How this calculator works
A cycle per second (cps) is one complete repetition each second, which is exactly one hertz. The two names describe the same physical quantity, so old equipment ratings in cps and modern ratings in hertz are numerically identical. A revolution per minute is one sixtieth of a hertz, because one minute holds 60 seconds. An angular rate expresses the same rotation in radians or degrees: one full turn is 2 pi radians or 360 degrees, so 1 Hz is 2 pi rad/s and 360 deg/s.
Formula
hertz = cycles per second = revolutions per minute / 60. cycles per minute = hertz x 60. radians per second = hertz x 2 pi. degrees per second = hertz x 360. kHz, MHz, GHz and THz are decimal multiples of hertz by 1,000, 10^6, 10^9 and 10^12.
Worked example
50 cps is 50 Hz, 3,000 RPM, 3,000 cycles per minute, 314.159 rad/s and 18,000 deg/s. A 2.4 GHz signal is 2,400,000,000 Hz, or 2,400,000 kcps in the older cycle-based naming.
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Frequently asked questions
Are cps and hertz the same thing?
Yes. The hertz was adopted in 1960 and replaced cycles per second as the SI name. A 60 cps motor and a 60 Hz motor run at the same speed.
Why is 1 Hz not equal to 1 RPM?
One hertz is one cycle each second, which is 60 cycles each minute. One revolution per minute is only one sixtieth of a hertz, so 1 Hz equals 60 RPM.
When should I use radians per second instead of hertz?
Use rad/s in formulas that contain angular velocity, such as torque times angular speed or the impedance of a capacitor. Convert first: multiply hertz by 2 pi to get rad/s.