(853 - (- 14,313)) / |- 14,313| × 100% = ? Calculate the Relative Percent Change From Number - 14,313 (Original, Reference) to 853 (New Value) and the Actual Change (Absolute Difference)

Relative percent change from - 14,313 to 853

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 = - 14,313, v2 = 853.


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: - 78.


Pick a random positive as the new value: 56.


Formula:


(56 - (- 78)) / - 78 =


(56 + 78) / - 78 =


134 / - 78


- 1.717948717949 ≈


- 1.72


Though the actual change is positive: 134,


... the relative change is negative: - 1.72. 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:

(853 - (- 14,313))/|- 14,313| =


(853 + 14,313)/|- 14,313| =


15,166/14,313 =


15,166 ÷ 14,313 =


15,166 ÷ 14,313 × 100/100 =


(15,166 × 100 ÷ 14,313)/100 =


(1,516,600 ÷ 14,313)/100


105.959617131279/100 =


105.959617131279% ≈


105.96%;


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 - 14,313 to the new value of 853:

Rounded to 12 decimals ≈ 105.959617131279%
Rounded to maximum 2 decimals ≈ 105.96%

Actual change:
853 - (- 14,313) = 853 + 14,313 = 15,166

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 - 14,313 to 852 = ?


From - 14,313 to 854 = ?


Online calculator: relative percent change

The latest calculated relative percentage changes

Relative percent change from the original number - 14,313 to the new value of 853 = 105.959617131279% May 17 13:25 UTC (GMT)
Relative percent change from the original number 999 to the new value of 984 = - 1.501501501502% May 17 13:22 UTC (GMT)
Relative percent change from the original number 100 to the new value of 2,702 = 2,602% May 17 13:22 UTC (GMT)
Relative percent change from the original number 3.375 to the new value of 3.5 = 3.703703703704% May 17 13:22 UTC (GMT)
Relative percent change from the original number 120 to the new value of 130 = 8.333333333333% May 17 13:21 UTC (GMT)
Relative percent change from the original number 0.072 to the new value of 324 = 449,900% May 17 13:16 UTC (GMT)
Relative percent change from the original number 100 to the new value of 487 = 387% May 17 13:08 UTC (GMT)
Relative percent change from the original number 450 to the new value of 1.6 = - 99.644444444444% May 17 13:07 UTC (GMT)
Relative percent change from the original number 3,250 to the new value of 5,550 = 70.769230769231% May 17 12:59 UTC (GMT)
Relative percent change from the original number 8.82 to the new value of 11 = 24.716553287982% May 17 12:57 UTC (GMT)
Relative percent change from the original number 104 to the new value of 163 = 56.730769230769% May 17 12:55 UTC (GMT)
Relative percent change from the original number - 1 to the new value of 880 = 88,100% May 17 12:50 UTC (GMT)
Relative percent change from the original number 700 to the new value of 1.42 = - 99.797142857143% May 17 12:48 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