# Convert percentage to number between 120 and 150

I am going to try to explain this as easily as possible. I am working on a computer program that takes input from a joystick and controls a servo direction and speed. I have the direction working just fine now I am working on speed. To control the speed of rotation on the servo I need to send it so many pulses per second using PWM. The servo that I am using takes arguments for speed between 120-150. 120 is %100 speed and 150 is %0 or stopped. 135 is %50 speed. How would I convert percentage from 0-100 into a number between 120-150 including 1/10ths? I hope this makes sense if you need me to explain further please let me know. I really don't know what tag this falls under either.

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It looks to be a linear relationship: in particular, if your percentage is $p$ (ranging from $0$ to $100$), then the number would be $150-0.3p$.

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Your formula worked perfect thank you so much. I am curious though math has never been a strong point of mine how did you come up with 0.3? – Yamaha32088 Apr 15 '13 at 23:33
Well, you want it to be a line. Two points on the line are (120,100) and (150,0). The general form for a line is $y = mx + b$. Plugging in these values gives you the values of $m$ and $b$. – Henry Swanson Apr 15 '13 at 23:38
@Yamaha32088: Put another way, I noticed that if I started at $0$, the number was $150$. Increasing the percentage by $100$ caused a decrease in the number by $30,$ which would correspond to a slope of $\frac{-30}{100}=-0.3$ if the function were linear. To confirm it, I noted that if it were linear, then the number would decrease by $15$ (half of $30$) if we had instead increased the percentage by $50$ (half of $100$), which was indeed the case. Thus, it seemed that we started at $150$ and lost $0.3$ for every percent point we ticked up--in math-speak $150-0.3p$. – Cameron Buie Apr 16 '13 at 0:29

$\text{Percentage speed}=100+\frac {100}{30}(120-\text{input})$

I expressed it that way to show the thought process. We need the $30$ step range of input to correspond to $100$ steps of output, thus the multiply by $\frac {100}{30}$. As the input rises the output falls, so we need a negative sign on the input. A little more thought gets us there. We can then do a little algebra to get

$\text{Percentage speed}=500-\frac {10}3 \text{input}$

To go the other way, $\text{input}=150-0.3 \text{Percentage speed}$

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