# 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