The U.S. Standard Atmosphere 1976 and the ICAO ISA
The U.S. Standard Atmosphere, 1976 (NOAA / NASA / USAF, NASA-TM-X-74335) is a defined, idealized vertical profile of temperature, pressure, and density for engineering and aviation work. Its lower 32 km is the same model as the ICAO Standard Atmosphere (Doc 7488) and ISO 2533 — the “ISA” used for altimeter calibration, performance charts, and most textbook atmosphere problems.
Sea-level defined values are T0 = 288.15 K (15 °C), P0 = 101,325 Pa, and ρ0 = 1.225 kg/m³. The speed of sound at sea level is 340.29 m/s. The tropopause sits at 11 km geopotential: 216.65 K and 22,632 Pa.
Geopotential and geometric altitude
The model is defined on geopotential altitude H, which absorbs the slight decrease of gravity with height so that the hydrostatic equation can be written with the constant standard gravity g0 = 9.80665 m/s². Geometric altitude Z — the height you would measure with a tape from the surface — is related by the 1976 document’s radius r0 = 6,356,766 m:
H = r0 Z / (r0 + Z)
Z = r0 H / (r0 − H)
The difference is small in the troposphere (about 19 m at 11 km) and grows with height. Always check which quantity a table or a problem statement is using. Flight levels and most aviation “pressure altitude” figures are geopotential, in the sense of the altimeter’s ISA calibration.
The seven temperature layers, to 86 km
From the surface to 86 km geometric (84.852 km geopotential) the molecular-scale temperature is piecewise linear. Layer bases (geopotential) and lapse rates L = dT/dH are:
| H (km) | T (K) | Lapse (K/km) |
|---|---|---|
| 0 | 288.15 | −6.5 |
| 11 | 216.65 | 0 |
| 20 | 216.65 | +1.0 |
| 32 | 228.65 | +2.8 |
| 47 | 270.65 | 0 |
| 51 | 270.65 | −2.8 |
| 71 | 214.65 | −2.0 |
| 84.852 | 186.95 | — |
In a gradient layer, pressure follows P / Pb = (T / Tb)−g0 M0 / (R* L). In an isothermal layer, P / Pb = exp(−g0 M0 (H − Hb) / (R* Tb)). Density comes from the equation of state with the 1976 constants R* = 8,314.32 N·m/(kmol·K) and M0 = 28.9644 kg/kmol. This page holds molecular weight at M0 through 86 km; the official tables apply a small M variation only above 80 km.
Speed of sound and Sutherland viscosity
With γ = 1.40, the speed of sound is a = √(γ R T). Dynamic viscosity uses Sutherland’s law as written in the 1976 document:
μ = β T3/2 / (T + S), with β = 1.458×10−6 kg/(s·m·K1/2) and S = 110.4 K.
Kinematic viscosity is ν = μ / ρ. At sea level these give μ ≈ 1.7894×10−5 kg/(m·s) and ν ≈ 1.4607×10−5 m²/s.
Pressure altitude and density altitude
Pressure altitude is the geopotential height in this model at which the standard pressure equals the pressure you enter. Density altitude is the same idea for density. Both inversions are unique between sea level and 86 km because P and ρ decrease monotonically. For a flight-planning density altitude from a met observation (altimeter, OAT, optional humidity), use the density altitude calculator, which applies the same troposphere constants to a non-standard temperature.
Worked example
At 11 km geopotential, the tropopause: T = 216.65 K, P = 22,632 Pa, ρ = 0.36392 kg/m³, a = 295.07 m/s. Eleven kilometres geometric is still in the troposphere (H ≈ 10,981 m), so the temperature is slightly warmer than 216.65 K — a reminder to pick the right altitude kind.
Frequently asked questions
What is the difference between the ISA and the U.S. Standard Atmosphere 1976?
They are the same model from sea level through 32 km. The 1976 U.S. Standard Atmosphere then continues, with defined temperature layers, through 86 km geometric (and, in the official document, on to 1,000 km with a different formulation). This calculator implements the 1976 layers through 86 km.
Why is 11 km geometric not exactly the tropopause?
The tropopause is defined at 11 km geopotential altitude. Geometric altitude is slightly higher than geopotential altitude at the same point, so 11 km geometric is still in the troposphere (about 10,981 m geopotential) and a little warmer than 216.65 K.
What viscosity law does this page use?
Sutherland’s law as given in the U.S. Standard Atmosphere 1976: μ = β T3/2 / (T + S), with β = 1.458×10−6 kg/(s·m·K1/2) and S = 110.4 K. Kinematic viscosity is μ divided by density.
Can I convert a pressure or a density back to an altitude?
Yes. Enter a pressure to get pressure altitude, or a density to get density altitude, in both geopotential and geometric height, plus the rest of the standard-atmosphere properties at that level. The model is valid from sea level to 86 km geometric.