The power evolutions of forward and backward Raman Stokes wave versus input pump power in a single mode fiber (SMF) are theoretically analyzed and simulated, which demonstrates an obvious threshold characteristic. A novel definition for Raman threshold in a SMF is proposed. The input pump power corresponding to the maximum of the second-order derivation of the power evolution curve of Raman Stokes wave versus input pump power is defined as the Raman threshold. A practical measurement approach for Raman threshold in a SMF is also demonstrated based on the proposed Raman threshold definition. By simulating and fitting the dependence of Raman threshold on the fiber characteristic parameter, the theoretical threshold equations for the forward and backward Raman scattering in a SMF are obtained, respectively. An experimental setup is established to verify the proposed definition and measurement method. The threshold characteristics for the forward and backward Raman scattering in a SMF with a length of 24 km are studied by using a pulsed pump. The experimental results agree well with the theoretical predictions and verify the effectiveness of the proposed definition and measurement method. The experimental results also demonstrate that the threshold of backward Raman scattering is approximately 24.9% in average higher than that of forward case at different fiber characteristic parameters in a SMF, which is coincident with the theoretical value of 25.3% obtained by simulation. The forward stimulated Raman scattering is relatively easier to occur in a SMF.