Absolute change (actual difference):

• The difference between two numerical quantities, y - x, is called absolute difference, actual change or actual difference.
• When y value is a reference value (the starting value that the value x is compared to) then the difference between y and x is called the absolute change.
• The actual difference or the actual change between two values is not always a good way to compare two numbers.
• The actual change of one unit between numbers 3 and 2 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,999,999 and 9,999,999,998.
• In this case we need to take into account the "size" of the quantities involved.

Relative change (increase or decrease) 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 relative increase.
• For values y that are smaller than the reference x value, the relative change is negative, and in this case we have a relative decrease.
• The relative change is not defined if the reference value is zero, y = 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 3 to 2) = ^{(2 - 3)} / _|3| = ^-1/₃ = -0.33 = -33%; this change is a relative percentage decrease;
• Relative change (from 9.999.999.999 to 9.999.999.998) = ^{(9.999.999.998 - 9.999.999.999)} / _{|9.999.999.999|} = ^-1/_{9.999.999.999} ≈ 0 = 0%;
• Relative change (from -3 to 2) = (2 - (-3)) / _|-3| = (2 + 3) / ₃ = ⁵/₃ = 1.67 = 167%; this change is a relative percentage increase;
• Relative change (from -9.999.999.999 to 9.999.999.998) = ^{(9.999.999.998 - (-9.999.999.999))} / _{|-9.999.999.999|} = ^{19.999.999.997}/_{9.999.999.999} ≈ 2 = 200%; this change is a relative percentage increase;
• Relative change (from 3 to -2) = ^{(-2 - 3)} / _|3| = ^-5/₃ = -1.67 = -167%; this change is a relative percentage decrease;
• Relative change (from 9.999.999.999 to - 9.999.999.998) = ^{(-9.999.999.998 - 9.999.999.999)} / _{|9.999.999.999|} = ^{-19.999.999.997}/_{9.999.999.999} ≈ -2 = -200%; this change is a relative percentage decrease.