One hertz is exactly 60 revolutions per minute. Both units measure how often something repeats, and the only difference between them is whether the period is a second or a minute — which is why this is the one pair in the category with real content about the units themselves.
About the units
The hertz is one cycle per second, the SI unit of frequency. Revolutions per minute counts complete rotations over sixty times longer. They describe the same physical quantity and are used by different professions: electrical and control engineering in hertz, mechanical engineering and everyday machinery in rpm. A motor running at 3,000 rpm is running at 50 Hz, which is not a coincidence — a two-pole AC motor on a 50 Hz supply turns at 3,000 rpm minus a small slip, and that direct link is why European and American machinery run at different speeds.
The exact factor
The factor is exactly 60. The mains frequency relationship is the practical payoff: a two-pole induction motor turns at 3,000 rpm on 50 Hz and 3,600 rpm on 60 Hz; a four-pole motor at 1,500 and 1,800 respectively. Equipment designed for one supply runs twenty per cent faster or slower on the other, which is why record players had a 50/60 Hz switch and why imported machinery sometimes needs regearing. In angular terms, 1 Hz is 2π radians per second, so 3,000 rpm is 314 rad/s.
Where you meet this conversion
Motors, engines, turbines and rotating machinery of every kind. Vibration analysis is where the two units meet most productively: a fault in a bearing on a shaft turning at 1,800 rpm shows up in the vibration spectrum at 30 Hz and its harmonics, and the diagnosis depends on converting between the two. Hard drive speeds, centrifuge settings and engine idle speeds are all in rpm while the control systems that regulate them compute in hertz.