Compute temperature, pressure, density, and the speed of sound at any geopotential altitude up to 20 km using the International Standard Atmosphere (ISA) model. ISA is the universal reference atmosphere for aircraft performance, instrument calibration, and aerodynamic testing. Inputs and outputs are in SI units.
The International Standard Atmosphere (ISA) is a mathematical model of how temperature, pressure, and density vary with altitude in a calm, dry, average atmosphere. It is the agreed reference against which aircraft performance, engine thrust, altimeters, and airspeed indicators are calibrated and compared. This calculator implements the ISA layers from sea level to 20 km and returns temperature, pressure, density, and the local speed of sound at any altitude you enter.
ISA defines sea-level conditions of 288.15 K (15 °C), 101,325 Pa, and 1.225 kg/m³, then prescribes how these change with geopotential altitude. From 0 to 11,000 m — the troposphere — temperature falls linearly at 6.5 K per kilometre:
T = 288.15 − 0.0065·h (K) p = 101325·(T / 288.15)^5.2561 (Pa)
From 11,000 to 20,000 m — the lower stratosphere — temperature holds constant at 216.65 K (an isothermal layer) and pressure decays exponentially:
p = 22632·exp[ −9.80665·(h − 11000) / (287·216.65) ]
Density follows from the ideal gas law, ρ = p / (R·T) with R = 287 J/kg·K.
The defining feature of the troposphere is its near-constant temperature lapse rate of 6.5 K per kilometre. This is an averaged value: real lapse rates depend on weather, humidity, and time of day, but ISA fixes 6.5 K/km so that everyone designs and certifies to the same standard. The lapse rate is why high-altitude air is cold — at the top of the troposphere it has dropped from 15 °C at sea level to about −56.5 °C — and why the speed of sound, which depends only on temperature, falls with altitude.
The boundary at 11,000 m is the tropopause, where the steady temperature decline of the troposphere stops. Above it, through the lower stratosphere up to about 20 km, ISA holds temperature constant at 216.65 K. In this isothermal layer pressure and density keep falling exponentially but temperature — and therefore the speed of sound — stays put. This is exactly the altitude band where most jet airliners cruise, which is no coincidence: stable cold air and thin density there give efficient high-subsonic cruise.
Aircraft and engine performance depends strongly on air density and temperature, which vary day to day. To compare aircraft fairly and to publish meaningful performance charts, manufacturers quote everything relative to ISA conditions — and deviations are written as "ISA+10" (10 °C warmer than standard) and so on. Altimeters are calibrated to the ISA pressure-altitude relationship, and indicated airspeed is referenced to ISA sea-level density. Knowing the ISA values at an altitude lets you correct measured data to standard conditions, or predict how an aircraft will perform on a hot, high day.
Geopotential altitude accounts for the slight weakening of gravity with height, letting the hydrostatic equations be written with a constant g. It differs from geometric (true) altitude by only a fraction of a percent below 20 km, so for most purposes the two are interchangeable. ISA tables and this calculator are defined in geopotential altitude.
This calculator covers the first two ISA layers: the troposphere (0–11 km) and the lower stratosphere (11–20 km), which span essentially all aircraft operations. Above 20 km ISA defines further layers where temperature rises again, but those altitudes are the domain of high-altitude research and rockets, not conventional aircraft, so they are outside the range here.
The speed of sound a = √(γ·R·T) depends only on temperature, not on pressure or density. Because temperature falls through the troposphere, the speed of sound drops from about 340 m/s at sea level to about 295 m/s at the tropopause, then stays constant through the isothermal stratosphere. This is why a fixed true airspeed corresponds to a higher Mach number as you climb.
Density falls steadily with altitude because pressure drops faster than temperature. At 5,500 m density is roughly half its sea-level value, and at 11 km only about a quarter. Lower density reduces lift, drag, and engine mass flow, which is why aircraft must fly faster (in true airspeed) and engines lose thrust as they climb.
It means the actual temperature is 15 °C above the ISA standard temperature for that altitude. Performance engineers use this shorthand because hotter-than-standard air is less dense, degrading takeoff, climb, and engine performance. To get the conditions for ISA+15, compute the ISA temperature here and add 15 K, then recompute density and the speed of sound from the warmer temperature.