Based on the Hagena scaling law, the cluster size in a gas jet is dependent on the equivalent diameter of a conical nozzle. In this work, the effect of the equivalent diameter deq of a conical nozzle on cluster size is separated into the individual effects of the throat diameter d and the half-opening angle α by comparing the Rayleigh scattering signals from gas jets. Nine types of conical nozzles with three different throat diameters (0.3, 0.5, and 0.7 mm) and three different half-opening angles (8.5°, 14.0°, and 24.2°) are used to produce argon gas jets at gas backing pressures from 10 up to 80 bar. The experimental results show that the effect of the throat diameter d is almost the same as that expected by the scaling law. However, the scaling law overestimates the effect of the half-opening angle α. The result is helpful for the precise characterization of cluster size and further understanding the interaction between intense laser and gas clusters.