Dry Adiabatic Lapse Rate Calculator

Calculate how much a rising, unsaturated air parcel cools as it climbs, using the dry adiabatic lapse rate of about 9.8 degrees C per kilometer.

🌡️ Dry Adiabatic Lapse Rate Calculator
Surface Temperature
°C
-20°C45°C
Altitude Gain
0 m5000 m
Temperature at Altitude
—
Total Temperature Drop
—
Dry Adiabatic Lapse Rate
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🌡️ What is the Dry Adiabatic Lapse Rate?

The dry adiabatic lapse rate is the rate at which a rising parcel of unsaturated air cools as it climbs through the atmosphere, approximately 9.8 degrees Celsius for every kilometer of altitude gained. As air rises, it moves into progressively lower atmospheric pressure and expands, and because this expansion happens without exchanging heat with its surroundings (an adiabatic process), the energy needed to do that expansion work comes from the parcel's own internal thermal energy, cooling it steadily and predictably as it climbs.

Meteorologists, pilots, glider pilots, and atmospheric scientists use the dry adiabatic lapse rate constantly. It is fundamental to forecasting thunderstorm potential, assessing atmospheric stability, understanding why mountain slopes create localized warm, dry winds like the Foehn or Chinook, and predicting how high convective clouds can grow before their rising air cools to the point where buoyancy runs out. Weather balloon soundings are routinely plotted against the dry adiabatic lapse rate on thermodynamic diagrams called Skew-T log-P diagrams to diagnose instability.

A common misconception is that rising air cools because it "loses heat" to the colder air above it. In reality, the dry adiabatic process assumes zero heat exchange with the surroundings, the cooling comes entirely from the parcel doing work as it expands against lower external pressure, not from heat transfer. Another important distinction is that "dry" here refers to the absence of active condensation, not to zero humidity, a very humid but unsaturated parcel still follows the dry adiabatic rate right up until water vapor inside it begins to condense.

This calculator lets you enter a surface temperature and an altitude gain to instantly see the resulting temperature, the total temperature drop, and the lapse rate itself, useful for classroom demonstrations, quick stability checks, or simply building intuition for how much cooler it gets as you climb a mountain or fly in an unpressurized aircraft.

📐 Formula

Γd  =  g / cp  ≈  9.8 °C/km     T(z)  =  T0 − Γdz
g = standard gravity = 9.80665 m/s²
cp = specific heat of dry air at constant pressure = 1004.68 J/(kg·K)
T0 = surface (starting) temperature
z = altitude gained (meters)
Example: T0 = 25°C, z = 1,000 m: Γd ≈ 9.761°C/km, T(z) ≈ 15.24°C

Per the American Meteorological Society Glossary and standard atmospheric physics references, this rate applies to unsaturated (dry) air parcels only.

📖 How to Use This Calculator

Steps

1
Enter the surface temperature - Type the starting temperature at ground level in degrees Celsius.
2
Enter the altitude gain - Type how high the air parcel rises, choosing meters or kilometers.
3
Click Calculate - Press Calculate to see the temperature at that altitude, the total temperature drop, and the dry adiabatic lapse rate itself.

💡 Example Calculations

Example 1 — A Warm Morning, Rising 1 km

Surface temperature = 25°C, altitude gain = 1,000 m (1 km)

1
Lapse rate: Γd = g/cp = 9.80665 / 1004.68 ≈ 0.009761 °C/m ≈ 9.761 °C/km
2
Temperature drop = 0.009761 °C/m × 1,000 m ≈ 9.76 °C
3
T(z) = T0 − drop = 25 − 9.76 ≈ 15.24 °C
Temperature at 1,000 m ≈ 15.24°C, a drop of 9.76°C from the surface
Try this example →

Example 2 — A Cool Day, Climbing to 3 km

Surface temperature = 15°C, altitude gain = 3,000 m (3 km)

1
Temperature drop = 0.009761 °C/m × 3,000 m ≈ 29.28 °C, three times the drop of Example 1 since altitude tripled
2
T(z) = 15 − 29.28 ≈ −14.28 °C, well below freezing despite a mild surface temperature
3
This illustrates why mountain summits and cruising-altitude aircraft cabins (before pressurization and heating) are dramatically colder than the ground below
Temperature at 3,000 m ≈ −14.28°C, a drop of 29.28°C from the surface
Try this example →

Example 3 — A Short Hill Climb

Surface temperature = 30°C, altitude gain = 500 m

1
Temperature drop = 0.009761 °C/m × 500 m ≈ 4.88 °C, half the drop of Example 1 since altitude gain is half as much
2
T(z) = 30 − 4.88 ≈ 25.12 °C
3
Even a modest 500 m climb, roughly the height of a tall hill or a short mountain trail, produces a noticeable, measurable cooling effect
Temperature at 500 m ≈ 25.12°C, a drop of 4.88°C from the surface
Try this example →

