One question decides which you need
Before reaching for a formula, ask: is one of these numbers the starting point?
- Yes — there is a before and an after. A price last month and this month, a score before and after study, revenue this year versus last. That is a percentage change, and it matters whether it went up or down.
- No — they are just two values being compared. Two suppliers’ quotes, two machines’ readings, two cities’ rents. Neither one is “first,” so that is a percentage difference.
Percentage change: a direction and a starting point
Change is measured against where you started. Divide the amount of the move by the starting value:
change % = (end − start) / |start| × 100
Because the denominator is the start, reversing the two numbers does not just flip the sign — it changes the size of the answer too. Going from 80 up to 100 is a move of 20 measured against 80. Going from 100 down to 80 is the same move of 20, but now measured against 100.
Percentage difference: no direction, measured against the average
Difference treats the two values as equals. It divides the gap between them by their average, not by either one:
difference % = |a − b| / ((a + b) / 2) × 100
Dividing by the average is what makes it symmetric — swap a and b and nothing moves. The absolute-value bars mean the result is never negative; it is a distance, not a move.
Same two numbers, three answers
Nothing about the values 80 and 100 changed between these rows — only the question did:
| Question | Tool | Answer |
|---|---|---|
| 80 → 100 | Percentage change (up) | +25% |
| 100 → 80 | Percentage change (down) | −20% |
| 80 compared with 100 | Percentage difference | 22.22% |
Which one do you want?
- Use percentage change when something moved over time or against a baseline — prices, headcounts, grades, growth — and the direction (up or down) is part of the answer.
- Use percentage difference when you are comparing two peers with no before/after — two quotes, two lab results, two plans — and you only need to know how far apart they are.
- If you would be annoyed to lose the “up or down,” you want change. Difference throws that information away on purpose.
Common mix-ups
- Calling a drop a “difference.” Saying two prices “differ by 20%” when one fell from $100 to $80 hides that it went down, and 20% here is really a change (÷ 100), not a difference (÷ 90 ≈ 22.22%).
- Averaging two percentage changes. A +25% then a −20% is not “+2.5% on average” — it lands you back where you started. Percent changes do not add or average because each one is measured against a different base. See reverse percentages.
- Using difference when there is a clear baseline. A budget, last year’s figure, a target — when one value is the reference, percentage change against it is the honest measure.
- Writing percentage difference as a negative number. It is an absolute gap, so it is always zero or more.
A related but separate case: when the two numbers are themselves percentages (say a rate moving from 20% to 25%), the gap is measured in percentage points, which is a third thing again.
Frequently asked questions
Why isn't going from 80 to 100 the same percentage as going from 100 to 80?
Percentage change divides by the starting value. From 80, a move of 20 is 20 / 80 = 25%. From 100, the same move of 20 is 20 / 100 = 20%. Different starting points, different percentages.
When should I use percentage difference instead of percentage change?
Use percentage difference when neither value is a 'before' — you are comparing two peers, like two quotes or two measurements, and only need to know how far apart they are. Use percentage change when one value is the starting point.
Can percentage difference be negative?
No. It uses the absolute gap between the values, so it is always zero or positive. If you need to show direction, you want percentage change, not percentage difference.
A report says two prices 'differ by 20%'. Is that change or difference?
It is ambiguous wording. If one price is clearly the reference (a list price, last year's price), it is almost always a percentage change. A true percentage difference divides by the average of the two, so the same pair usually gives a slightly larger number.