# How to find percentage change between original and final BPM

I am working on a random beat generator and one of the things it does is randomly select the BPM (beats per minute) from a database in between 50 and 200 BPM.

The starting BPM of the files will always be 100 no matter what. I need to find a simple formula to get the percentage of what the new BPM will be from the starting 100.

Examples

• If the new randomly selected BPM is 200 it would be $100 + 100\% = 200$.
• If the new randomly selected BPM is 150 it would be $100 + 50\% = 150$
• If the new randomly selected BPM is 50 it would be $100 - 50\% = 50$

How do I find the percentage? The values I will always have are:

• starting BPM = 100
• new BPM = $y$
• percentage = $x$

If your initial number is $a$ and your final number is $b$, then the percentage change $x$ from $a$ to $b$ is given by $$x = \frac{b - a}{100}$$ For example, if $a = 100$ and $b = 134$, then $$x = \frac{134 - 100}{100} = 0.34 = 34\%$$ If $a = 100$ and $b = 78$, then $$x = \frac{78 - 100}{100} = -0.22 = -22\%$$