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Cycles, Hertz & Angular Frequency Table

Convert cycles per second to hertz scales, cycles per minute and corresponding angular rates.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

One cycle per second is one hertz, 60 cycles per minute or 360 degrees per second. Its corresponding angular frequency is exactly 2π radians per second.

Hz = cycles/s; cycles/min = 60 × Hz; angular frequency = 2π × Hz rad/s

Worked example

Enter these known values and leave the other values blank.

Cycles per second
1 cps
Cycles per minute or selected frequency unit
60 cpm
Rotational rate or selected frequency unit
60 RPM
Hertz or selected frequency unit
1 Hz
Kilohertz or selected frequency unit
0.001 kHz
Megahertz or selected frequency unit
0.000001 MHz
Gigahertz or selected frequency unit
1e-9 GHz
Degree rate or selected frequency unit
360 deg/s
Radian rate or selected frequency unit
6.283 rad/s

Assumptions and limitations

  • One full cycle corresponds to 360 degrees or 2π radians. The angular-rate columns describe that same cycle rate.
  • The RPM comparison assumes one counted cycle per revolution. Electrical cycles need not equal shaft revolutions when a motor has multiple pole pairs.
  • Zero and signed values are supported. A negative value can represent a chosen rotation direction; an ordinary count of repeated events is nonnegative.
  • Fields with a unit selector can show another frequency unit. Read the selected unit before interpreting or entering a value.

Common questions

Can I convert in the opposite direction?

Yes. Enter the known value in any editable field. The other representations update in their selected units; changing a unit preserves the physical quantity.

Is one radian per second one hertz?

No. One full cycle spans 2π radians, so 1 rad/s corresponds to 1/(2π) Hz. A hertz counts full cycles per second.

References

Angular frequency uses exactly 2π radians per cycle instead of a rounded 2π factor.

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