(185 - 165) / |165| × 100% = ? Calculate the Relative Percent Change From Number 165 (Original, Reference) to 185 (New Value) and the Actual Change (Absolute Difference)

Relative percent change from 165 to 185

Detailed calculations below

Introduction. Percent, p%

'Percent (%)' means 'out of one hundred':

p% = p 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100.

100% = 100/100 = 100 ÷ 100 = 1.


Relative change. Definition:

Relative change is the difference in an indicator over two periods in time, v2 - v1, 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.

In our case: v1 = 165, v2 = 185.


Relative change. Formula:

(v2 - v1) / |v1| =

Actual change / |v1|


Legend:

v1 - original number

|v1| - positive value of v1, |v1| >= 0

v2 - new value

Actual change = v2 - v1

/ - fraction bar, division bar:

Actual change / |v1| = Actual change ÷ |v1|


Why using |v1| in the formula, instead of v1?

Calculate the Relative change by using v1 instead of |v1|:

Pick a random negative as original number: - 65.

Pick a random positive as the new value: 46.

Formula:

(46 - (- 65)) / - 65 =

(46 + 65) / - 65 =

111 / - 65 ≈

- 1.707692307692 ≈

- 1.71


Though the actual change is positive: 111,

... the relative change is negative: - 1.71. Not good!

By using |v1| instead of v1, the error is corrected.


Note:

Multiply a number by the fraction 100/100,
... and its value doesn't change.

100/100 = 100% = 100 ÷ 100 = 1.

n/100 = n%, any number.


Relative percent change. Formula:

Relative percent change =

Relative change × 100/100 =

(Relative change × 100)/100 =

(Relative change × 100)% =


Calculate the Relative percent change:

(185 - 165)/|165| =

20/165 =

20 ÷ 165 =

20 ÷ 165 × 100/100 =

(20 × 100 ÷ 165)/100 =

(2,000 ÷ 165)/100 ≈

12.121212121212/100 =

12.121212121212% ≈

12.12%;


Relative percent change is positive,
so in this case we have a relative percent increase.


Answer:
:: written in two ways ::

Relative percent change from the original number 165 to the new value of 185:

Rounded to 12 decimals ≈ 12.121212121212%
Rounded to maximum 2 decimals ≈ 12.12%

Actual change:
185 - 165 = 20

Signs: % percent, ÷ divide, × multiply, = equal, / fraction bar (division bar), ≈ approximately equal, |n| - absolute value of n, |n| >= 0;

Writing numbers: comma ',' as thousands separator; point '.' as a decimal mark;

More operations of this kind,
Relative percent change:

From 165 to 184 = ?

From 165 to 186 = ?


Online calculator: relative percent change

The latest calculated relative percentage changes

Relative percent change from the original number 165 to the new value of 185 = 12.121212121212% May 17 14:28 UTC (GMT)
Relative percent change from the original number 332 to the new value of 313 = - 5.722891566265% May 17 14:28 UTC (GMT)
Relative percent change from the original number 7.1 to the new value of 7.4 = 4.225352112676% May 17 14:27 UTC (GMT)
Relative percent change from the original number 246 to the new value of 242 = - 1.626016260163% May 17 14:26 UTC (GMT)
Relative percent change from the original number 50 to the new value of 151 = 202% May 17 14:26 UTC (GMT)
Relative percent change from the original number 10 to the new value of 10.6 = 6% May 17 14:26 UTC (GMT)
Relative percent change from the original number 8.99 to the new value of 13 = 44.60511679644% May 17 14:25 UTC (GMT)
Relative percent change from the original number 152 to the new value of 173 = 13.815789473684% May 17 14:25 UTC (GMT)
Relative percent change from the original number 7.2 to the new value of 7.33 = 1.805555555556% May 17 14:25 UTC (GMT)
Relative percent change from the original number 350 to the new value of 515 = 47.142857142857% May 17 14:24 UTC (GMT)
Relative percent change from the original number 62,361.36 to the new value of 82,208.91 = 31.826679212897% May 17 14:24 UTC (GMT)
Relative percent change from the original number 6,826 to the new value of 8,876 = 30.032229709933% May 17 14:23 UTC (GMT)
Relative percent change from the original number 0.12 to the new value of 0.9 = 650% May 17 14:19 UTC (GMT)
All the relative percentage changes, calculated by users


>> Calculate the Relative Percentage Decrease

Relative percentage change (relative percentage increase or decrease)

The absolute change (actual difference):

  • The difference between two numerical quantities, y - x, is called absolute difference, actual change or actual difference.
  • When x value is a reference value (the starting value that the value of y is compared to) then the difference between y and x is called the absolute change.
  • The actual difference (actual change) between two values is not always a good way to compare two numbers.
  • The actual change of one unit from number 8 to 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.

Relative change (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 so called relative increase.
  • For values y that are smaller than the reference x 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, x = 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 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%; this change is a relative percentage increase;
  • 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%;
  • Relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%; this change is a relative percentage decrease;
  • 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 percentage decrease;
  • Relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%; this change is a relative percentage increase;
  • 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 percentage increase.

>> Calculate the Relative Percentage Decrease