Neglecting the electron mass (i.e. me/m μ << 1 ), and without electromagnetic radiative corrections, the "total decay width" of the μ is given by:
                GF mμ5
   Γμ   =   ---------- ,
                192π3

and the lifetime    τ = 1/&Gammaμ

(this is in "natural units", where ћ = c = 1)
(in these units, every quantity can be expressed in terms of powers of energy; &Gammaμ has dimension of energy, time and length have dimension (energy)-1
To get an expression in more familiar units, replace GF by GF /(ћc)3 and m by mc2.

                GF/(ћc)3  (mμc2)5
   Γμ   =   -----------------------.
                       192π3

In these units, the relation between τ and Γμ is τ = ћ/Γμ.

Note:
        mμ = 105.658 MeV/c2
        ћc = 197.326 MeV fm
        GF/(ћc)3 = 1.16637(1) x 10-5 GeV-2
        GF = 8.962 x 10-5 MeV fm3