Standard Atmosphere Density from Altitude (11 to 20 km)

Between 11 and 20 kilometres the standard atmosphere is isothermal: the temperature is fixed at 216.65 K. That makes the density easy, because with the temperature constant the density falls by the same fraction per metre as the pressure does. The formula is the equation of state, $\rho = p/(R\,T)$, with $R$ the specific gas constant of air (the universal gas constant divided by the molar mass), and with the pressure written as its exponential decline from the value at 11 000 m. This continues the library's troposphere page above the tropopause, where an airliner flies, and it is the density the equivalent-airspeed page needs there.

Reading the exponent. $H - 11\,000$ is the height above the bottom of the layer, and $\rho_{11}$ is the density there. The exponent divides $g_0$ times that height by $R\,T$, so each step upward multiplies the density by the same factor, which is why the profile is a pure exponential. Solving for $H$ gives the altitude from a density: $H = 11\,000 - (R\,T/g_0)\ln(\rho\,R\,T/p_{11})$. The altitude is the geopotential altitude that the standard uses.

Worked values. The U.S. Standard Atmosphere 1976 tabulates 0.36392 kg/m³ at 11 km, 0.31083 at 12 km, 0.22675 at 14 km and 0.19367 at 15 km, and the page reproduces each to its printed digits. At 11 000 m the exponent is zero, so the page returns the layer's starting density, 0.36392 kg/m³. Backward, the altitude at which the standard density is 0.19367 kg/m³ is 15 000 m.

Source and limits. The source is the COESA U.S. Standard Atmosphere, 1976 (NASA TM-X-74335, public domain), Table I in metric units, where the temperature is 216.650 K through this layer. The formula applies only between 11 000 m and 20 000 m. It gives the standard density, not the density of the air on a given day: in the real atmosphere the density at a given height changes with the weather and the temperature. A pilot's density altitude is the standard altitude that has the density the air actually has.