Percentage Difference,
Percentage Error,
Percentage Change

They are very similar ...

They all show a difference between two values as a percentage of one (or both) values

  • Use Percentage Change when comparing an Old Value to a New Value
  • Use Percentage Error when comparing an Approximate Value to an Exact Value
  • Use Percentage Difference when both values mean the same kind of thing (one value is not obviously older or better than the other).

(Refer to those links for more details)

How to Calculate

Step 1: Subtract one value from the other

Step 2: Then divide by ... what?

  • Percentage Change: Divide by the Old Value
  • Percentage Error: Divide by the Exact Value
  • Percentage Difference: Divide by the Average of The Two Values

Step 3: Is the answer negative?

  • Percentage Change: a positive value is an increase, a negative value is a decrease.
  • Percentage Error: ignore a minus sign (just leave it off), unless you want to know if the error is under or over the exact value
  • Percentage Difference: ignore a minus sign, because neither value is more important, so being "above" or "below" does not make sense.

Step 4: Convert this into a percentage (multiply by 100 and add a % sign)

The Formulas

(Note: the "|" symbols mean absolute value, so negatives become positive.)

Percent Change =  
  New Value - Old Value  
× 100%
|Old Value|

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

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

A 20% increase.

 

Percent Error =  
  |Approximate Value - Exact Value| 
× 100%
|Exact Value|

Example: I thought 70 people would turn up to the concert, but in fact 80 did!

  |70 - 80|  
× 100% = (10/80) × 100% = 12.5%
|80|

I was in error by 12.5%

(Without using the absolute value, the error is -12.5%, meaning I under-estimated the value)

 

Percentage Difference = |
  First Value - Second Value  
|   × 100%
(First Value + Second Value)/2

Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers:

|
  240 - 200  
|   × 100% = |40/220| × 100% = 18.18...%
(200+240)/2