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Converting between revolutions per minute (RPM) and revolutions per second (RPS) is not straightforward for me in Mathematica.

I know that $1\; \text{RPM} = \frac{2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}$. To get RPS then, it is just a matter to remove the factor of $60$ in the denominator.

Taking a numerical example, I can convert say $500$ RPM to Hertz as follows:

$[\text{Convert}[\frac{500\; \times\; 2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}, \text{Hertz}],9]$

which gives me $52.3597776\; \text{Hertz}$

But now if I want to convert $500$ RPM to RPS, the following does not work as in the Convert command, the second argument has also numerical values in it:

$[\text{Convert}[\frac{500\; \times\; 2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}, \frac{2\; \times\; \Pi\; \text{Radian}}{\text{Second}}],9]$

which gives me as output: $\frac{52.3598776\; \text{Radian}}{\text{Second}}$ instead of the desired answer of about $8.33\:$ . The factor of $2\; \Pi$ is the troublemaker.

So how to do an appropriate conversion from RPM to RPS?


I am using version 9.

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closed as too broad by m_goldberg, MarcoB, Louis, blochwave, Jens May 11 at 15:55

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

Which version of Mathematica are you using? – Mr.Wizard Dec 18 '13 at 9:45
If You are using Mathematica 9 You can try UnitConvert[] function. I'm using ver. 7.0 so I can't check if it works in Your case. – Wojciech Dec 18 '13 at 9:48
@Wojciech yes, N@UnitConvert[Quantity[500,"Revolutions"/"Minutes"], "Revolutions"/"Seconds"] does give the result 8.333... – cormullion Dec 18 '13 at 11:28
That one was pretty straightforward, since it is in the documentation center :) – Wojciech Dec 18 '13 at 11:49
As does UnitConvert[Quantity[500., "RPM"], "RPS"] – bobthechemist Dec 18 '13 at 13:55