Increased speed compliance and reduced speeds are important factors in achieving increased traffic safety since it affects both the number of crashes and the injury severity. Lower speeds reduce the reaction distance leading to greater opportunities to avoid a crash, to reduced impact forces and to less severe injuries in the crash. The aim of this study is to investigate how many lives that could be saved if all drivers complied with the speed limit on the Swedish road network. The study is based on results from extensive speed measurements done on the rural and urban road network in Sweden and crash statistics from the crash data base Strada (Swedish Traffic Data Acquisition). To estimate the traffic safety effects the Exponential model is used. The results show that if everyone kept the speed limit in Sweden, about 50 lives could be saved yearly representing 25 % of all fatalities.