The ion current to a cylindrical or spherical Langmuir probe can be represented as ii = I(0)a(- X)(b), where I-0 is the ion flux to the edge of the probe sheath, X is the dimensionless probe potential, and a and b are parameters depending on the ratio of the probe radius r(p) to the Debye length lambda (D) and the probe geometry. We present analytical expressions for a and b which are valid over a wide range of r(p) /lambda (D). We also discuss under which conditions the end of a cylindrical probe contributes appreciably to the probe current. Neglecting the end effect may lead to a significant overestimate of the ion density.