測高公式
∫ p ( z 1 ) p ( z 2 ) d P P = ∫ z 1 z 2 − g R ⋅ T d z . {\displaystyle \ \int _{p(z_{1})}^{p(z_{2})}{\frac {\mathrm {d} P}{P}}=\int _{z_{1}}^{z_{2}}{\frac {-g}{R\cdot T}}\,\mathrm {d} z.}
∫ p ( z 1 ) p ( z 2 ) d P P = − g R ⋅ T a ∫ z 1 z 2 d z . {\displaystyle \ \int _{p(z_{1})}^{p(z_{2})}{\frac {\mathrm {d} P}{P}}={\frac {-g}{R\cdot Ta}}\int _{z_{1}}^{z_{2}}\,\mathrm {d} z.}
ここで Ta は気柱の平均気温である。
この積分により:
ln  ( P ( z 2 ) P ( z 1 ) ) = − g R ⋅ T a ( z 2 − z 1 ) {\displaystyle \ln \left({\frac {P(z_{2})}{P(z_{1})}}\right)={\frac {-g}{R\cdot Ta}}(z_{2}-z_{1})}