# (x - y) / |x| × 100% = ? Calculate the relative percent (decrease) change from the original (reference, initial, x) to a new value (the end value, y) & the absolute change (the actual difference)

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## The relative percent change (the relative percent increase or decrease). The absolute difference (the actual change). The relative change. Examples

### The absolute difference (the actual change):

• The difference between two numerical quantities, y - x, is called the absolute difference, the actual change or the actual difference.
• When y value is the reference value (the starting value that the value of x is compared to) then the difference between y and x is called the absolute change.
• The actual difference (the actual change) between two values is not always a good way to compare two numbers.
• The actual change of one unit between the 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.

### The relative change (increase or decrease) from a number x to another number y

• The relative change (from x to y) = (The 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.

### The relative percent change

• The relative percent change is the relative change calculated as a percentage;
• Relative percent 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.