Relative Percent Change From 23 To 21.5. What Is the Absolute and Relative Change and How To Calculate the Result? Formula and Calculator

Calculate the Relative Percent Change From 23 to 21.5 and the Absolute Difference

The relative change. Definition and Formula:

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

The relative change =

The absolute difference / |v1| =

(v2 - v1) / |v1|


  • Legend:
  • v2 = 21.5 - new value (the end value)
  • v1 = 23 - reference value (original, initial number)
  • / - the fraction bar (division)
  • |v1| - the positive value of v1, |v1| >= 0
  • Example: if v1 = -10, |v1| = 10; if v1 = 10, |v1| = 10
  • The absolute difference = v2 - v1

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


The relative percent 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 change. Formula:

The relative percent change =

The relative change × 100/100 =

(The relative change × 100)/100 =

(The relative change × 100)%


Calculate the relative percent change:

(21.5 - 23)/|23| =

- 1.5/23 =

- 1.5 ÷ 23 =

- 1.5 ÷ 23 × 100/100 =

(- 1.5 × 100 ÷ 23)/100 =

(- 150 ÷ 23)/100 ≈

- 6.521739130435/100 =

- 6.521739130435% ≈

- 6.52%
(Rounded off to max. 2 decimal places)

The relative percent change
from the original (initial) value 23 to the final, end value 21.5:

Rounded off to max. 12 decimal places ≈ - 6.521739130435%
Rounded off to max. 2 decimal places ≈ - 6.52%

The absolute difference
21.5 - 23 = - 1.5

By what percentage has 23 increased?
Answer: By ≈ - 6.52%

By what percentage is 21.5 greater than 23?
Answer: By ≈ - 6.52%

The relative percent change is negative,
so in this case we have a relative percent decrease.
(the number's 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 change:

Steps to calculate the relative percent change: 1. The absolute difference (the actual change) of the values. 2. The relative change. 3. The relative percent change. 4. Why do we use |v1| for the reference value? 5. Examples


1. The absolute difference (the actual change) of the two values:

  • The difference between two numerical values:
  • v2 - v1
  • ... is called the absolute difference, the actual change or the actual difference.
  • When the value of v1 is the reference value (the starting value that the value of v2 is compared to) then the difference between v2 and v1 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 from the number 8 to the 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.
  • That's why we need a better indicator to compare two values, The Relative Change:

2. The relative change from a number v1 to another number, v2:

  • The relative change:
  • the difference in an indicator 'v' over two periods in time, (v2 - v1), relative to the value of the indicator in the earlier period, v1:
  • (The absolute change from v1 to v2) / |v1| =
  • (v2 - v1) / |v1|
  • ... where v1 is the reference value that v2 is being compared to,
  • ... and |v1| is the positive value of v1; |2| = 2, |-2| = 2, |12| = 12, |-12| = 12.
  • See below, at point 4, why do we use the value of |v1| instead of the value of v1.
  • For values v2 larger than the reference value v1, the relative change is a positive number, and in this case we have a so called relative increase.
  • For values v2 that are smaller than the reference v1 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, v1 = 0.

3. The relative percent change

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

4. Why do we use |v1| for the reference value instead of the value of v1?

  • The relative change: (v2 - v1) / |v1|
  • Let's see what happens with the Relative Change indicator if we use v1 instead of |v1| in the formula above:
  • Let's say that the initial value, the reference, is negative: v1 = - 2.
  • Choose a random positive number for the end value, let's say v2 = 3.
  • (v2 - v1) / v1 =
  • (3 - (- 2)) / - 2 =
  • (3 + 2) / - 2 =
  • 5 / - 2 =
  • - 2.5
  • Although the absolute change is positive: 5, the relative change is negative: - 2.5!
  • By using |v1| instead of v1, the error is corrected:
  • (v2 - v1) / |v1| =
  • (3 - (- 2)) / |- 2| =
  • (3 + 2) / 2 =
  • 5 / 2 =
  • 2.5
  • » Go back up to the operation of calculating the Relative Change.

5. Examples of calculating the relative percent change (increase or decrease)

  • The relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%
    This change is equivalent to a relative percent increase.
  • The 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%;
  • The relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%
    This change is equivalent to a relative percent decrease.
  • The 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 percent decrease.
  • The relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%
    This change is a relative percent increase.
  • The 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 percent increase.

» Calculate the Relative Percent Decrease (Difference)