Editing Barometric formula (section)

==Density equations==
{{further|Atmospheric density}}

The expressions for calculating density are nearly identical to calculating pressure.  The only difference is the exponent in Equation 1.

There are two equations for computing density as a function of height. The first equation is applicable to the standard model of the [[troposphere]] in which the temperature is assumed to vary with altitude at a [[lapse rate]] of <math>L_b</math>; the second equation is applicable to the standard model of the [[stratosphere]] in which the temperature is assumed not to vary with altitude.

Equation 1:
<math display="block">\rho = \rho_b \left[\frac{T_b - (h-h_b) L_b}{T_b}\right]^{\left(\frac{g_0 M}{R^*  L_b}-1\right)}</math>

which is equivalent to the ratio of the relative pressure and temperature changes

<math display="block">\rho = \rho_b \frac{P}{T} \frac{T_b}{P_b} </math>

Equation 2:
<math display="block">\rho =\rho_b \exp\left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right]</math>

where
*<math>{\rho}</math> = mass density (kg/m<sup>3</sup>)
*<math>T_b</math> = standard temperature (K)
*<math>L</math> = standard temperature lapse rate (see table below) (K/m) in [[International Standard Atmosphere|ISA]]
*<math>h</math> = height above sea level (geopotential meters)
*<math>R^*</math> = [[universal gas constant]] 8.3144598&nbsp;N·m/(mol·K)
*<math>g_0</math> = gravitational acceleration: 9.80665&nbsp;m/s<sup>2</sup>
*<math>M</math> = molar mass of Earth's air: 0.0289644&nbsp;kg/mol

or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.):<ref name="conversion"/>
*<math>{\rho}</math> = mass density ([[slug (unit)|slug]]/ft<sup>3</sup>)
*<math>{T_b}</math> = standard temperature (K)
*<math>{L}</math> = standard temperature lapse rate (K/ft)
*<math>{h}</math> = height above sea level (geopotential feet)
*<math>{R^*}</math> = universal gas constant: 8.9494596×10<sup>4</sup>&nbsp;ft<sup>2</sup>/(s·K)
*<math>{g_0}</math> = gravitational acceleration: 32.17405&nbsp;ft/s<sup>2</sup>
*<math>{M}</math> = molar mass of Earth's air: 28.9644&nbsp;lb/lb-mol

The value of subscript ''b'' ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. The reference value for ''ρ<sub>b</sub>'' for ''b'' = 0 is the defined sea level value, ''ρ''<sub>0</sub> = 1.2250&nbsp;kg/m<sup>3</sup> or 0.0023768908&nbsp;slug/ft<sup>3</sup>. Values of ''ρ<sub>b</sub>'' of ''b'' = 1 through ''b'' = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when ''h'' = ''h''<sub>''b''+1</sub>.<ref name=USSA1976/>

In these equations, ''g''<sub>0</sub>, ''M'' and ''R''<sup>*</sup> are each single-valued constants, while ''ρ'', ''L'', ''T'' and ''h'' are multi-valued constants in accordance with the table below. The values used for ''M'', ''g''<sub>0</sub> and ''R''<sup>*</sup> are in accordance with the [[U.S. Standard Atmosphere]], 1976, and that the value for ''R''<sup>*</sup> in particular does not agree with standard values for this constant.<ref name="USSA1976"/>

{| class="wikitable"
|-
! rowspan="2"|Subscript ''b''
! colspan="2"|Geopotential
height above MSL
(h)
! colspan="2"|Mass Density (<math>\rho</math>)
! rowspan="2"|Standard Temperature (''T''')<br> (K)
! colspan="2"|Temperature Lapse Rate (''L'')
|-
! (m) !! (ft)!! (kg/m<sup>3</sup>) !! (slug/ft<sup>3</sup>) !! (K/m) !! (K/ft)
|-
| align="center" |0
| align="center" |0
| align="center" |0
| align="center" |1.2250
| align="center" |{{val|2.3768908|e=-3}}
| align="center" |288.15
| align="center" |0.0065
| align="center" |0.0019812
|-
| align="center" |1
| align="center" |11 000
| align="center" |36,089.24
| align="center" |0.36391
| align="center" |{{val|7.0611703|e=-4}}
| align="center" |216.65
| align="center" |0.0
| align="center" |0.0
|-
| align="center" |2
| align="center" |20 000
| align="center" |65,616.79
| align="center" |0.08803
| align="center" |{{val|1.7081572|e=-4}}
| align="center" |216.65
| align="center" |-0.001
| align="center" |-0.0003048
|-
| align="center" |3
| align="center" |32 000
| align="center" |104,986.87
| align="center" |0.01322
| align="center" |{{val|2.5660735|e=-5}}
| align="center" |228.65
| align="center" |-0.0028
| align="center" |-0.00085344
|-
| align="center" |4
| align="center" |47 000
| align="center" |154,199.48
| align="center" |0.00143
| align="center" |{{val|2.7698702|e=-6}}
| align="center" |270.65
| align="center" |0.0
| align="center" |0.0
|-
| align="center" |5
| align="center" |51 000
| align="center" |167,322.83
| align="center" |0.00086
| align="center" |{{val|1.6717895|e=-6}}
| align="center" |270.65
| align="center" |0.0028
| align="center" |0.00085344
|-
| align="center" |6
| align="center" |71 000
| align="center" |232,939.63
| align="center" |0.000064
| align="center" |{{val|1.2458989|e=-7}}
| align="center" |214.65
| align="center" |0.002
| align="center" |0.0006096
|}