From 1,219 To 1,178.8 Relative Percent Decrease (Change, Difference), What Is It?

Calculate the Relative Percent Decrease (Change) From 1,219 to 1,178.8 and the Absolute Difference

The relative decrease (change). Definition:

The relative decrease (change) is the difference in an indicator over two periods in time, v1 - v2, relative to the value of the indicator in the earlier period, v1.


  • Namely:
  • v1 - is called the reference value (original, initial number);
  • v2 - is called the new value (the end value).
  • In our case: v1 = 1,219, v2 = 1,178.8.

The relative decrease (change). Formula:

The relative decrease (change) =

The actual change / |v1|

(v1 - v2) / |v1| =


  • Legend:
  • v1 - the original number
  • |v1| - the positive value of v1, |v1| >= 0. By example: |10| = 10; |-10| = 10.
  • v2 - the new value
  • The actual change = v1 - v2
  • / - the fraction bar (division)

Why do we use |v1| in the formula instead of v1?

  • Let's see what happens if we use v1 instead of |v1|:
  • Choose a random negative number as the initial value: - 98.
  • Choose a random positive number for the end value: 15.

Formula and calculation:

(v1 - v2) / v1 =

(- 98 - 15) / - 98 =

-113 / - 98 ≈

1.15306122449 ≈

1.15


Although the absolute difference is negative: -113, the relative decrease (change) is positive: 1.15. By using |v1| instead of v1, the error is corrected.


The relative percent decrease (change). Detailed calculations below

By multiplying a number by the fraction 100/100,
we change only the form of the result, not the result.

  • 100/100 = 100% = 100 ÷ 100 = 1.
  • n × 100/100 = (n × 100)/100 = (n × 100)%, any number.

The relative percent decrease (change). Formula:

The relative percent decrease (change) =

The relative decrease (change) × 100/100 =

(The relative decrease (change) × 100)/100 =

(The relative decrease (change) × 100)%


Calculate the relative percent decrease (change):

(1,219 - 1,178.8)/|1,219| =

40.2/1,219 =

40.2 ÷ 1,219 =

40.2 ÷ 1,219 × 100/100 =

(40.2 × 100 ÷ 1,219)/100 =

(4,020 ÷ 1,219)/100 ≈

3.297785069729/100 =

3.297785069729% ≈

3.3%
(Rounded off to max. 2 decimal places)

The relative percent decrease (change)
from the original, initial value 1,219 to the final, end value 1,178.8:

Rounded off to max. 12 decimal places ≈ 3.297785069729%
Rounded off to max. 2 decimal places ≈ 3.3%

The absolute (actual) difference
1,219 - 1,178.8 = 40.2

The relative percent decrease (change) is positive,
so we really have a relative percent decrease
(the value goes down).

The symbols used: % percent, ÷ division, × multiplication, = the equal sign, / the fraction bar, ≈ approximately the same, |n| - the positive value of n, |n| >= 0. Writing numbers: comma ',' - as a thousands separator, point '.' as a decimal mark.

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The relative percent decrease (change). The absolute difference (the actual variation). Examples

The absolute difference (the actual variation):

  • 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 decrease (change) from a number x to another number y

  • The relative decrease (from x to y) = (The absolute variation from x to y) / |x| = (x - y) / |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 decrease is a negative number, and in this case we have a relative increase instead.
  • For values y that are smaller than the reference x value, the relative decrease is positive, and in this case we really have a relative decrease.
  • The relative decrease (change) is not defined if the reference value is zero, y = 0.

The relative percent decrease

  • The relative percent decrease is the relative difference calculated as a percentage;
  • Relative percent decrease = Relative decrease × 100/100 = (Relative decrease × 100)%.

Examples of calculating the relative percent decrease (change)

  • Relative change (from 3 to 2) = (3 - 2) / |3| = 1/3 = 0.33 = 33%
    This change is a relative percentage decrease;
  • Relative decrease (from 9,999,999,999 to 9,999,999,998) = (9,999,999,999 - 9,999,999,998) / |9,999,999,999| = 1/9,999,999,999 ≈ 0 = 0%;
  • Relative decrease (from -3 to 2) = (- 3 - 2) / |-3| = - 5/3 = -1.67 = -167%.
    The relative percent decrease is negative so we have in fact a relative percent increase;
  • The relative percent decrease (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 percent increase;
  • Relative percent decrease (from 3 to -2) = (3 - (-2)) / |3| = (3 + 2) / |3| = 5/3 = 1.67 = 167%
    This change is a relative percentage decrease;
  • Relative decrease (from 9,999,999,999 to - 9,999,999,998) = (9,999,999,998 - (-9,999,999,999)) / |9,999,999,999| = (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.

» Calculate The Relative Percent Increase (Change)