Percent Change: Increase and Decrease

Q: Is percent change the same as percentage points?

No. Moving from 40% to 50% is a 10 percentage point rise, but a 25% relative increase ((50−40)÷40).

Published July 16, 2026By Samson PG

Quick answer

From 50 to 65 is a 30% increase. The trap is always the same: divide by the starting value, not the ending one.

Percent change answers how much a value moved relative to where it started. Students see it in science labs; everyone else sees it in prices, headcount, and “up 10% this month.”

Core percent-change formula

change % = ((new − old) ÷ old) × 100

Positive result → increase
Negative result → decrease
old = 0 → undefined (you cannot divide by zero)

Example: 50 → 65 → ((65 − 50) ÷ 50) × 100 = 30% increase.

Example: 80 → 60 → ((60 − 80) ÷ 80) × 100 = −25% (a 25% decrease).

Increase or decrease by a percent

When you know the starting value and a percent to apply:

new = old × (1 + percent ÷ 100)   // increase
new = old × (1 − percent ÷ 100)   // decrease

Example: 200 increased by 10% → 220. Example: 200 decreased by 10% → 180.

Note: up 10% then down 10% does not return to the start (200 → 220 → 198).

Worked examples across the sign

From	To	Working	Result
50	65	(65 − 50) ÷ 50	+30%
80	60	(60 − 80) ÷ 80	−25%
200	200	(200 − 200) ÷ 200	0%
40	120	(120 − 40) ÷ 40	+200%
120	40	(40 − 120) ÷ 120	−66.7%

The last two pairs are the same two numbers in opposite order, and they are not mirror images: tripling is +200%, but going back down is −66.7%. Percent change is asymmetric because the denominator changes with the direction.

The mistake that reverses your answer

Dividing by the wrong value is the single most common error. The denominator is always the starting number — the baseline you are measuring movement from:

WRONG:  (65 − 50) ÷ 65 = 23.1%
RIGHT:  (65 − 50) ÷ 50 = 30%

If a result feels suspiciously small on an increase, check which number you divided by.

Why a rise then an equal fall does not return you home

Take 200, add 10%, then subtract 10%:

200 × 1.10 = 220
220 × 0.90 = 198

You end 2 below where you started. The increase was calculated on 200; the decrease on the larger 220, so it removes more. This is why a stock down 50% needs +100% to recover, not +50% — and why “we cut prices 20% after raising them 20%” is not a return to the original price.

Percent change vs percentage points

These are different measurements and mixing them misstates things badly. If an interest rate moves from 4% to 5%:

It rose 1 percentage point — the arithmetic difference.
It rose 25% — the relative change, (5 − 4) ÷ 4.

Both are correct; they answer different questions. Use percentage points when comparing two figures that are themselves percentages, and relative change when describing growth.

Exam scores use a different question — “X is what % of Y?”:

percent = (marks scored ÷ total marks) × 100

That is not percent change. Details: exam marks to percent.

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