Potential Temperature Calculator
Potential temperature is the temperature a dry air parcel would reach if moved adiabatically to a reference pressure of 1,000 hPa. Because it strips out the warming and cooling that comes purely from pressure change, it stays constant as a parcel rises or sinks, which makes it central to stability analysis and air-mass identification. This calculator takes the air temperature in degrees Celsius and the actual pressure in hectopascals, applies the Poisson equation with the standard dry-air exponent of 0.2854, and reports potential temperature in both kelvin and Celsius.
Potential temperature formula
T_kelvin = temperature in C + 273.15
theta = T_kelvin * (P_ref / P) ^ 0.2854
theta in C = theta - 273.15
Exponent R/cp = 287.05 / 1004.5 = 0.2854 (dry air)
The reference pressure is conventionally 1,000 hPa. Above the reference level (P below 1,000) the potential temperature exceeds the measured temperature; below it the relation reverses.
Potential temperature context
- Potential temperature is conserved under dry adiabatic vertical motion.
- The standard dry-air exponent kappa is R/cp, about 0.2854.
- If theta increases with height, the layer is statically stable; if it decreases, the layer is unstable.
- The conventional reference pressure is 1,000 hPa, editable here for nonstandard references.
- For moist parcels, equivalent or virtual potential temperature is used instead; this tool covers the dry case.
Potential temperature: frequently asked questions
What is potential temperature?
Potential temperature is the temperature a parcel of dry air would have if brought adiabatically (without heat exchange) to a standard reference pressure of 1,000 hPa. Because it removes the temperature change caused purely by pressure, it is conserved during vertical motion and is a key variable in atmospheric thermodynamics.
What is the Poisson equation for potential temperature?
Potential temperature theta equals T times (reference pressure divided by actual pressure) raised to the power R/cp, where R/cp for dry air is about 0.2854. T and theta are in kelvin, and the reference pressure is conventionally 1,000 hPa.
Why is the temperature input in kelvin internally?
The Poisson relation is a ratio of absolute temperatures, so it must use kelvin. This calculator lets you enter the air temperature in degrees Celsius and converts to kelvin by adding 273.15 before applying the equation, then reports potential temperature in both kelvin and Celsius.
What does the exponent R/cp equal?
For dry air R is the specific gas constant (287.05 J per kg per K) and cp is the specific heat at constant pressure (about 1004.5 J per kg per K), so R/cp is about 0.2854. This is the standard kappa value used in operational meteorology.
When is potential temperature useful?
It is used to assess atmospheric stability, identify air masses, and analyze vertical soundings. If potential temperature increases with height the layer is statically stable; if it decreases with height the layer is unstable and prone to convection.
Official sources
- NOAA NWS JetStream: JetStream weather education.
- American Meteorological Society: Glossary of Meteorology.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.