Contrail Formation Threshold Calculator
Apply the Schmidt-Appleman criterion to find the temperature below which an aircraft exhaust plume forms a contrail, and whether that contrail persists.
✈️ What is the Contrail Formation Threshold Calculator?
The contrail formation threshold calculator applies the Schmidt-Appleman criterion, the thermodynamic rule that decides whether an aircraft leaves a visible trail behind it. Hot exhaust leaving an engine carries both water vapour and waste heat. As that exhaust mixes with the cold air around it, the mixture traces a straight line in a diagram of water vapour pressure against temperature. If any point on that mixing line touches or crosses saturation with respect to liquid water, tiny droplets condense on soot and sulfate particles, freeze almost instantly, and become the ice crystals you see as a contrail. If the line stays entirely below liquid saturation, no contrail appears no matter how cold the air is.
Meteorologists, flight planners, climate researchers, and aviation students use this calculation in several ways. A forecaster overlays the threshold temperature onto a numerical weather model to predict where contrails will appear on satellite imagery. An operations team testing contrail-avoidance routing checks how many thousand feet of altitude change would take a flight above or below the layer that produces persistent trails. A researcher comparing kerosene with liquid hydrogen recomputes the threshold for each fuel to see how much wider the hydrogen contrail window becomes. A student verifying a textbook chapter reproduces the classic result that at typical cruise levels the threshold sits near -42 degrees Celsius.
The most common misconception is that contrails and persistent contrails are the same thing. They are not, and the calculator reports them separately. Formation is governed by temperature relative to the threshold. Persistence is governed by whether the surrounding air is supersaturated with respect to ice. Air can easily be 65 percent humid with respect to liquid water and simultaneously 107 percent humid with respect to ice at cruise temperatures, because ice has a lower saturation vapour pressure than supercooled water. A second misconception is that more efficient engines produce fewer contrails. The opposite is true thermodynamically: a higher overall propulsion efficiency converts more fuel energy into thrust and leaves less waste heat in the plume, which steepens the mixing line and raises the threshold temperature.
This calculator is useful because the criterion is awkward to evaluate by hand. The threshold at full liquid saturation comes from a fitted polynomial in the logarithm of the mixing-line slope, and the threshold at a lower humidity has no closed-form solution at all, so it must be found numerically. The tool does both, converts pressure altitude to ambient pressure with the International Standard Atmosphere, converts humidity over water into humidity over ice, and plots the whole threshold profile against altitude so you can see at a glance where contrails become possible on a standard day.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Typical Kerosene Cruise, Ice-Supersaturated Air
35,000 ft, ambient −55 °C, 65 % RH over water, η = 0.30, Jet A-1
Example 2 — Lower Cruise Level in Dry Air
28,000 ft, ambient −40 °C, 50 % RH over water, η = 0.30, Jet A-1
Example 3 — A Liquid Hydrogen Aircraft at the Same Flight Level
35,000 ft, ambient −55 °C, 65 % RH over water, η = 0.35, liquid hydrogen
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Schmidt-Appleman criterion?
The Schmidt-Appleman criterion is the thermodynamic condition for contrail formation. As hot, moist engine exhaust mixes with cold ambient air, the mixture follows a straight line in a vapour-pressure versus temperature diagram. If any point on that mixing line reaches or exceeds saturation with respect to liquid water, water droplets condense and freeze into a contrail. If the line stays below liquid saturation, no contrail forms.
What is the contrail formation threshold temperature?
It is the highest ambient temperature at which a contrail can still form for a given pressure, humidity, engine efficiency, and fuel. Below the threshold a contrail forms, above it none forms. At typical cruise conditions for kerosene aircraft, roughly 240 hPa and 30 percent propulsion efficiency, the threshold is near -42 degrees Celsius at full liquid saturation and several degrees colder in drier air.
What is the mixing-line slope G?
G is the slope of the exhaust mixing line in pascals of water vapour pressure per kelvin, calculated as G = EI * cp * p / (epsilon * Q * (1 - eta)). EI is the water vapour emission index in kg per kg fuel, cp is 1004 J per kg per K, p is ambient pressure in pascals, epsilon is 0.622, Q is the specific combustion heat in J per kg, and eta is the overall propulsion efficiency. A larger G means a steeper mixing line and a warmer threshold temperature.
Why does higher engine efficiency make contrails more likely?
Overall propulsion efficiency eta is the share of fuel energy converted into useful thrust work rather than plume heat. A higher eta leaves less waste heat in the exhaust for the same amount of emitted water, which steepens the mixing line, raises G, and therefore raises the threshold temperature. Modern high-bypass engines with eta near 0.35 form contrails at conditions where a 1960s engine with eta near 0.2 would not.
What is the difference between a short-lived and a persistent contrail?
A short-lived contrail forms and then evaporates within seconds to minutes because the ambient air is subsaturated with respect to ice, so the crystals sublimate. A persistent contrail forms in air that is supersaturated with respect to ice, so the crystals keep growing, the trail can last for hours, and it can spread into contrail cirrus. Persistent contrails carry essentially all of aviation's contrail climate forcing.
How is relative humidity over ice calculated from relative humidity over water?
Multiply the relative humidity over water by the ratio of the saturation vapour pressure over liquid water to that over ice at the same temperature, RH_ice = RH_water * e_liquid(T) / e_ice(T). At -55 degrees Celsius that ratio is about 1.65, so 65 percent relative humidity over water corresponds to about 107 percent over ice, which is ice-supersaturated.
What water vapour emission index should I use?
Kerosene jet fuels release about 1.25 kg of water per kg of fuel burned, which is the standard value used in contrail studies. Paraffinic sustainable aviation fuels are slightly more hydrogen-rich at roughly 1.35 kg per kg. Liquid hydrogen releases about 8.94 kg of water per kg of fuel, since water is its only combustion product.
Why do hydrogen aircraft form contrails more easily?
Hydrogen emits about seven times more water per kilogram of fuel than kerosene and has a much higher specific combustion heat, and the net effect on G is a roughly threefold increase. That pushes the threshold temperature from about -42 degrees Celsius to about -31 degrees Celsius at the same cruise altitude and efficiency, so hydrogen aircraft form contrails over a much wider range of conditions, though the resulting crystals are fewer and larger because there is no soot.
Does the calculator use a standard atmosphere for pressure?
Yes. Entering a pressure altitude converts to ambient pressure with the International Standard Atmosphere, using the troposphere power law up to 36,089 ft and the isothermal exponential above it. The chart also plots the ISA temperature profile, so the altitude where the ISA line crosses the threshold line is roughly the lowest altitude at which contrails would form on a standard day.
Can I avoid contrails by flying at a different altitude?
Often yes. Ice-supersaturated regions are usually thin layers a few thousand feet deep, so a modest climb or descent can move a flight out of the layer that produces persistent contrails. Studies suggest that rerouting a small percentage of flights could remove a large share of contrail forcing for a fuel penalty of well under one percent fleet-wide, though the extra fuel adds CO2 that must be weighed against the contrail saving.
How much of aviation's climate impact comes from contrails?
In the Lee et al. (2021) assessment, contrail cirrus contributed about 57 mW per square metre of effective radiative forcing in 2018 against about 34 mW per square metre for aviation CO2, so contrail cirrus was the single largest aviation forcing term. The contrail estimate carries a much wider uncertainty range than the CO2 estimate, which is why it remains an active research area.