Normalizing one range of values to another range of values.
To add another generic answer. If you want to map the linear range [A..B] to [C..D], you can apply the following steps: Shift the range so the lower bound is 0. (subract A from both bounds: [ A .. B ] -> [ 0. . B - A ] Scale the range so it is [0..1]. (divide by the upper bound): [ 0. . B - A ] -> [ 0. . 1 ] Scale the range so it has the length of the new range which is D-C. (multiply with D-C): [ 0. . 1 ] -> [ 0. . D - C ] Shift the range so the lower bound is C. (add C to the bounds): [ 0. . D - C ] -> [ C .. D ] Combining this to a single formula, we get: ( D - C )*( X - A ) X ' = ----------- + C ( B - A ) Eg : Normalizing a range of 0.5 ----> 1.0 to 0 ------> 1 A=0.5, B=1, C=0, D=1 you get: ( X - 0.5 ) X ' = ------- = 2X - 1 ( 0.5 ) Note, if you have to convert a lot of X to X', you can change the formula to: ( D - C ) C * B - A * D X ' = --