Encouraged by the good sales figures of the two single-cylinder models BMW R 2 and BMW R 4, BMW designed the BMW R 3 in 1936. This was another single-cylinder model with a pressed steel frame. However, a capacity of 300 cc gave the model an unfortunate position in the market. It neither had the power output of the BMW R 4 nor the benefit of exemption from the requirement to have a motorcycle licence and no tax to pay which made the BMW R 2 so attractive. With only 740 machines sold, the BMW R 3 fell significantly short of the company's expectations.