How this calculator works
Frequency counts complete cycles per second, while angular frequency measures phase advance in radians per second. One cycle advances phase by 2 pi radians. Displacement divided by time gives average angular rate; interpreting it as a periodic frequency assumes the motion repeats uniformly.
Formula
omega = 2 pi f = 2 pi/T = delta theta/delta t; rpm = 60 f.
Worked example
A frequency of 2 Hz corresponds to 12.56637 rad/s, a 0.5 s period and 120 rpm. A 6 rad displacement in 2 s gives 3 rad/s.
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Frequently asked questions
Are hertz and radians per second equal?
No. Multiply hertz by 2 pi to obtain radians per second.
Does period mean one full cycle?
Yes. It is the time required for the complete repeating pattern.
Can frequency be zero?
A static state has zero frequency, but its period is infinite. This finite-period converter requires positive frequency.