❓ Frequently Asked Questions

What is the dry adiabatic lapse rate?+
The dry adiabatic lapse rate is the rate at which a rising parcel of unsaturated (dry, meaning no condensation happening) air cools as it climbs through the atmosphere, about 9.8 degrees Celsius for every kilometer of altitude gained. It comes from dividing standard gravity by the specific heat of dry air at constant pressure, Gamma_d = g / c_p.
What is the formula for the dry adiabatic lapse rate?+
Gamma_d equals g divided by c_p, where g is standard gravity (9.80665 m/s squared) and c_p is the specific heat of dry air at constant pressure (1004.68 J per kg per K). This gives Gamma_d approximately 0.00976 K per meter, or about 9.76 to 9.8 degrees C per kilometer, commonly rounded to 9.8 degrees C/km in textbooks.
How do I calculate temperature at a given altitude?+
Use T(z) = T0 minus Gamma_d times z, where T0 is the surface (starting) temperature, Gamma_d is the dry adiabatic lapse rate (about 0.00976 degrees C per meter), and z is the altitude gained in meters. For example, starting at 25 degrees C and rising 1,000 meters gives a temperature of about 15.24 degrees C.
Why does rising air cool even though nothing is removing heat from it?+
As a parcel of air rises, it moves into a region of lower atmospheric pressure and expands. That expansion requires the parcel to do work pushing against its surroundings, and since the process happens quickly enough that no heat is exchanged with the environment (adiabatic), the energy for that work comes from the parcel's own internal (thermal) energy, cooling it in the process.
What does 'dry' mean in dry adiabatic lapse rate?+
Dry does not mean zero humidity, it means the air parcel is unsaturated, meaning no water vapor is currently condensing into liquid droplets inside it. As soon as a rising parcel cools to its dew point and water starts condensing, latent heat is released, slowing the cooling rate to the smaller moist adiabatic lapse rate, typically around 4 to 7 degrees C per km depending on temperature and moisture content.
How does the dry adiabatic lapse rate compare to the average observed atmospheric lapse rate?+
The dry adiabatic lapse rate (about 9.8 degrees C/km) is steeper than the internationally standardized average environmental lapse rate (about 6.5 degrees C/km) used in the International Standard Atmosphere. The difference exists because real atmospheric air is rarely unsaturated all the way up, most rising air eventually condenses and switches to the shallower moist adiabatic rate.
Why do the constants g and cp determine this specific cooling rate?+
For an adiabatic process (no heat exchange) in a hydrostatic atmosphere, the first law of thermodynamics combined with the hydrostatic equation shows that temperature change with height depends only on how much work is done against gravity per unit mass (proportional to g) versus how much energy is needed to change the air's temperature (c_p). Dividing these two quantities gives the lapse rate directly, independent of the starting temperature or pressure.
Does the dry adiabatic lapse rate change with altitude or location?+
The dry adiabatic lapse rate itself is essentially constant, since both g and c_p barely change across the altitude ranges relevant to weather (the troposphere). Small variations in g with latitude and altitude exist but are negligible for practical purposes, which is why 9.8 degrees C/km is treated as a fixed constant in meteorology.
How is the dry adiabatic lapse rate used to assess atmospheric stability?+
Meteorologists compare the dry adiabatic lapse rate to the environment's actual observed lapse rate. If the environment cools with altitude faster than the dry adiabatic rate, a displaced parcel stays warmer (and less dense) than its surroundings as it rises, so it keeps accelerating upward, an unstable atmosphere. If the environment cools more slowly, rising parcels cool faster than their surroundings and sink back, a stable atmosphere.
Can this calculator be used for descending air as well as rising air?+
Yes, in principle the same linear relationship applies symmetrically, a descending unsaturated parcel warms at the same 9.8 degrees C per kilometer rate it would have cooled at while rising, this is exactly how strong, warm, dry downslope winds like the Foehn or Chinook form on the lee side of mountain ranges.
What altitude does this calculator work up to?+
This calculator applies the linear dry adiabatic formula, which is a good approximation throughout the troposphere (roughly the lowest 10 to 12 kilometers of the atmosphere) where g and c_p stay nearly constant. It is not intended for stratospheric or higher-altitude calculations, where different physics and temperature structure dominate.
Tags: Dry Adiabatic Lapse Rate Calculator Temperature vs Altitude Calculator Adiabatic Cooling Rate Atmospheric Lapse Rate Formula Air Parcel Temperature Calculator Calculator Formula Free Online

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What is the dry adiabatic lapse rate?

The dry adiabatic lapse rate is the rate at which a rising parcel of unsaturated (dry, meaning no condensation happening) air cools as it climbs through the atmosphere, about 9.8 degrees Celsius for every kilometer of altitude gained. It comes from dividing standard gravity by the specific heat of dry air at constant pressure, Gamma_d = g / c_p.

What is the formula for the dry adiabatic lapse rate?

