How does one calculate the value within range -1.0 - 1.0 to be a number within the range of e.g. 0 - 200, or 0 - 100 etc. ?

  • $\begingroup$ For example $x ↦ 100(x + 1)$? Or do you mean something else? $\endgroup$ – k.stm Apr 30 '13 at 12:24

If you have numbers $x$ in the range $[a,b]$ and you want to transform them to numbers $y$ in the range $[c,d]$ you need to do this:


  • $\begingroup$ Thanks. What is the name/tag of such a formula? $\endgroup$ – jarryd Apr 30 '13 at 13:17
  • $\begingroup$ I'd say it's an affine transformation. $\endgroup$ – Matt L. Apr 30 '13 at 15:33
  • $\begingroup$ This is brilliant!! I'm surprised I've never seen something like this before. I knew what I was trying to do was simple, yet I couldn't do it mentally. $\endgroup$ – Michael Lewis Nov 6 '13 at 4:31
  • $\begingroup$ That's slope intercept form of line equation and that's brilliant indeed. $\endgroup$ – Ankit singh kushwah Jul 23 '17 at 13:03
  • $\begingroup$ Thanks it works, but why? $\endgroup$ – Veneet Reddy Aug 9 '17 at 12:14

A short proof of Matt L.'s answer:

We want a function $f: [a, b] \rightarrow [c, d]$ such that

$$ \begin{alignat}{2} f&(&a) &= c \\ f&(&b) &= d. \end{alignat} $$

If we assume the function is to be linear (that is, the output scales as the input does), then

$$\dfrac{d - c}{b - a} = \dfrac{f(x) - f(a)}{x - a}.$$ Simplifying yields the desired formula for $y = f(x)$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.