 K/km. If cp increases, the lapse rate decreases. If g increases, the lapse rate increases. Small changes can matter in sensitivity studies.
The altitude method applies T₂ = T₁ − Γd·Δz. For a 1000 m rise with Γd = 9.77 K/km, a parcel starting at 20 °C cools by 9.77 °C to about 10.23 °C. For a descent, the sign reverses, and temperature increases. This simple approach is widely used for quick estimates.
The pressure method uses the Poisson relation T₂ = T₁ (p₂/p₁)^(R/cp). It is useful when pressure levels are known, such as 1000 hPa to 900 hPa. With R ≈ 287.05 J/kg·K and cp ≈ 1004, the exponent κ = R/cp ≈ 0.286. This method aligns with adiabatic thermodynamics for ideal gases.
Potential temperature θ is the temperature a parcel would have at 1000 hPa. For dry adiabatic motion, θ remains nearly constant, making it a powerful diagnostic. In this calculator, θ is computed for both p₁ and p₂ to confirm adiabatic consistency and to support comparisons between different pressure layers.
The DALR applies best to unsaturated air. Once condensation begins, latent heat release reduces the cooling rate, and the moist adiabatic lapse rate becomes appropriate. Dry adiabatic behavior is common in well-mixed daytime boundary layers, descending air, and dry downslope winds.
Aviation uses lapse rates to anticipate icing risk and density altitude effects. Fire weather analysis uses lapse rate signals for plume rise potential. Sounding interpretation often compares observed environmental lapse rates to Γd to infer stability. If the environment cools faster than Γd, convection is more likely.
Results are idealized. Real cp varies with temperature and composition, and g varies slightly with latitude and height. Units must be consistent, especially for Δz and pressure. For best results, enter measured constants when available, enable both methods, and compare outputs for internal consistency and sanity checks.
Using g = 9.80665 m/s² and cp = 1004 J/kg·K gives about 9.77 K/km. Many references round this to roughly 9.8 K/km for practical estimates.
The lapse rate is Γd = g/cp. A larger cp means more energy is needed to change temperature, so the parcel cools more slowly with height.
Use it when you know pressure levels, such as 1000 hPa to 850 hPa. The Poisson relation is a thermodynamic form of the dry adiabatic process.
A negative Δz represents descent. In that case, T₂ = T₁ − Γd·Δz increases, meaning the parcel warms as it compresses while moving downward.
For dry adiabatic motion, potential temperature is nearly conserved. Matching θ values between levels is a quick check that inputs and assumptions are consistent with adiabatic behavior.
Not well. Saturated ascent releases latent heat, reducing the cooling rate. For cloudy, saturated conditions, the moist adiabatic lapse rate is more appropriate.
Start with standard constants and a 1000 m rise. You should see a drop near 9.8 °C. Then enable both methods and confirm the outputs agree within reasonable tolerance.
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