Percent Change: Increase and Decrease

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).

Related: marks to percent

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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FAQ

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).

Can the result exceed 100%?

Yes — e.g. 10 → 30 is a 200% increase.

Which value is “old”?

The baseline you are comparing against — usually the earlier time or the original price.

Why do two calculators disagree slightly?

Rounding mid-steps. Prefer full precision until the final display.