Air gets colder with height, and for the first eleven kilometres it does so almost linearly. That one fact sits behind cabin temperature at cruise, the snow line on a mountain, icing forecasts and engine performance charts. The International Standard Atmosphere pins the behaviour down as an agreed reference so aircraft, instruments and engines can be compared on the same basis anywhere.
Arb Digital builds free physics calculators that each own one job. The live air pressure at altitude calculator is the closest neighbour: its subject is pressure, it inverts to give altitude from a pressure reading, and it reports the standard temperature only as a supporting figure. This page makes temperature the subject and adds what a pressure page has no room for — the ISA deviation for a non-standard day, the dry and saturated adiabatic rates that describe a rising parcel rather than the atmosphere, a custom rate from your own observation, and the freezing level. The live air density calculator takes a temperature as an input, so this page produces the number that one consumes.
What This Temperature at Altitude Calculator Does
The default model is the International Standard Atmosphere, implemented with its published layer structure rather than a single lapse rate stretched over all heights. Below the tropopause temperature falls at 6.5 K per kilometre from 15 °C at mean sea level. Between 11 km and 20 km it is constant at 216.65 K. From 20 km to 32 km it rises again at 1 K per kilometre, then at 2.8 K per kilometre to 47 km, and so on up to the model's ceiling. NASA's Earth Atmosphere Model in metric units presents the same three-part structure, giving the troposphere as T = 15.04 − 0.00649h in degrees Celsius with h in metres and the lower stratosphere as a constant −56.46 °C.
Three other models are available. The dry adiabatic lapse rate of about 9.8 K per kilometre describes how a parcel of unsaturated air cools as it rises and expands — a different question from how the surrounding atmosphere is stratified. The saturated adiabatic rate of roughly 5 K per kilometre applies once that parcel is condensing and releasing latent heat, and it varies with temperature and pressure rather than being a true constant. Custom mode takes any rate, including a negative one for an inversion.
The results give the temperature in Celsius, Fahrenheit and kelvin, the deviation from the standard atmosphere at that height, and the altitude of the freezing level implied by your reference conditions. Temperature scale conversions follow the standard definitions set out by OpenStax in section 13.1, Temperature, of College Physics 2e.
How to Use It
- Enter the altitude and pick its unit. Aviation works in feet, meteorology in metres, and the selector handles both without you converting anything.
- Choose the model. Leave it on ISA unless you specifically want a parcel lapse rate or a rate you measured yourself.
- Set the reference temperature to 15 °C for a standard day, or to the actual reported temperature to get an ISA deviation applied through the whole column.
- Set the reference altitude if your observation came from an elevated station rather than sea level.
- Read the deviation, not just the temperature. ISA plus or minus a number of degrees is the form performance charts use, and it tells you whether the day is unusual.
The Formula: How the Layered Model Works
Within any layer of the standard atmosphere temperature is linear in geopotential height:
T = Tbase − L × (h − hbase), with L the lapse rate for that layer.
The base values are fixed by the standard: 288.15 K at 0 m, 216.65 K at 11,000 m, 216.65 K at 20,000 m, 228.65 K at 32,000 m and 270.65 K at 47,000 m. The corresponding lapse rates are 6.5, 0, −1.0, −2.8 and 0 K per kilometre, where a negative value means temperature rising with height. The calculator walks up the layer list until it finds the one containing your altitude, then applies the linear relation inside it.
Work the default by hand. At 5,000 m you are in the troposphere, so T = 15 − 6.5 × 5 = −17.5 °C. That is 255.65 K, and in Fahrenheit 9/5 × (−17.5) + 32 = 0.5 °F. At 15,000 m the troposphere calculation stops at 11 km, where T = 15 − 6.5 × 11 = −56.5 °C, and the isothermal layer holds that value all the way to 20 km — so 15,000 m is also −56.5 °C. At 25,000 m the temperature has started climbing again: −56.5 + 1.0 × 5 = −51.5 °C.
The freezing level uses the same relation solved for height. With a standard 15 °C surface and a 6.5 K/km lapse rate, 0 °C occurs at 15 ÷ 0.0065 = 2,308 m, or about 7,570 feet. A warm day of 25 °C at the surface pushes that to 3,846 m, roughly 12,600 feet, which is why the snow line and the icing level move so much from day to day.
Why the Standard Atmosphere Is Not the Weather
The ISA is a reference, not a forecast, and this is the single most important thing to understand about it. It defines one fixed vertical profile so that an engine, an airframe or an altimeter can be specified and compared consistently. It does not describe the atmosphere over any particular place on any particular day.
Real soundings differ from it constantly and by large margins. Surface temperature swings tens of degrees between a polar night and a desert afternoon. Tropopause height varies from about 8 km over the poles to 17 km over the tropics, so the isothermal layer does not really begin at a fixed 11 km. Inversions routinely reverse the sign of the lapse rate near the ground, which is why valley fog and trapped pollution behave as they do. None of that is captured by a standard profile, and none of it should be.
For that reason aviation does not plan on standard values. Flight planning uses reported and forecast conditions — the temperature in a METAR or TAF, the winds and temperatures aloft in a forecast product, and the pressure setting for the day. Performance charts are then read at an ISA deviation, which is precisely why this page reports one. An aircraft's book figures at ISA+20 are very different from its figures at ISA, and using the standard value where a reported value exists is a planning error rather than a simplification.
Environmental Lapse Rate Against Adiabatic Lapse Rate
Two different quantities get called "the lapse rate" and confusing them is the commonest conceptual mistake in this subject.
