# Transform pulses per second (pps) to rpm

I have a stepper motor that turns at 5000 PPS and has a step angle of 1.8º.

What would be the formula to transform these pps into rpm?

Thanks in advance!

## 2 Answers

Using dimensional analysis, and cancelling out units (i.e., "dimensions") just like they are numbers, gives you a clear answer: $$\frac{1 \ step}{pulse} \ \times \frac{5000 \ pulse}{1\ sec} \times \frac{1.8 \ degrees}{1 \ step}\times \frac{1 \ revolution}{360 \ degrees}\times \frac{60\ sec}{1\ min} = \frac{1500\ revolution}{min}$$

step, pulse, sec, degrees all cancel out, leaving an answer in revolutions/min

With a step angle of 1.8 degrees and 360 degrees in a single revolution, that's 200 steps per revolution (i.e. 360 / 1.8).

So 5000 pulses per second equates to 25 revolutions per second (i.e. 5000 / 200), which is 1500 rpm (i.e. 25 * 60).

• Its amazing how maths is independent of different thought processes. 2 people arrive at the same answer using maths but through different lines of thought! – crowie May 6 '16 at 15:11
• Same process, actually. I was just a tad more descriptive so the asker might be able to follow along a bit more readily (teach a man to fish....). – Scott Seidman May 6 '16 at 15:53
• @ScottSeidman Yes, my answer is how I was taught to fish, at least the OP has two approaches to choose from. I remember dimensional analysis from my first year in A level physics in 1976 and it can be a very useful tool. – Roger Rowland May 6 '16 at 17:54