Radians per Second Converter

What the Radians per Second Converter does

Radians per Second Converter: 1 rad/s = 9.549296586 rpm, so multiply a radian per second value by 9.549296586 to get revolution per minute, or divide to go back. Example: 1 rad/s = 9.549296586 rpm.

From Value, From and To, this tool derives Result, How it was calculated and Reverse conversion. Edit a field and the answer updates in place.

Typical users are people following a recipe or spec written elsewhere. Two industries often use the same word for slightly different quantities.

There is no back end here. The calculation runs where you are sitting, not on a server somewhere.

The method, a field-by-field reference and a worked example built from the defaults are all on this page.

What do the Radians per Second Converter fields mean?

The Radians per Second Converter uses 3 inputs. Each input has a default that makes sense on its own, so a partial edit still gives a valid result.

How does the Radians per Second Converter work?

Both units are converted through frequency's base unit (Hz), so any of the 7 units in the dropdowns can be paired in either direction without loss of accuracy.

Factors follow the internationally agreed definitions. The inch has been exactly 25.4 mm since 1959, and an exact definition is used wherever one exists. Where a unit is fixed by measurement rather than by agreement, the accepted CODATA or IAU value is used.

Worked example

These are the values the Radians per Second Converter loads by default, and the result it produces from them. Here is the calculation as it stands the moment the page loads.

Angular frequency: radians per second vs. hertz

Ordinary frequency (hertz, cycles per second) and angular frequency (radians per second) describe the same rotation but on different scales: angular frequency ω equals 2π times the frequency in hertz, since one full cycle corresponds to 2π radians, not 1.

Worth knowing

• This factor of 2π (roughly 6.283) is one of the more common sources of error in physics and engineering calculations: plugging a plain hertz value into a formula that expects angular frequency (or vice versa) gives an answer off by that same factor.
• Angular frequency is the natural unit in the mathematics of oscillation and waves (simple harmonic motion, AC circuit analysis, signal processing) because it makes those equations cleaner, even though hertz remains the more intuitive, everyday-facing unit.
• Mains electricity at 50 Hz corresponds to an angular frequency of about 314.16 rad/s, and 60 Hz corresponds to about 376.99 rad/s: figures that appear directly in AC circuit calculations even though nobody describes household electricity that way in conversation.

Definitions: BIPM SI Brochure · NIST reference on units

How to use it

1. Fill in Value.
2. Pick a value for From: the options are Hertz (Hz), Kilohertz (kHz), Megahertz (MHz), Gigahertz (GHz), Terahertz (THz) or Revolution per minute (rpm).
3. Pick a value for To: the options are Hertz (Hz), Kilohertz (kHz), Megahertz (MHz), Gigahertz (GHz), Terahertz (THz) or Revolution per minute (rpm).
4. Watch the results panel as you type: it recalculates on every keystroke.
5. The panel reports Result, How it was calculated and Reverse conversion.
6. Copy Link is the quickest way to send the exact scenario to someone else.

What this tool does not do

• Repeated conversions compound rounding, so convert once from the original value where you can.
• Conversion factors use SI definitions; some industries use their own rounded factors.
• It cannot detect a typo that happens to fall inside the valid range.
• Confirm the units before you act on the output. The arithmetic is only as sound as what went in.

Frequently asked questions

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