Formally, the winding number is defined as follows:

If γ is a closed curve in **C**, and *z*_{0} is a point in **C** not on γ, then the *winding number* of γ with respect to *z*_{0} (alternately called the *index* of γ with respect to *z*_{0}) is defined by the formula:

*I*(γ,*z*_{0}) = 1/(2π*i*) ∫_{γ}1/(*z*–*z*_{0})*dz*