The Smith machine (SM) (vertical motion of bar on fixed path; fixed-form exercise) and free weights (FWs) (free-form path) are commonly used strength training modes. Exercisers may need to alternate between types of equipment, depending on testing, training, rehabilitation, and/or the exercisers' goals. The purposes of this study were to compare muscle force production for SM and FWs using a 1 repetition maximum (1RM) for the parallel back squat and supine bench press exercises and to predict the 1RM for one mode from 1RM on the other mode. Men (n = 16) and women (n = 16) alternately completed 1RM testing for squat and bench press using SM and FWs. Analyses of variance (type of equipment x sex) and linear regression models were calculated. A significant difference was found between bench press and squat 1RMs for each mode of equipment for all participants. The squat 1RM was greater for the SM than the FWs; conversely, the bench 1RM was greater for FWs than the SM. When sex was considered, bench 1RM for FWs was greater than SM for men and women. The squat 1RM was greater for SM than FWs for women only. The 1RM on one mode of equipment was the best predictor of 1RM for the other mode. For both sexes, the equation SM bench 1RM (in kilograms) = -6.76 + 0.95 (FW bench 1RM) can be used. For women only, SM squat 1RM (in kilograms) = 28.3 + 0.73 (FW squat 1RM). These findings provide equations for converting between SM and FW equipment for training.