# Calculate relative percentage decrease change from the original (reference, initial) to a new value and the absolute change (actual difference)

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## Relative percentage change (decrease or increase)

### 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.