The environmental lapse rate is a property of the air column as it sits: measure temperature at two heights and take the gradient. The ISA figure of 6.5 K per kilometre is a standardised environmental rate. The adiabatic lapse rate belongs to a parcel moving vertically: as it rises it expands against lower pressure and cools without exchanging heat, at about 9.8 K per kilometre while unsaturated.
Comparing the two is how stability is judged. If the environment cools with height faster than a rising parcel does, a displaced parcel stays warmer and less dense than its surroundings and keeps rising — that is instability, and it is what builds convective cloud. If the environment cools more slowly, or warms, the parcel is soon colder and denser than its surroundings and sinks back, which is stability. Once a rising parcel saturates, condensation releases latent heat and slows its cooling to roughly 5 K per kilometre, which is why an atmosphere can be stable for dry parcels and unstable for saturated ones. The cloud base calculator takes the next step, using the convergence of temperature and dew point to find the height where a rising parcel first condenses; this page gives the temperature profile, not the condensation level.
What the Temperature at Altitude Feeds Into
Temperature at height is rarely the end of a calculation. It is the input to density, and density is what determines lift, thrust, drag and engine mass flow. Feed the value from this page into the air density calculator along with the pressure at that height from the air pressure at altitude calculator and you get the moist air density that actually matters. The density altitude calculator compresses those two into a single equivalent standard height, which is the form performance charts want.
Temperature also fixes the speed of sound, which falls with temperature and therefore with height through the troposphere, before flattening out in the isothermal layer — the reason a true airspeed at a given Mach number is lower at altitude. And it sets the relationship between temperature and humidity: the dew point calculator and the relative humidity calculator both need an air temperature, and for simple scale conversions the temperature converter handles Celsius, Fahrenheit, kelvin and Rankine.
One limitation worth naming: the standard atmosphere is defined in geopotential altitude, which folds the small variation of gravity with height into the height coordinate. Below about 20 km the difference from geometric altitude is under a tenth of a per cent, but it is a real distinction and it grows with height.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using 6.5 K/km all the way up — above the tropopause the atmosphere is isothermal and then warms again. A single lapse rate extrapolated to 30 km gives a temperature colder than anywhere in the real atmosphere.
- Confusing the environmental and adiabatic lapse rates — 6.5 K/km describes the standing air column, 9.8 K/km describes a rising parcel. They answer different questions and comparing them is how stability is judged.
- Treating the standard atmosphere as today's weather — it is a fixed reference profile. Real soundings differ by tens of degrees, and flight planning uses reported and forecast conditions, not standard values.
- Forgetting the reference altitude — a temperature reported at a mountain airfield is not a sea-level value, and treating it as one shifts the whole profile.
- Ignoring inversions near the surface — on clear calm nights temperature often rises with height for the first few hundred metres, and no positive lapse rate will reproduce that.
Related Free Tools From Arb Digital
For the pressure at the same height, and for the inverse problem of altitude from a pressure reading, use the air pressure at altitude calculator. The air density calculator turns temperature, pressure and humidity into a density, and the density altitude calculator expresses the result as an equivalent standard height. For the height at which rising air condenses, use the cloud base calculator, and for the moisture side the dew point calculator and relative humidity calculator. Simple scale changes are handled by the temperature converter. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
In the standard atmosphere it falls about 1.98 °C per 1,000 feet, which is the 6.5 K per kilometre lapse rate expressed in aviation units and usually rounded to 2 °C. That holds only up to the tropopause at about 36,000 feet.
It is an agreed reference model of how pressure, temperature and density vary with height, starting from 15 °C and 1013.25 hPa at mean sea level. It exists so that aircraft, engines and instruments can be specified and compared on a common basis, not to describe the weather on a given day.
Because the tropopause marks the top of the convective layer. Above it, in the lower stratosphere, the standard model holds temperature constant at 216.65 K, and higher still absorption of ultraviolet light by ozone makes temperature rise again with height.
The environmental lapse rate is the temperature gradient of the air column as it stands, measured between two heights. The adiabatic lapse rate is the rate at which a parcel of air cools as it rises and expands, about 9.8 K per kilometre when unsaturated and roughly 5 K per kilometre once condensation is releasing latent heat.
It is the difference between the actual temperature and the standard value at the same height, written as ISA+15 or ISA−10. Aircraft performance charts are read at a deviation rather than an absolute temperature, because take-off distance, climb rate and engine output all change with how far the day departs from standard.
Divide the surface temperature in degrees Celsius by the lapse rate in degrees per unit height and add the surface elevation. With a standard 15 °C surface and 6.5 K per kilometre, the 0 °C level sits at about 2,308 metres or 7,570 feet.
Yes. A surface inversion, common on clear calm nights and in valleys, has temperature rising for the first few hundred metres. The standard atmosphere also has temperature increasing with height above 20 kilometres, where ozone absorbs ultraviolet radiation.
No. It is a reference profile only. Real soundings depart from it by large margins, tropopause height varies with latitude, and aviation plans on reported and forecast conditions such as METAR temperatures and forecast winds and temperatures aloft.
This tool is provided for educational and study use. It implements the published layer structure of the International Standard Atmosphere and simple constant-lapse-rate parcel models; it is not a weather forecast, not a sounding, and not an approved flight-planning aid. Real atmospheric profiles differ substantially from the standard model, and operational decisions must be based on reported and forecast conditions and on the approved flight manual for the aircraft.
