(1,655 - 1,547) / |1,547| × 100% = ? Calculate the Relative Percent Change From the Number 1,547 (Original, Reference, Initial) to 1,655 (New Value, End Value) and the Actual Change (Absolute Difference)

The relative percent change, from 1,547 to 1,655

Introduction. Definitions and formulas

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.


The relative change. Definition:

The 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.


The relative change. Formula:

(v2 - v1) / |v1| =


The actual change / |v1|


Legend:


v2 - is the new value (the end value)


v1 - is the reference value (original, initial number)


In our case: v1 = 1,547, v2 = 1,655.


/ - the fraction bar (division)


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

Example: if v1 = -10, |v1| = 10


The actual change = v2 - v1


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, v1: - 64.


Choose a random positive number for the end value, v2: 57.


Formula and calculation:

(v2 - v1) / v1 =


(57 - (- 64)) / - 64 =


(57 + 64) / - 64 =


121 / - 64 =


- 1.890625 ≈


- 1.89


Although the absolute change is positive 121


... the relative change is negative: - 1.89.


This is not good!


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


Detailed calculations below

A quick note:

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


100/100 = 100% = 100 ÷ 100 = 1.


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


n/100 = n%, 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:

(1,655 - 1,547)/|1,547| =


108/1,547 =


108 ÷ 1,547 =


108 ÷ 1,547 × 100/100 =


(108 × 100 ÷ 1,547)/100 =


(10,800 ÷ 1,547)/100


6.981254040078/100 =


6.981254040078% ≈


6.98%

The answer (scroll down)...
:: written in two ways ::

The relative percent change...
from the initial value 1,547 to the final value 1,655:

Rounded off to max. 12 decimal places ≈ 6.981254040078%
Rounded off to max. 2 decimal places ≈ 6.98%

The actual change
1,655 - 1,547 = 108

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

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.

The latest 5 calculated relative percentage changes

The relative percent change from the original value of 1,547 to the final value of 1,655 = 6.981254040078% Feb 02 11:40 UTC (GMT)
The relative percent change from the original value of 264 to the final value of 307 = 16.287878787879% Feb 02 11:39 UTC (GMT)
The relative percent change from the original value of 800 to the final value of 5,770 = 621.25% Feb 02 11:39 UTC (GMT)
The relative percent change from the original value of 124,677 to the final value of 83,365 = - 33.135221412129% Feb 02 11:38 UTC (GMT)
The relative percent change from the original value of 2,829.5 to the final value of 3,157 = 11.574483124227% Feb 02 11:38 UTC (GMT)
All the relative percentage changes calculated by users

Online calculator: Relative Percent Change



The relative percent change (the relative percent increase or decrease): 1. The absolute difference (the actual change). 2. The relative change. 3. The relative percent change. 4. Examples

1. The absolute difference (the actual change):

2. The relative change (from a number x to another number, y):

3. The relative percent change

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


Calculate the Relative Percent Decrease (Change)