(33 - 300) / |300| × 100% = ? Calculate the Relative Percent Change From the Number 300 (Original, Reference, Initial) to 33 (New Value, End Value) and the Actual Change (Absolute Difference)

The relative percent change, from 300 to 33

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 = 300, v2 = 33.


/ - 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: - 55.


Choose a random positive number for the end value, v2: 32.


Formula and calculation:

(v2 - v1) / v1 =


(32 - (- 55)) / - 55 =


(32 + 55) / - 55 =


87 / - 55


- 1.581818181818 ≈


- 1.58


Although the absolute change is positive 87


... the relative change is negative: - 1.58.


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:

(33 - 300)/|300| =


- 267/300 =


- 267 ÷ 300 =


- 267 ÷ 300 × 100/100 =


(- 267 × 100 ÷ 300)/100 =


(- 26,700 ÷ 300)/100 =


- 89/100 =


- 89%

The answer (scroll down)...

The relative percent change...
from the initial value 300 to the final value 33:
= - 89%

The actual change
33 - 300 = - 267

The relative percent change is negative...
so in this case we have a relative percent decrease.

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 300 to the final value of 33 = - 89% Feb 02 11:28 UTC (GMT)
The relative percent change from the original value of 8.9 to the final value of 26 = 192.134831460674% Feb 02 11:28 UTC (GMT)
The relative percent change from the original value of 50 to the final value of 55.1 = 10.2% Feb 02 11:26 UTC (GMT)
The relative percent change from the original value of 5.56 to the final value of 4.33 = - 22.122302158273% Feb 02 11:26 UTC (GMT)
The relative percent change from the original value of 58 to the final value of 90 = 55.172413793103% Feb 02 11:26 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)