Gamma_d equals g divided by c_p, where g is standard gravity (9.80665 m/s squared) and c_p is the specific heat of dry air at constant pressure (1004.68 J per kg per K). This gives Gamma_d approximately 0.00976 K per meter, or about 9.76 to 9.8 degrees C per kilometer, commonly rounded to 9.8 degrees C/km in textbooks.

How do I calculate temperature at a given altitude?

Use T(z) = T0 minus Gamma_d times z, where T0 is the surface (starting) temperature, Gamma_d is the dry adiabatic lapse rate (about 0.00976 degrees C per meter), and z is the altitude gained in meters. For example, starting at 25 degrees C and rising 1,000 meters gives a temperature of about 15.24 degrees C.

Why does rising air cool even though nothing is removing heat from it?

As a parcel of air rises, it moves into a region of lower atmospheric pressure and expands. That expansion requires the parcel to do work pushing against its surroundings, and since the process happens quickly enough that no heat is exchanged with the environment (adiabatic), the energy for that work comes from the parcel's own internal (thermal) energy, cooling it in the process.

What does 'dry' mean in dry adiabatic lapse rate?

Dry does not mean zero humidity, it means the air parcel is unsaturated, meaning no water vapor is currently condensing into liquid droplets inside it. As soon as a rising parcel cools to its dew point and water starts condensing, latent heat is released, slowing the cooling rate to the smaller moist adiabatic lapse rate, typically around 4 to 7 degrees C per km depending on temperature and moisture content.

How does the dry adiabatic lapse rate compare to the average observed atmospheric lapse rate?

The dry adiabatic lapse rate (about 9.8 degrees C/km) is steeper than the internationally standardized average environmental lapse rate (about 6.5 degrees C/km) used in the International Standard Atmosphere. The difference exists because real atmospheric air is rarely unsaturated all the way up, most rising air eventually condenses and switches to the shallower moist adiabatic rate.

Why do the constants g and cp determine this specific cooling rate?

For an adiabatic process (no heat exchange) in a hydrostatic atmosphere, the first law of thermodynamics combined with the hydrostatic equation shows that temperature change with height depends only on how much work is done against gravity per unit mass (proportional to g) versus how much energy is needed to change the air's temperature (c_p). Dividing these two quantities gives the lapse rate directly, independent of the starting temperature or pressure.

Does the dry adiabatic lapse rate change with altitude or location?

The dry adiabatic lapse rate itself is essentially constant, since both g and c_p barely change across the altitude ranges relevant to weather (the troposphere). Small variations in g with latitude and altitude exist but are negligible for practical purposes, which is why 9.8 degrees C/km is treated as a fixed constant in meteorology.

How is the dry adiabatic lapse rate used to assess atmospheric stability?

Meteorologists compare the dry adiabatic lapse rate to the environment's actual observed lapse rate. If the environment cools with altitude faster than the dry adiabatic rate, a displaced parcel stays warmer (and less dense) than its surroundings as it rises, so it keeps accelerating upward, an unstable atmosphere. If the environment cools more slowly, rising parcels cool faster than their surroundings and sink back, a stable atmosphere.

Can this calculator be used for descending air as well as rising air?

Yes, in principle the same linear relationship applies symmetrically, a descending unsaturated parcel warms at the same 9.8 degrees C per kilometer rate it would have cooled at while rising, this is exactly how strong, warm, dry downslope winds like the Foehn or Chinook form on the lee side of mountain ranges.

What altitude does this calculator work up to?

This calculator applies the linear dry adiabatic formula, which is a good approximation throughout the troposphere (roughly the lowest 10 to 12 kilometers of the atmosphere) where g and c_p stay nearly constant. It is not intended for stratospheric or higher-altitude calculations, where different physics and temperature structure dominate.

📌 Quick Tips

💡The dry adiabatic lapse rate, about 9.8 degrees C per kilometer, applies only to unsaturated air. Once water vapor condenses inside a rising parcel, the rate slows to the smaller moist adiabatic lapse rate because condensation releases latent heat.
💡This rate comes directly from two constants, standard gravity (9.80665 m/s squared) and the specific heat of dry air at constant pressure (1004.68 J per kg per K), it is not an empirically fitted number.
💡A rising, unsaturated air parcel cools purely because it expands as atmospheric pressure drops with altitude, doing work on its surroundings, not because it loses heat to the environment (the process is adiabatic, meaning no heat exchange).
💡The dry adiabatic lapse rate is steeper than the observed average atmospheric lapse rate (about 6.5 degrees C per km), because most real atmospheric air eventually reaches saturation and switches to the shallower moist rate as it continues rising.
💡Pilots, glider enthusiasts, and meteorologists use the dry adiabatic lapse rate to assess atmospheric stability, comparing a parcel's adiabatic cooling rate to the environment's actual lapse rate determines whether rising air keeps rising (unstable) or sinks back (stable).