From 10.27 To 9.78 Relative Percent Increase (Change, Difference), What Is It?

Calculate the Relative Percent Increase (Change) From 10.27 to 9.78 and the Absolute Difference

The relative increase (change). Definition and Formula:

The relative increase (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 increase (change) =

The absolute difference / |v1| =

(v2 - v1) / |v1|


  • Legend:
  • v2 = 9.78 - new value (the end value)
  • v1 = 10.27 - 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 increase (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 increase (change). Formula:

The relative percent increase (change) =

The relative increase (change) × 100/100 =

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

(The relative increase (change) × 100)%


Calculate the relative percent increase (change):

(9.78 - 10.27)/|10.27| =

- 0.49/10.27 =

- 0.49 ÷ 10.27 =

- 0.49 ÷ 10.27 × 100/100 =

(- 0.49 × 100 ÷ 10.27)/100 =

(- 49 ÷ 10.27)/100 ≈

- 4.7711781889/100 =

- 4.7711781889% ≈

- 4.77%
(Rounded off to max. 2 decimal places)

The relative percent increase (change)
from the original (initial) value 10.27 to the final, end value 9.78:

Rounded off to max. 12 decimal places ≈ - 4.7711781889%
Rounded off to max. 2 decimal places ≈ - 4.77%

The absolute difference
9.78 - 10.27 = - 0.49

The relative percent increase (change) is negative,
so in this case we really have a relative percent decrease instead.
(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 increase (change):

Steps to calculate the relative percent increase (change): 1. The absolute difference (the actual change) of the values. 2. The relative increase (change). 3. The relative percent increase (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 increase (change) from a number v1 to another number, v2:

  • The relative increase (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 increase (change)

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