How to Calculate Percentage Increase and Decrease
Learn percentage change formulas with price, salary and everyday examples.
Percentage change describes how much a value rose or fell relative to its starting amount. The denominator matters: use the original value, not the new value, when measuring change from the original.
Percentage increase formula
Percentage increase = (new value − original value) ÷ original value × 100
For example, a price increases from $80 to $100. The difference is $20, so the increase is 20 ÷ 80 × 100 = 25%.
Percentage decrease formula
Percentage decrease = (original value − new value) ÷ original value × 100
If a subscription drops from $100 to $85, the decrease is 15 ÷ 100 × 100 = 15%. State the reference price so readers can interpret the percentage correctly.
Calculate the new amount after a change
Multiply the original amount by (1 + p/100) for an increase of p percent. For a decrease, multiply it by (1 − p/100).
An original salary of $50,000 after a 6% increase becomes $50,000 × 1.06 = $53,000. An $80 product after a 20% discount becomes $80 × 0.80 = $64 before applicable tax.
Why percentage changes do not always cancel
An increase of 20% followed by a decrease of 20% does not return the original value. Starting at $100, the first change gives $120; decreasing $120 by 20% gives $96. The second percentage uses a different base.
Reverse percentage calculations
When you know the final amount and the percentage change, divide by the multiplier. For example, if a post-discount price is $72 after a 10% discount, the original price was 72 ÷ 0.90 = $80.
Watch for zero values and percentage points
Percentage change from an original value of zero is undefined under the ordinary formula; a calculator should not display an infinite or misleading result. Also distinguish percent from percentage points: moving from a 10% rate to a 12% rate is a 2-percentage-point increase, but a 20% relative increase.
Practical uses
Compare prices, growth, grade changes, and business metrics. For comparisons across multiple periods, use a compound growth approach when appropriate rather than simply adding period-to-period percentage changes.