(272 - 231) / |231| × 100% = ? Calculate the Relative Percent Change From the Number 231 (Original, Reference, Initial) to 272 (New Value, End Value) and the Actual Change (Absolute Difference)

The relative percent change, from 231 to 272

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 = 231, v2 = 272.


/ - 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: - 93.


Choose a random positive number for the end value, v2: 60.


Formula and calculation:

(v2 - v1) / v1 =


(60 - (- 93)) / - 93 =


(60 + 93) / - 93 =


153 / - 93


- 1.645161290323 ≈


- 1.65


Although the absolute change is positive 153


... the relative change is negative: - 1.65.


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:

(272 - 231)/|231| =


41/231 =


41 ÷ 231 =


41 ÷ 231 × 100/100 =


(41 × 100 ÷ 231)/100 =


(4,100 ÷ 231)/100


17.748917748918/100 =


17.748917748918% ≈


17.75%

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

The relative percent change...
from the initial value 231 to the final value 272:

Rounded off to max. 12 decimal places ≈ 17.748917748918%
Rounded off to max. 2 decimal places ≈ 17.75%

The actual change
272 - 231 = 41

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 231 to the final value of 272 = 17.748917748918% Feb 02 10:55 UTC (GMT)
The relative percent change from the original value of 2,508 to the final value of 2,974 = 18.580542264753% Feb 02 10:55 UTC (GMT)
The relative percent change from the original value of - 0.09 to the final value of - 0.08 = 11.111111111111% Feb 02 10:55 UTC (GMT)
The relative percent change from the original value of 400,000 to the final value of 540,000 = 35% Feb 02 10:55 UTC (GMT)
The relative percent change from the original value of 0.0008054532 to the final value of 0.000806 = 0.067887246584% Feb 02 10:55 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)