Equivalent Potential Temperature Calculator
Find equivalent potential temperature (theta-e) from air temperature, relative humidity, and pressure, combining moisture and pressure effects into one variable.
🌪️ What is Equivalent Potential Temperature?
Equivalent potential temperature (θe, theta-e) is the temperature an air parcel would have if all of its water vapor condensed out, releasing its latent heat into the parcel, and the resulting dry parcel were then brought to a reference pressure of 1000 hPa. It folds the moisture content of the air into the same kind of pressure-normalized temperature that potential temperature already provides for dry air.
Forecasters and atmospheric scientists rely on theta-e heavily, to identify pools of warm, moist, high-energy air near the surface that can fuel severe thunderstorms, to compare the total thermal-plus-moisture energy of air parcels at different altitudes on a single consistent scale, to track air mass boundaries and drylines where theta-e changes sharply over a short distance, and as a near-conserved quantity through both dry and moist adiabatic ascent, useful for following a parcel as it rises and its vapor condenses.
A common point of confusion is treating theta-e as just another name for potential temperature. It is not, potential temperature (θ) only removes the effect of pressure on a dry parcel, while equivalent potential temperature adds the latent heat locked up in water vapor on top of that pressure correction, so θe is always greater than or equal to θ for any parcel with nonzero moisture.
This calculator uses a standard simplified approximation, θe = θ×exp(Lvw / (cpT)), built directly on the mixing ratio and potential temperature calculated by the two calculators it links to. It shows every intermediate step so you can see exactly how moisture and pressure combine into the final theta-e value.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Warm Humid Surface Air
T = 25°C, RH = 60%, P = 1000 hPa
Example 2 — Hot Tropical Air at a Mountain Station
T = 30°C, RH = 80%, P = 950 hPa
Example 3 — Cooler Mid-Level Air
T = 15°C, RH = 50%, P = 850 hPa
❓ Frequently Asked Questions
🔗 Related Calculators
What is equivalent potential temperature?
Equivalent potential temperature (theta-e) is the temperature an air parcel would have if all of its water vapor condensed, releasing its latent heat, and the resulting dry parcel were then brought to a reference pressure of 1000 hPa. It combines the effects of pressure and moisture into a single conserved variable.
How do you calculate equivalent potential temperature?
Using the simplified approximation theta_e = theta * exp(Lv*w / (cp*T)), where theta is the potential temperature, w is the mixing ratio in kg/kg, Lv is the latent heat of vaporization (2.5x10^6 J/kg), cp is the specific heat of dry air (1004 J/(kg K)), and T is the actual temperature in Kelvin.
Why is theta-e higher than potential temperature?
Because the exponential term exp(Lv*w/(cp*T)) is always greater than 1 whenever mixing ratio w is positive, theta-e always exceeds the plain potential temperature theta for any parcel that contains water vapor. The wetter the air, the larger the gap between theta and theta-e.
Why do meteorologists use equivalent potential temperature in severe weather forecasting?
Theta-e is approximately conserved during both dry and moist adiabatic ascent, so it tracks the total energy, thermal plus latent, available to a rising air parcel. Forecasters look for high theta-e air near the surface underneath lower theta-e air aloft, since that vertical gradient signals instability that can fuel strong thunderstorm updrafts.
What is the difference between theta and theta-e?
Potential temperature (theta) accounts only for the pressure change an air parcel would undergo moving to 1000 hPa. Equivalent potential temperature (theta-e) goes further, adding the latent heat that would be released if all the water vapor in the parcel condensed, so it reflects both pressure and moisture effects.
Is this the exact theta-e formula used in professional sounding software?
No, this calculator uses a widely taught simplified approximation, theta_e = theta * exp(Lv*w/(cp*T)), accurate for typical tropospheric temperatures and moisture. Professional software often uses more elaborate formulations (such as Bolton 1980) that adjust for saturation and pseudo-adiabatic effects, giving slightly different results at extreme temperatures or very high moisture.
How does mixing ratio affect theta-e?
Mixing ratio w enters theta-e through the exponential term Lv*w/(cp*T), so higher moisture content directly increases theta-e. Because Lv is a large number (2.5 million J/kg), even modest increases in mixing ratio produce a noticeable rise in equivalent potential temperature.
Why does theta-e rise so quickly at high temperature and humidity?
Warmer air holds exponentially more water vapor at saturation (via the Tetens formula for saturation vapor pressure), so mixing ratio w grows quickly as temperature rises at a fixed relative humidity. Since theta-e depends exponentially on w, the combined effect makes theta-e increase sharply in hot, humid conditions, exactly the kind of environment associated with high instability.
How is theta-e related to CAPE and thunderstorm energy?
Both theta-e and CAPE quantify the energy available for convection, but theta-e is a single-level diagnostic of a parcel's combined thermal and moisture energy, while CAPE integrates the buoyancy of a rising parcel through the full depth of the atmosphere. A large theta-e difference between the surface and mid-levels often corresponds to large CAPE values.
What input range does this calculator accept?
This calculator accepts air temperatures from -10 to 40 degrees Celsius, relative humidity from 1 to 100 percent, and pressure from 500 to 1050 hectopascals, covering typical surface and low-to-mid tropospheric conditions where theta-e is most commonly evaluated.