Equivalent Potential Temperature Calculator
Estimate equivalent potential temperature (θₑ) from temperature, pressure and mixing ratio.
About the Equivalent Potential Temperature Calculator
Equivalent potential temperature (θₑ) is the temperature a parcel would reach if all its water vapor condensed and it descended to 1000 hPa. It is conserved during moist adiabatic processes and is a key stability indicator.
$$ \theta_e \approx \theta\,\exp\!\left(\frac{L_v\,w}{c_p\,T}\right) $$
How to use
Enter temperature (°C), pressure (hPa) and mixing ratio (g/kg), then click Calculate.
Worked example
20 °C, 850 hPa, 10 g/kg → θₑ ≈ 330 K.
How to use this calculator
- Enter the air temperature, pressure, and mixing ratio.
- Make sure the temperature is in kelvin and the pressure is in hPa.
- Click calculate to estimate equivalent potential temperature.
- Read the result and compare it with the formula and example if you need a check.
The formula explained
$$ \theta_e = \theta \exp\left(\frac{L_v r}{c_p T}\right), \text{ where } \theta = T\left(\frac{1000}{p}\right)^{R_d/c_p} $$
- \(\theta_e\) = equivalent potential temperature
- \(\theta\) = potential temperature
- \(T\) = temperature in kelvin
- \(p\) = pressure in hPa
- \(r\) = mixing ratio in kg per kg
- \(L_v\) = latent heat of vaporization
- \(c_p\) = specific heat of dry air at constant pressure
- \(R_d\) = gas constant for dry air
Step by step method
- Start with the air temperature in kelvin, because the calculation uses absolute temperature.
- Use the pressure in hPa to find the potential temperature part of the formula.
- Combine that with the mixing ratio to account for moisture effects.
- The calculator returns the estimated equivalent potential temperature, \(\theta_e\).
Worked example
Here is a simple weather example using warm, moist air near the surface.
- Use \(T = 300\,\text{K}\), \(p = 1000\,\text{hPa}\), and \(r = 0.010\,\text{kg/kg}\).
- First compute potential temperature: \(\theta = 300\left(\frac{1000}{1000}\right)^{R_d/c_p} = 300\,\text{K}\).
- Then apply the moisture term to get an equivalent potential temperature of about \(324\,\text{K}\).
Answer. Equivalent potential temperature is about 324 K.
Tips and common mistakes
- Use kelvin for temperature, not Celsius.
- Keep pressure in hPa, since that is the usual input for this formula.
- Check that mixing ratio is entered as kg per kg unless the tool says otherwise.
- Remember that equivalent potential temperature is higher when air is warmer or more humid.
Frequently asked questions
What is θₑ used for?+
Diagnosing atmospheric instability and tracking air masses in convection.
Why is it conserved?+
It accounts for latent heat release, so it stays constant through condensation and evaporation.
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