Altitude Temperature Calculator
ISA lapse-rate model: temperature vs altitude from sea level to 20 km. Three modes — altitude → temperature, temperature → altitude, and the full 0–20 km profile chart.
ISA temperature profile, 0–20 km. Dashed line marks the 11 km tropopause where cooling stops.
The model
T = −56.5 °C (11 < h ≤ 20 km)
Inverse (troposphere only): h = (15 − T) / 6.5. Below −56.5°C the stratosphere is isothermal, so temperature cannot be inverted to a unique altitude — the calculator says so instead of guessing.
What this tool is (and isn't)
This page answers temperature from altitude via the ISA lapse rate. Related but different tools:
- Air Pressure at Altitude — pressure vs altitude (barometric formula); temperature there is only an input.
- Density Altitude Lab — aviation suite: density altitude, TAS/Mach and performance.
- Air Density Calculator — air density from temperature, pressure and humidity.
Frequently asked questions
What is the formula for temperature at altitude?
The ISA troposphere formula is T = 15 − 6.5 × h, where T is in °C and h is altitude in kilometres. For example, at 5 km: T = 15 − 6.5 × 5 = −17.5°C (0.5°F). Above 11 km the lower stratosphere is isothermal at −56.5°C, so the formula no longer falls with height.
What is the standard lapse rate?
The ISA tropospheric lapse rate is 6.5°C per kilometre, which equals about 3.57°F per 1,000 feet. Real lapse rates vary: dry air cools near 9.8°C/km while moist, cloudy air cools closer to 5°C/km — so ISA is a standard reference, not a weather forecast.
What is the temperature at 10 km altitude?
Under ISA, 10 km gives T = 15 − 6.5 × 10 = −50°C (−58°F). At 11 km, the tropopause, it reaches −56.5°C and then stays constant through the lower stratosphere up to 20 km.
How cold is it at the top of Mount Everest?
Everest summit is 8,848 m (8.848 km). ISA gives T = 15 − 6.5 × 8.848 = −42.512°C, about −42.5°C. Actual summit temperatures are often colder because of wind and weather — ISA is a standard-day model.
Can I convert a temperature back into altitude?
Yes, but only inside the troposphere. The inverse is h = (15 − T) / 6.5, so −17.5°C maps back to exactly 5 km, and −56.5°C maps to the 11 km tropopause. Below −56.5°C the stratosphere is isothermal, so one temperature matches many altitudes and the calculator honestly refuses instead of guessing.
Does the ISA model match real weather?
No. ISA is a fixed standard atmosphere used by aviation and engineering; real temperature profiles shift with weather, season, latitude, and humidity. Actual lapse rates commonly range from about 5 to 9.8°C per km. Use this tool for estimates, planning, and education — not for flight or safety decisions.
What is the tropopause?
The tropopause is the boundary between the troposphere and the stratosphere, at 11 km in the ISA model. Temperature stops decreasing there and holds at −56.5°C. In reality its height varies roughly between 8 km (poles) and 18 km (equator).
Why does temperature drop as altitude increases?
Air pressure falls with height, so rising air expands and cools (adiabatic cooling). The surface also heats the air from below, so the higher — and farther from that heat source — the colder it gets, roughly 6.5°C per kilometre in the standard model.
Free tool by NRTechStudio