ISA Standard Atmosphere Calculator

What Is the ISA Standard Atmosphere? The International Standard Atmosphere (ISA) is a model of how pressure, temperature, and density change with altitude. It was standardized by ICAO (International Civil Aviation Organization) in 1964 and is used worldwide for aircraft performance, altimetry, and aerospace engineering. The ISA defines standard sea-level conditions: T₀ = 288.15 K (15°C), P₀ = 101,325 Pa (1 atm), ρ₀ = 1.225 kg/m³.

Atmospheric Layers Troposphere (0 to 11 km, or 0 to 36,089 ft): Temperature decreases at 6.5°C per 1000 m (the lapse rate). Tropopause and lower stratosphere (11 to 20 km): Temperature is constant at -56.5°C. Upper stratosphere (20 to 32 km): Temperature increases slightly, 1°C per 1000 m. Most aviation operates in the troposphere; airliners cruise near 35,000 ft (10.7 km), just under the tropopause.

Temperature Model (Troposphere) T(h) = T₀ - L × h = 288.15 - 0.0065 × h (K, where h is in meters) At 11,000 m: T = 288.15 - 71.5 = 216.65 K, which is -56.5°C, and it holds constant above that.

The pilot’s version of the same lapse rate

Aviation quotes the lapse rate as 2°C per 1,000 feet, and flight-planning tools including this site’s true airspeed calculator use it. The exact ISA figure is 6.5°C per 1,000 m, which works out to 1.98°C per 1,000 ft.

That rounding costs about 0.15°C at 8,000 ft and roughly 0.5°C at 25,000 ft, which is well inside the error of the outside air temperature gauge. Use 2 per thousand in the cockpit; use the number this page gives when you need the model itself.

Pressure Model (Troposphere) P(h) = P₀ × (T/T₀)^(g/RL) = 101325 × (T/288.15)^5.2561 Pa Where g = 9.80665 m/s², R = 287.058 J/(kg·K), L = 0.0065 K/m. Above 11 km the layer is isothermal, so pressure falls exponentially instead: P = 22,632 × exp(-g(h-11000)/(RT₁)) Pa.

Air Density ρ = P / (R × T) using the ideal gas law for air. Sea level ISA density: 1.225 kg/m³. At 10,000 m: ρ ≈ 0.414 kg/m³, about 34% of sea level. Lift and engine power drop with it, which is why an airliner at cruise is flying at a much higher true airspeed than its indicated airspeed.

Speed of Sound a = √(γRT) where γ = 1.4 (ratio of specific heats for air) and R = 287.058 J/(kg·K). At sea level ISA: a = 340.3 m/s (661 knots, 1,225 km/h). At 11 km: a = 295.1 m/s (574 knots). Note what that does not depend on: pressure or density. The speed of sound in air is a function of temperature alone, so it stops falling the moment the tropopause stops cooling.

Density Altitude Density altitude is the altitude in the standard atmosphere that has the same density as the actual air at the airfield. Heat and humidity push it above the real elevation, and aircraft performance follows the density rather than the elevation. This matters most at high-elevation airports on hot days: Denver, Mexico City, Kathmandu, Leadville.

ISA Deviations The real atmosphere is never the standard one. “ISA +20” means 20°C warmer than standard for that altitude, and aircraft performance charts are laid out in exactly those terms. Radiosonde balloons measure the actual temperature, pressure and humidity profile twice a day from hundreds of stations, and the answer is different every time.