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 (0–11 km / 0–36,089 ft): Temperature decreases at 6.5°C per 1000 m (lapse rate). Tropopause / Lower Stratosphere (11–20 km): Temperature is constant at −56.5°C. Upper Stratosphere (20–32 km): Temperature increases slightly (1°C per 1000 m). Most aviation operates in the troposphere; airliners cruise near 35,000 ft (10.7 km) at 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 (−56.5°C) — held constant above.

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 (isothermal): 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. Aircraft lift and engine power drop proportionally.

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 cruise altitude (11 km): a = 295.1 m/s — Mach 1 is slower at altitude, but TAS is higher for same Mach number.

Density Altitude Density altitude is the altitude in the standard atmosphere that has the same density as actual air at the airfield. High temperature or humidity increases density altitude above actual altitude — reducing aircraft performance. This is critical for takeoff performance calculations, especially at high-elevation airports (Denver, Mexico City, Kathmandu).

ISA Deviations (ISA+/−) Real atmosphere deviates from ISA. “ISA +20” means 20°C warmer than standard for that altitude. Aircraft performance charts often show corrections for ISA deviations. Atmospheric sounding balloons (radiosondes) measure actual T, P, humidity profiles daily at thousands of stations worldwide.