Potential Temperature Calculator
Find the potential temperature of an air parcel from its actual temperature and pressure using the Poisson equation.
🎈 What is Potential Temperature?
Potential temperature (θ, theta) is the temperature an air parcel would have if it were brought dry adiabatically, without exchanging heat with its surroundings, down (or up) to a standard reference pressure of 1000 hPa. It strips out the effect of pressure changes on temperature so that parcels sampled at different altitudes can be compared on equal terms.
Meteorologists rely on potential temperature constantly, to plot vertical temperature profiles on skew-T log-P diagrams in a way that reveals atmospheric stability at a glance, to identify temperature inversions and mixed layers where theta is nearly constant with height, to track air masses as they move and mix without needing to correct for pressure changes, and as the foundation for equivalent potential temperature, which adds the effect of moisture.
A common point of confusion is expecting potential temperature to match actual temperature. It only does at exactly 1000 hPa. Below that pressure, actual air temperature typically drops with altitude even though potential temperature rises, because the pressure correction factor (P0/P) grows larger than 1 faster than the physical cooling reduces T. This is precisely what makes theta useful, it isolates the part of the temperature change that isn't just due to expansion and compression.
This calculator computes potential temperature directly from actual temperature and pressure using the Poisson equation, the standard formula used throughout operational and academic meteorology, and shows every step of the calculation. The result feeds directly into the equivalent potential temperature calculator, which adds the effect of water vapor mixing ratio.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Mid-Level Parcel at 850 hPa
T = 15°C, P = 850 hPa
Example 2 — Cold Upper-Level Parcel at 500 hPa
T = -5°C, P = 500 hPa
Example 3 — Surface Parcel at the Reference Pressure
T = 25°C, P = 1000 hPa
❓ Frequently Asked Questions
🔗 Related Calculators
What is potential temperature?
Potential temperature (theta) is the temperature an air parcel would have if it were brought dry adiabatically, without gaining or losing heat, down to a standard reference pressure of 1000 hPa. It removes the effect of pressure changes so that parcels at different altitudes can be compared directly.
How do you calculate potential temperature?
Using the Poisson equation: theta = T * (P0/P)^0.286, where T is the actual temperature in Kelvin, P is the actual pressure in hectopascals, P0 is the reference pressure of 1000 hPa, and 0.286 is R/cp for dry air. Convert temperature to Kelvin first by adding 273.15 to the Celsius value.
Why is potential temperature useful?
Potential temperature is conserved during dry adiabatic vertical motion, meaning an air parcel keeps the same theta as it rises or sinks without condensation, even though its actual temperature changes with pressure. This makes it the standard variable meteorologists use to track and compare air masses at different altitudes.
What does R/cp = 0.286 mean?
R is the specific gas constant for dry air (287 J/(kg K)) and cp is the specific heat of dry air at constant pressure (1004 J/(kg K)). Their ratio, about 0.286, is known as the Poisson constant and comes directly from the first law of thermodynamics applied to a dry adiabatic process.
Why does potential temperature increase with altitude in a stable atmosphere?
As pressure drops with altitude, the (P0/P) term in the formula grows larger than 1, so potential temperature rises even if the actual temperature is falling, as it typically does in the troposphere. A profile where theta increases steadily with height indicates a statically stable atmosphere that resists vertical mixing.
Is potential temperature the same as actual temperature at the surface?
Only when the surface pressure is exactly 1000 hPa, since the pressure ratio term (P0/P) then equals 1 and theta equals T. At any other pressure, potential temperature differs from the actual temperature, higher pressures give theta slightly less than T, lower pressures give theta greater than T.
How is potential temperature used in forecasting?
Meteorologists plot potential temperature on skew-T diagrams to assess atmospheric stability, identify temperature inversions, and track air mass boundaries. It's also the base variable for equivalent potential temperature, which adds the effect of moisture and is central to severe weather and convective forecasting.
What is the difference between potential temperature and equivalent potential temperature?
Potential temperature accounts only for the effect of pressure changes on dry air. Equivalent potential temperature goes further, adding the latent heat that would be released if all the water vapor in the parcel condensed, making it a better single measure of the total energy available to a rising, moistening air parcel.
Does potential temperature depend on humidity?
No, this standard (dry) potential temperature formula depends only on temperature and pressure. A separate quantity, virtual potential temperature, accounts for the effect of water vapor on air density, and equivalent potential temperature accounts for latent heat release, but the basic Poisson equation used here ignores moisture.
What input range does this calculator accept?
This calculator accepts air temperatures from -80 to 50 degrees Celsius and pressures from 100 to 1050 hectopascals, covering the full range from the surface up through the tropopause and into the lower stratosphere.