The percentage increase formulas
- Percentage change = (new value − starting value) ÷ starting value × 100. Positive means an increase, negative a decrease.
- Multiplier = new value ÷ starting value = 1 + percentage ÷ 100. A 25% increase is × 1.25, a 12% decrease is × 0.88.
- Value after an increase or decrease = starting value × (1 + percentage ÷ 100).
- Starting value = final value ÷ (1 + percentage ÷ 100).
- Reverse percentage (to get back to the start) = (starting value ÷ new value − 1) × 100.
It is the same percent change formula statisticians use: the U.S. Bureau of Labor Statistics applies it to the Consumer Price Index, subtracting the earlier index value from the later one, dividing by the earlier value and multiplying by 100.
A worked example: one year of inflation
In its own example, the BLS takes the CPI for all urban consumers, which went from 278.802 in December 2021 to 296.797 in December 2022. The change is (296.797 − 278.802) ÷ 278.802 × 100 = 6.45%, published as 6.5% once rounded to one decimal place. Enter 278.802 and 296.797 in the calculator to get the same result.
The reverse percentage is −6.06%: a price that followed inflation would have to drop by about 6%, not 6.5%, to get back to its December 2021 level.
The most common mistakes
Dividing by the wrong value. A percentage change is always measured against the starting value. From 80 to 100, the increase is 25%; from 100 to 80, the decrease is 20%. The difference is the same (20), the base is not.
Adding up successive percentages. Two 10% increases make 21%, not 20%: 1.10 × 1.10 = 1.21. Over several years, you multiply the multipliers.
Mixing up percent and percentage points. When a rate moves from 4.0% to 4.5%, it gains 0.5 percentage points, but it rises by 12.5% in relative terms (0.5 ÷ 4.0). Both numbers are right; they don't measure the same thing. Say which one you mean in a report or a slide.
In a business, this calculation tracks revenue growth from one year to the next, sizes a price increase before you announce it, and measures the effect of a promotion on sales. For a discount, also check what it costs you in margin with the discount calculator.
Frequently asked questions
How do you calculate a percentage increase?
Divide the change by the starting value, then multiply by 100: (new value − old value) ÷ old value × 100. A price that goes from $80 to $100 rises by 20 ÷ 80 × 100 = 25%. If the result is negative, it is a decrease.
How do I add a percentage to a number?
Multiply the number by 1 + the percentage ÷ 100. A 5% increase on $200 gives 200 × 1.05 = $210. For a decrease, the multiplier is 1 − the percentage ÷ 100: 12% off $250 gives 250 × 0.88 = $220.
How do I find the original price before an increase?
Divide the final price by the multiplier: don't subtract the percentage. A $120 price after a 20% increase was $120 ÷ 1.20 = $100 before. Taking 20% off $120 would give $96, which is wrong.
Why don't a 20% increase and a 20% decrease cancel out?
Because the decrease applies to a bigger base. $100 increased by 20% gives $120, and $120 decreased by 20% gives $96. To get from $120 back to $100, you only need a 16.67% decrease: that is the reverse percentage, which the calculator shows.