Standard Atmosphere Calculator

International Standard Atmosphere (ISA) model up to 32 km – temperature, pressure, density, speed of sound. Compliant with ISO 2533.

Model coverage: 0–32 km (0–105,000 ft). Uses standard sea-level values: T₀=288.15 K, P₀=101325 Pa, ρ₀=1.225 kg/m³, lapse rate 6.5 K/km up to 11 km.

Sea level Tropopause (11 km) 20 km 30 km 36,089 ft 45,000 ft
Computing atmosphere...
Atmospheric Properties at Selected Altitude
Temperature
288.15
K / 15.0 °C
Pressure
101325
Pa · 1013.25 hPa
Density
1.225
kg/m³
Speed of Sound
340.3
m/s
Geopotential altitude: 0 m
Pressure altitude (ISA): 0 m
Temperature profile (K)
Selected altitude

Understanding the International Standard Atmosphere (ISA)

The International Standard Atmosphere (ISA) is a static atmospheric model defined by the International Organization for Standardization (ISO 2533). It provides a baseline for pressure, temperature, density, and viscosity at various altitudes, assuming dry air and constant composition. It is fundamental for aircraft performance calculations, altimeter calibration, and engineering design.

Standard Sea Level Conditions (ISA):

  • Pressure P₀ = 101325 Pa = 1013.25 hPa = 29.92 inHg
  • Temperature T₀ = 288.15 K = 15 °C = 59 °F
  • Density ρ₀ = 1.225 kg/m³ = 0.002378 slugs/ft³
  • Speed of sound a₀ = √(γ·R·T₀) = 340.3 m/s = 1116.4 ft/s
  • Specific gas constant for air R = 287.05287 J/(kg·K)
  • Ratio of specific heats γ = 1.40
  • Gravitational acceleration g₀ = 9.80665 m/s² (constant, geopotential altitude)

ISA Layer Structure and Governing Equations

The model is divided into layers with constant temperature gradients (lapse rates). For each layer, the hydrostatic equation combined with the ideal gas law yields exact formulas for pressure and density.

Layer Altitude range (km) Temperature T (K) Lapse rate Γ (K/km) Pressure formula
Troposphere 0 – 11 T = T₀ – Γ₀·h Γ₀ = 6.5 P = P₀·(T/T₀)^(g₀/(R·Γ₀))
Tropopause 11 – 20 T = 216.65 K (constant) 0 P = P₁₁·exp[–g₀/(R·T₁₁)·(h – 11000)]
Stratosphere (lower) 20 – 32 T = 216.65 + Γ₁·(h – 20000) Γ₁ = –1.0 (increase) P = P₂₀·(T₂₀/T)^(g₀/(R·Γ₁))

Note: h is geopotential altitude in meters. The exponent g₀/(R·Γ) is dimensionless; for Γ₀ it equals 5.25588, for Γ₁ it equals –34.1632 (negative due to positive lapse).

Derivation Highlights

Starting from the hydrostatic equation dP/dh = –ρ·g and the ideal gas law ρ = P/(R·T), we obtain dP/P = –g/(R·T) dh. In a layer where T varies linearly with h, integration yields the formulas above. The constants are chosen so that pressure and temperature are continuous at layer boundaries.

ISA Reference Values at Key Altitudes

Altitude (km) Pressure (Pa) Temperature (K) Density (kg/m³) Speed of sound (m/s)
0 101325 288.15 1.2250 340.3
1 89876 281.65 1.1117 336.4
2 79501 275.15 1.0065 332.5
5 54048 255.65 0.7364 320.5
11 22632 216.65 0.3639 295.1
20 5474.9 216.65 0.0880 295.1
30 1197.0 226.65 0.0184 301.7
32 868.0 228.65 0.0132 303.1

Applications of the ISA Model

  • Aviation: Altimeter setting (QNE, QNH), true airspeed (TAS) from indicated airspeed (IAS), aircraft performance charts.
  • Aerospace Engineering: Thrust, drag, and fuel consumption calculations; trajectory simulations.
  • Meteorology: Reduction of pressure to sea level, standard atmosphere for weather balloon data.
  • Engineering: Design of engines, wings, and environmental control systems.

Did you know? The ISA model assumes dry air, but in reality humidity slightly reduces density. For high‑precision work, corrections for humidity and non‑standard temperatures (ΔT) are applied. This calculator uses the pure ISA, which is the international reference.

Further Reading & References

ISO 2533:1975 "Standard Atmosphere"; U.S. Standard Atmosphere, 1976; ICAO Manual of the ICAO Standard Atmosphere (Doc 7488).