ユニバーサル横メルカトル図法
λ = λ 0 + tan − 1  ( sinh  η ′ cos  ξ ′ ) , {\displaystyle \lambda =\lambda _{0}+\tan ^{-1}\left({\frac {\sinh \eta '}{\cos \xi '}}\right),}
k = k 0 A a { 1 + ( 1 − n 1 + n tan  φ ) 2 } cos 2  ξ ′ + sinh 2  η ′ σ ′ 2 + τ ′ 2 , {\displaystyle k={\frac {k_{0}A}{a}}{\sqrt {\left\{1+\left({\frac {1-n}{1+n}}\tan \varphi \right)^{2}\right\}{\frac {\cos ^{2}\xi '+\sinh ^{2}\eta '}{\sigma '^{2}+\tau '^{2}}}}},}
γ = H e m i × tan − 1  ( τ ′ + σ ′ tan  ξ ′ tanh  η ′ σ ′ − τ ′ tan  ξ ′ tanh  η ′ ) . {\displaystyle \gamma =\mathrm {H} \mathrm {e} \mathrm {m} \mathrm {i} \times \tan ^{-1}\left({\frac {\tau '+\sigma '\tan \xi '\tanh \eta '}{\sigma '-\tau '\tan \xi '\tanh \eta '}}\right).}