TL;DR: Percent change = (new − old) / old × 100. Base selection means old is the starting value named by time or by “original,” not the bigger number, not the average of old and new (that is a different statistic), not the new value because it is sitting closer to your pencil.
Old is a time or a labeled original
Monday 80, Friday 60: old = 80 if the story is the week’s change. If the story is “Friday compared with a goal of 60,” you are not doing this formula; you are doing part/whole versus a target. Labels first.
When a table has no time, you cannot compute change. You can compute “A is what percent of B.” People still subtract and divide because subtraction feels like change. Change needs a direction in time or a declared original. Inventing Monday is fiction.
Why not the average as base
Some economics measures use a midpoint base so up and down look symmetric. That is not intro homework percent change. (100−80)/90 is a midpoint-ish thing. (100−80)/80 is percent change from 80. If your teacher did not say midpoint, do not be a hero. Hero bases tank answer keys.
Using the larger number as base (always divide by 100 if 80 and 100 appear) makes every rise look smaller and every fall look larger or vice versa depending on which is larger. It is a bias, not a convenience.
Sign is information
Negative percent change is a decrease. Drop the minus and write “decrease” if the worksheet wants words. Keep the minus if it wants a signed number. Do not do both and also take absolute value “to be safe.” Triple reporting is how 25% and −25% both appear and a grader picks the wrong one.
From 80 to 80 is 0%, not “undefined because nothing happened.” 0% is a percent. From 80 to 0 is −100% if 80 was old. From 0 to 80 is not +100% of 0; it is undefined. Zero old is the actual undefined case.
Index numbers and “rebased” olds
If a chart rebases last year to 100, then this year’s 110 is +10% from that base. If you take raw dollars instead, you get a different percent. Use the series the question points at. Mixing index points with raw dollars is a classic chart crime.
Splicing two methodologies (old census vs new) means the “old” might not be comparable. Then a percent change is a comparison of two different machines. Report the break. Do not paper it over with extra decimal places on a calculator.
Multiple periods
Year 1 → 2 and year 2 → 3 are two percent changes, two olds. A “two-year change” uses year 1 as old and year 3 as new, skipping the middle as a base. That two-year number is not the sum of the two one-year percents. Summing 10% and 10% to 20% is the add-percents error again. Prefer the direct two-year ratio.
CAGR is yet another object: a constant annual rate that compounds to the two-year ratio. Not this article’s one-step formula. If the homework says CAGR, stop using (new−old)/old for the whole span as if it were annual.
Sanity: direction and size
If new > old, the percent change should be positive. If your calculator says −25% you swapped. If the values are 80 and 81, a 50% result means you used 1 as old or subtracted wrong. Neighborhood: 1/80 is 1.25%. Results like 125% on an 80-to-81 story are a misplaced point.
Write old, new, difference, difference/old, ×100 as five short tokens. Five tokens beat a blob of keystrokes when you have to defend a 25% vs 33% at a whiteboard.
Inflation, real change, and two olds
A 10% raise in a year of 10% price growth can be ~0% real, depending on the price index you pick. That is two percent changes with two olds (last year’s wage, last year’s index), then a comparison of factors: 1.10/1.10 = 1. Nominal 10% is still true. Real ~0% is also true. Homework will say nominal or real. News may say neither. If you only have one pair of numbers, you only have one percent change. Do not subtract inflation as 10−10 in percentage points unless you mean a rough talk and you label it rough. Factors first when you need to be careful.
Rebasing an index to a new year changes the displayed levels, not the percent change between two years that both exist in the new series. If a year is missing after a methodology break, skip the fake change across the break or footnote it. Extra decimals will not glue a break.
Seasonal “old” values
Comparing December sales to November is a percent change. Comparing December to last December is another, often more honest for seasonal shops. Using November as old for a toy store manufactures a +80% that is calendar, not genius. Name the old as “prior month” or “prior year.” If a dashboard defaults to prior month, do not paste that +80% into a year-end boast without a second line for year-over-year. Two olds, two percents, one December.
