Hadronic events produced in e+e- collisions by the LEP collider and recorded by the OPAL detector are used to form distributions based on the number of reconstructed jets. The data were collected between 1995 and 2000 and corresponds to energy ranges of 130 - 136 GeV and 161 - 207 GeV, together with several periods at a centre of mass energy of 91 GeV. The jet rates are determined using the Durham and Cambridge algorithms. The differential 2-jet rate and the average jet rate are used to determine a value of alpha_s(M_Z) by fitting to an expression in which O(alpha_s^2) calculations are matched to a NLLA prediction.