A detailed analysis of ground-based CCD UBV photometry and space-based Gaia Data Release 3 (DR3) data for the open clusters King 6 and NGC 1605 was performed. Using the pyUPMASK algorithm on Gaia astrometric data to estimate cluster membership probabilities, we have identified 112 stars in King 6 and 160 stars in NGC 1605 as the statistically most likely members of each cluster. We calculated reddening and metallicity separately using UBV two-color diagrams to estimate parameter values via independent methods. The color excess E(B-V) and photometric metallicity [Fe/H] for King 6 are 0.515(0.030) mag and 0.02(0.20) dex, respectively. For NGC 1605, they are 0.840(0.054) mag and 0.01(0.20) dex. With reddening and metallicity kept constant, we have estimated the distances and cluster ages by fitting PARSEC isochrones to color-magnitude diagrams based on the Gaia and UBV data. Photometric distances are 723(34) pc for King 6 and 3054(243) pc for NGC 1605. The cluster ages are 200(20) Myr and 400(50) Myr for King 6 and NGC 1605, respectively. Mass function slopes were found to be 1.29(0.18) and 1.63(0.36) for King 6 and NGC 1605, respectively. These values are in good agreement with the value of Salpeter (1955). The relaxation times were estimated as 5.8 Myr for King 6 and 60 Myr for NGC 1605. This indicates that both clusters are dynamically relaxed since these times are less than the estimated cluster ages. Galactic orbit analysis shows that both clusters formed outside the solar circle and are members of the young thin-disc population.