What is potential temperature?

Potential temperature (θ) is the temperature an unsaturated air parcel would reach if brought adiabatically to a reference pressure of 1000 hPa. It is conserved during dry adiabatic vertical motion, making it useful for tracing air parcel origins.

What is the Poisson formula?

The Poisson formula is θ = T × (P₀ / P)^(R/cₚ), where T is absolute temperature in Kelvin, P is the parcel pressure in hPa, P₀ is the reference pressure (1000 hPa), and R/cₚ ≈ 0.2857 for dry air.

Why use 1000 hPa as the reference pressure?

1000 hPa is approximately mean sea-level pressure and is the conventional reference in atmospheric science. It provides a consistent baseline for comparing air parcels at different altitudes.

Can I enter temperature in Celsius?

Yes. The tool accepts both Kelvin and Celsius. When Celsius is selected, the value is converted to Kelvin internally before applying the Poisson formula, so results are always accurate.

What is a typical range for potential temperature?

Near the surface, potential temperature is close to actual temperature (around 280–310 K in the mid-latitudes). In the stratosphere, it can exceed 400 K. A vertical increase in potential temperature indicates a stable atmosphere.

Does this account for moisture?

No. This calculator computes dry potential temperature only. For moist air, equivalent potential temperature (θ e ) would be needed, which accounts for latent heat release.

Potential Temperature Calculator

Name: Potential Temperature Calculator
Availability: InStock
Author: Nham Vu

Enter air temperature and pressure to compute potential temperature using the Poisson formula, the key quantity in atmospheric thermodynamics.

Input Parameters

Air Temperature

Temperature of the air parcel at its current location.

Pressure

hPa

Atmospheric pressure at the parcel's current altitude. Surface is ~1013 hPa.

Reference pressure (P₀): 1000 hPa (WMO standard)

Result

Enter values and click Calculate to see the result.

Poisson Formula

θ = T × (P₀ / P)^R/c_p

T = actual temperature (K) P = parcel pressure (hPa) P₀ = 1000 hPa (reference) R/c_p = 0.2857 (dry air)

Interpreting θ

dθ/dz > 0 — potential temperature increases with altitude: stable atmosphere.
dθ/dz = 0 — dry adiabatic lapse rate: neutral stability.
dθ/dz < 0 — potential temperature decreases with altitude: absolutely unstable.

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Summary

Enter air temperature and pressure to compute potential temperature using the Poisson formula, the key quantity in atmospheric thermodynamics.

How it works

Enter the actual air temperature (in Kelvin or Celsius — tool converts automatically).
Enter the actual pressure at the parcel's location in hPa (millibars).
The calculator applies the Poisson formula with a reference pressure of 1000 hPa.
The result shows potential temperature in both Kelvin and Celsius.
Use the worked example panel to understand what different values mean physically.

Use cases

Verify atmospheric stability by comparing potential temperature at different altitudes.
Track the origin of air masses during weather analysis.
Calculate theta for radiosonde (weather balloon) data.
Teach atmospheric thermodynamics in university courses.
Cross-check numerical weather model output.
Quickly test different T and P scenarios during field studies.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu