Question

For example, I have a number between 1~100 and I need to scale it to be between 20~80.

Examples:

1 scales to 20
100 scales to 80
50 scales to 50

Answer 1

You’re looking for a function f such that :

f(x) = ax +b

f(1)=20
f(100)=80

Then

a+b=20
100a+b=80

You get :

99a +20 = 80

then a =60/99=20/33
and b = 20 - 20/33 = 20*(32/33)

Have a look at this question for more information :

Invert and convert slider value

Note: if 50 scales to 40 your transformation is not linear. So you need to look for another type of function:

f(x) = ax**2 + b x + c