Math CentralQuandaries & Queries


Question from Anna, a student:

I just want to if the following formula is used for the computation of a PERCENTAGE DECREASE:

Old Value - New Value/ Old Value x 100%

My immediate superior is under the impression that the said formula works ONLY for the computation of a percentage INCREASE. He believes that the formula for a percentage DECREASE:

Old Value - New Value/ NEW Value x 100%
On this score, I want to know the correct formula for the computation of percentage decrease. Thank you so much.

Hi Anna,

I would calculate the difference as the new value minus the old value. If this difference is positive there has been an increase and if it is negative there has been a decrease. You then want to state this change as a percentage but the question is a percentage of what? Not everyone does the same thing. I think you should report the percentage change as a percentage of the old value so the expression would be

(new value - old value)/old value ×100

What is important is how you state the result so it is clear what you did.

Suppose the 2005 value was 400 and the 2005 value was 500 then I would calculate

(500 - 400)/400 ×100 = 25%

and say "In 2006 we had an increase of 25% of the 2005 value".

Suppose the 2006 value was 500 and the 2007 value was 300 then I would calculate

(300 - 500)/500 ×100 = -40%

and say "In 2007 we had an decrease of 40% of the 2006 value".

I hope this helps,

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