Percentage Change

Subtract the old from the new, then divide by the old value. Show that as a Percentage.

Comparing Old to New

Change: subtract old value from new value.

Example: You had 5 books, but now have 7. The change is: 7-5 = 2.

Percentage Change: show that as a percent of the old value ... so divide by the old value and make it a percentage:

So the percentage change from 5 to 7 is: 2/5 = 0.4 = 40%

Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options.

How to Calculate

Here are two ways to calculate a percentage change, use whichever method you prefer:

Method 1

Step 1: Calculate the change (subtract old value from the new value)
Step 2: Divide that change by the old value (you will get a decimal number)
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
 
Note: if the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.

Method 2

Step 1: Divide the New Value by the Old Value (you will get a decimal number)
Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
Step 3: Subtract 100% from that
 
Note: if the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease.

Examples

Example: A pair of socks went from $5 to $6, what is the percentage change?

Answer (Method 1):

  • Step 1: $5 to $6 is a $1 increase
  • Step 2: Divide by the old value: $1/$5 = 0.2
  • Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.

Answer (Method 2):

  • Step 1: Divide new value by old value: $6/$5 = 1.2
  • Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)
  • Step 3: Subtract 100%: 120% - 100% = 20%, and that means a 20% rise.

Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage change?

  Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease.
   
  Answer (Method 2): Compare today's value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value.
Subtract 100% and you get -27.5%, or a 27.5% decrease.

Why Compare to Old Value?

Because you are saying how much a value has changed.

Example: Milk was $2, now it is $3 ... did it rise $1 compared to $2 or $3 ?

We compare to the original $2 value, so we say the change is $1/$2 = 0.5 which is a 50% increase.

The Formula

You can also put the values into this formula:

  New Value - Old Value  
× 100%
|Old Value|

(The "|" symbols mean absolute value, so negatives become positive)

Example: There were 200 customers yesterday, and 240 today:

  240 - 200  
× 100% = (40/200) × 100% = 20%
|200|

A 20% increase.

Example: But if there were 240 customers yesterday, and 200 today we would get:

  200 - 240  
× 100% = (-40/240) × 100% = -16.6...%
|240|

A 16.6...% decrease.

How to Reverse a Rise or Fall

Some people think that a percentage increase can be "reversed" by the same percentage decrease. But no!

Example: 10% of 100

A 10% increase from 100 is an increase of 10, which equals 110 ...

... but a 10% reduction from 110 is a reduction of 11 (10% of 110 is 11)

So we ended up at 99 (not the 100 we started with)

What happened?

  • 10% took us up 10
  • Then 10% took us down 11

 

Because the percentage rise or fall is in relation to the old value:

  • The 10% increase was applied to 100.
  • But the 10% decrease was applied to 110.
 

How to do it properly

To "reverse" a percentage rise or fall, use the right formula here:

To Reverse: Use this Percent: Example 10%
An "x" percent rise:
x/(1+x/100)
10/(1+10/100) = 10/(1.1) = 9.0909...
An "x" percent fall:
x/(1-x/100)
10/(1-10/100) = 10/(0.9) = 11.111...

Or use this handy-dandy calculator (just type in a value and click in the other box)
Percent Rise: <=> Percent Fall: