Three small tools: percent change between two values, a value moved by a percent, and what percent one number is of another.
1. Percent change is the ending value minus the starting value, over the absolute value of the starting value, times 100. It also prints the plain difference and the ending value as a percent of the starting one. A starting value of exactly zero is refused: no percentage of zero exists.
2. A value moved by a percent is the value times (1 + percent / 100).
3. The reverse is the same arithmetic with the roles named: compared minus base, over the absolute value of the base, times 100. Which number is the base is the whole question, and the two orders are not mirrors.
12 to 15 is +25.00% - the gap of 3 over a base of 12. Backwards, 15 down to 12 is -20.00% - that same 3 over a base of 15. A 25% gain then a 20% loss lands where you started, and 15 is 125.00% of 12.
Tool 2 reads 12.00 x (1 + 25.00/100) = 15.00, added 3.00. Tool 3 reads -20.00%: 12 is 20.00% less than 15.
Negative values are where the convention bites. A loss that shrinks from -4 to -2 prints +50.00%: the change of +2 over an absolute base of 4. Divide by the signed base and the same move prints -50.00%, which reads like a further loss when it is an improvement - so tool 1 shows both whenever the start is negative, and you can tell which convention a spreadsheet used.
A percentage change over a period is not an annual rate: a 25% move across three years is 7.72% a year compounded, and nothing here annualises. Percentages do not average either - a +50% year and a -50% year average to zero and leave you 25% down.
With a base near zero the answer is correct but meaningless: 0.01 to 0.05 is a real +400.00% and a trivial three cents. A percentage of a negative figure describes a swing, not a return on capital.
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