Key takeaway
Percentage increase uses ((new − old) ÷ old) × 100 when the value rises; decrease uses the same formula when it falls (giving a negative). The base is always the *old* value — that single rule prevents almost every error. An increase then a decrease of the same percent never cancels, because the second base is smaller.
Scope and assumptions
General arithmetic. Compounded or tiered changes need the net method (see net-percentage-change). This site is informational and not official.
Short answer: Percentage increase uses ((new − old) ÷ old) × 100 when the value rises; decrease uses the same formula when it falls (giving a negative). The base is always the old value — that single rule prevents almost every error. An increase then a decrease of the same percent never cancels, because the second base is smaller.
Quick navigation
- Percent increase → calculate-percent-increase
- Percent decrease → calculate-percent-decrease
- Change of two numbers → percent-change-between-two-numbers
- Net change → net-percentage-change
- The calculator → Percentage Calculator
1. One formula, two readings
% change = ((new − old) ÷ old) × 100
- new > old → positive → increase
- new < old → negative → decrease
2. Increase example
Price 50 → 60.
((60 − 50) ÷ 50) × 100 = +20%
3. Decrease example
Price 80 → 60.
((60 − 80) ÷ 80) × 100 = −25%
A 25% drop, not 20% — because the base is 80.
4. Comparison table
| Old | New | ((new−old)÷old)×100 | Read |
|---|---|---|---|
| 50 | 60 | +20% | increase |
| 80 | 60 | −25% | decrease |
| 100 | 150 | +50% | increase |
| 150 | 100 | −33.3% | decrease |
5. The "same percent" trap
A value rises 20% then falls 20%:
- 100 → 120 (+20%)
- 120 → 96 (−20% of 120)
You end at 96, not 100. The drop acts on the bigger number. See net-percentage-change for why sums mislead.
6. Common mistakes
- Using the new value as base — change is always relative to old.
- Adding increases and decreases — +20% and −20% are not 0% net.
- Dropping the sign — a decrease is negative; report it.
- Confusing with part-of-whole — this compares two states, not a slice of a total.
7. Increase then decrease, stated
A value that rises 20% then falls 20% ends below where it started, because the fall acts on the larger number. Say that explicitly: "up 20% to 120, then down 20% of 120 to 96". Naming the intermediate value keeps the base honest. The same logic means a 50% fall needs a 100% rise to recover — a fact many people get wrong until they write the steps out and see the base shift at each stage.
8. Sign and base, the two things to state
Every change answer needs two facts stated: the sign and the base. The sign tells increase from decrease; the base tells the reader you divided by the starting value, not the ending one. A price 80 to 60 is −25% because the base is 80, and writing the base is what stops someone re-deriving it as −33% from 60. Get in the habit of "from old to new, base old" and both the sign and the size are fixed by the sentence, leaving no room for the classic reversal error that flips the answer.
9. The base decides the size
The same two numbers can look like different changes depending only on which is the base, and the base is always the old value. 50 to 60 is +20% with base 50; read backward as 60 to 50 it is −16.7% with base 60. The pair did not change, only the starting point did, and that starting point is what the formula demands. Lock "old is the base" in your head and the size of every percent change falls out correctly, with no temptation to divide by the number you ended at instead of the one you began with.
FAQ
Q: What is the formula for increase and decrease? ((new − old) ÷ old) × 100. Positive = increase, negative = decrease.
Q: A price went 50 to 60, what is the change? ((60 − 50) ÷ 50) × 100 = +20% — an increase.
Q: Why doesn't +20% then −20% return to start? The −20% acts on the larger 60, not the original 50, so you land at 48, not 50.
Q: What base do I use? Always the old (starting) value, never the new one.
Q: Is decrease just a negative increase? Yes — same formula; a fall gives a negative percent.
Sources: Investopedia — Percentage Change; Khan Academy percentages.
Disclaimer: General arithmetic. Compounded or tiered changes need the net method (see net-percentage-change). This site is informational and not official.
Sources and references
- Investopedia — Percentage Changehttps://www.investopedia.com/terms/p/percentage-change.asp
- Khan Academy percentageshttps://www.khanacademy.org/math/pre-algebra/x31947de81e3f6453:percentages