Question 1

What is the formula for percentage change?

Accepted Answer

Percentage Change = ((New − Old) / |Old|) × 100. Compute the difference (New − Old), divide by the absolute value of the original, and multiply by 100. If Old is positive (the usual case), just divide by Old. The absolute value |Old| only matters when the original value is negative (e.g., a company with negative earnings).

Question 2

How do I know if the result is an increase or decrease?

Accepted Answer

The sign of the result tells you the direction. Positive percentage change = increase (New > Old). Negative percentage change = decrease (New < Old). Zero = no change. Example: 50 → 75 gives (25/50)×100 = +50% (increase). 75 → 50 gives (−25/75)×100 = −33.3% (decrease). Note that increasing 50 by 50% gives 75, but decreasing 75 by 33.3% returns to 50.

Question 3

What is the difference between percentage change and percentage difference?

Accepted Answer

Percentage change uses one value as the reference (the "old" or "original"). It is directional — the result depends on which value is the starting point. Percentage difference is symmetric — it compares two values without designating either as the reference, using the average as the denominator: |v1 − v2| / ((v1 + v2)/2) × 100. Use percentage change when there is a clear "before" and "after"; use percentage difference when comparing two measurements of equal standing.

Question 4

Can percentage change exceed 100%?

Accepted Answer

Yes — percentage increase can exceed 100% (the value more than doubled). For example, going from 50 to 150 is a +200% increase. Percentage decrease, however, is bounded at −100% (the value reaches zero). A drop from 50 to 0 is exactly −100%. Values cannot decrease by more than 100% unless they go negative.

Question 5

What happens when the original value is zero?

Accepted Answer

The formula is undefined when Old = 0 because you cannot divide by zero. In practice, this appears in situations like a product that had zero sales last month and now has positive sales. You cannot express this as a percentage change; instead, report it as "from zero to X" or describe the absolute change.

Question 6

How do I calculate average percentage change over multiple periods?

Accepted Answer

For multiple periods, use the Compound Annual Growth Rate (CAGR): CAGR = ((End / Start)^(1/n) − 1) × 100, where n is the number of periods. Simply averaging period-by-period percentage changes gives an arithmetically distorted result. Example: +100% followed by −50% looks like +25% average, but the ending value is the same as the start (doubled then halved). CAGR correctly gives 0%.

Old Value	New Value	Change	% Change
100	125	+25	+25.0%
100	75	-25	-25.0%
50	100	+50	+100.0%
200	150	-50	-25.0%
1000	1200	+200	+20.0%
500	400	-100	-20.0%
80	100	+20	+25.0%
250	300	+50	+20.0%

Percentage Change Calculator

Formula

Percentage Change Calculator

Percentage Change Quick Reference

Related Calculators

Disclaimer

Frequently Asked Questions