Relative percentage change (relative percentage increase or decrease)
The absolute change (actual difference):
- The difference between two numerical quantities, y - x, is called absolute difference, actual change or actual difference.
- When x value is a reference value (the starting value that the value of y is compared to) then the difference between y and x is called the absolute change.
- The actual difference (actual change) between two values is not always a good way to compare two numbers.
- The actual change of one unit from number 8 to number 9 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,998 and 9,999,999.
- In this case we need to take into account the "size" of the quantities involved.
Relative change (from a number x to another number, y):
- Relative change (from x to y) = (Absolute change from x to y) / |x| = (y - x) / |x|, where x is the reference value that y is being compared to and |x| is the positive value of x.
- For values y larger than the reference value x, the relative change is a positive number, and in this case we have a so called relative increase.
- For values y that are smaller than the reference x value, the relative change is negative and in this case we have what it's called a relative decrease.
- The relative change is not defined if the reference value is zero, x = 0.
Relative percentage change
- Relative percentage change is the Relative change calculated as a percentage;
- Relative percentage change = Relative change × 100/100 = (Relative change × 100)%.
Examples of calculating the relative percentage change (increase or decrease)
- Relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%; this change is a relative percentage increase;
- Relative change (from 9.999.999.998 to 9.999.999.999) = (9.999.999.999 - 9.999.999.998) / |9.999.999.998| = 1/9.999.999.998 ≈ 0 = 0%;
- Relative change (from 2 to -3) =
(-3 - 2) / |2| = -5/2 = -2.5 = -250%; this change is a relative percentage decrease;
- Relative change (from 9.999.999.998 to -9.999.999.999) = (-9.999.999.999 - 9.999.999.998) / |9.999.999.998| = -19.999.999.997/9.999.999.998 ≈ -2 = -200%; this change is a relative percentage decrease;
- Relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%; this change is a relative percentage increase;
- Relative change (from -9.999.999.998 to 9.999.999.999) = (9.999.999.999 - (-9.999.999.998)) / |-9.999.999.998| = (9.999.999.999 + 9.999.999.998) / 9.999.999.998 = 19.999.999.997/9.999.999.998 ≈ 2 = 200%; this change is a relative percentage increase.