The formula
Percentage change = (new value minus old value) / old value × 100. The old value is always the base, because the question is how much something changed compared with where it started.
Example: monthly sales went from 1,250 to 1,100. The difference is 1,100 minus 1,250 = minus 150. Divide by the old value: minus 150 / 1,250 = minus 0.12. Multiply by 100: minus 12 percent, a decrease of 12 percent. In the Percentage change card of the calculator, type 1,250 as the Old value and 1,100 as the New value; the sentence under the result says that it is a decrease of 12%.
Try it here: Percentage Change Calculator
Open the full tool pageIncrease and decrease are not symmetric
Going from 80 to 100 is an increase of 25 percent, but going back from 100 to 80 is a decrease of only 20 percent. The difference is the same 20, but it is compared with a different starting value. This is why a 50 percent loss needs a 100 percent gain to recover: 100 falls to 50, and 50 has to double to get back to 100.
The same logic explains why a 20 percent rise followed by a 20 percent fall leaves you below where you started: 100 becomes 120, and 20 percent of 120 is 24, so you end at 96. Successive changes multiply rather than add. Two increases of 10 percent are 1.1 × 1.1 = 1.21, a total of 21 percent, not 20.
| Change | Result on 100 | Total change |
|---|---|---|
| Plus 10%, then plus 10% | 121 | Plus 21% |
| Plus 20%, then minus 20% | 96 | Minus 4% |
| Minus 50%, then plus 50% | 75 | Minus 25% |
| Minus 50%, then plus 100% | 100 | 0% |
| Minus 20%, then minus 10% | 72 | Minus 28% |
Worked examples
These cover the most common everyday cases. In each one, the old value is the base.
| Situation | Old | New | Calculation | Change |
|---|---|---|---|---|
| Price rise | 45 | 54 | 9 / 45 | Plus 20% |
| Salary raise | 3,200 | 3,440 | 240 / 3,200 | Plus 7.5% |
| Website visitors | 18,000 | 22,500 | 4,500 / 18,000 | Plus 25% |
| Sale price | 80 | 56 | minus 24 / 80 | Minus 30% |
| Weight loss | 92 kg | 85 kg | minus 7 / 92 | Minus 7.6% |
| Exam score | 64 | 80 | 16 / 64 | Plus 25% |
Percent or percentage points?
When the values themselves are percentages, such as interest rates, unemployment or a share of votes, there are two different ways to describe a change. If a mortgage rate goes from 4 percent to 5 percent, it rose by 1 percentage point. It also rose by 25 percent relative to its old level, because 1 is a quarter of 4. Both statements are correct, but they are not interchangeable, and confusing them can make a change look four times bigger or smaller than it is.
News reports and financial documents should use percentage points (sometimes written pp) for the plain difference between two rates. Use percent for the relative change. Entering 4 and 5 in the percentage change calculator gives the relative change of 25 percent; the point difference is simply 5 minus 4.
Reverse percentages: finding the original value
Sometimes you know the value after the change and the percentage, and you need the value before. Do not subtract the percentage from the new value. A price of 120 that includes 20 percent tax was 100 before tax, not 96, because the 20 percent was calculated on 100. Divide instead: original = new value / (1 + rate). Here 120 / 1.2 = 100.
For a decrease, divide by 1 minus the rate. If you paid 60 after a 25 percent discount, the original price was 60 / 0.75 = 80. The Value before an increase card in the calculator does the first case for you: enter the Value after increase and the Percent. For discounts, use the division above, or check your answer with the Decrease by a percent card.
- After an increase of p%: original = new / (1 + p/100).
- After a decrease of p%: original = new / (1 minus p/100).
- Check: apply the percentage to your answer and you should get the new value back.
Common mistakes
- Dividing by the new value instead of the old one: from 80 to 100 is 25 percent, not 20 percent.
- Adding successive percentages: 10 percent plus 10 percent is 21 percent over two periods, not 20.
- Mixing percent and percentage points when the values are already rates.
- Calculating change from zero: any change from 0 is not defined as a percentage. The calculator says so instead of showing an infinite number.
- Negative starting values: from minus 50 to 25 is not a meaningful percentage. Describe the absolute change instead.
- Rounding too early: keep full numbers until the last step, especially when chaining several changes.
Related measures: percent difference and growth per year
Percentage change has a direction: from old to new. When two values have no natural order, such as the prices of the same product in two shops, people often use percent difference instead: the absolute difference divided by the average of the two values. For 80 and 100 that is 20 / 90, about 22.2 percent, which is the same whichever value you start with.
For changes over several years, the average yearly growth is not the total change divided by the number of years. Use the compound annual growth rate: (end / start) to the power of 1 / years, minus 1. Revenue that grows from 100 to 150 in 3 years grew by 50 percent in total, but about 14.5 percent per year, not 16.7.
In Excel or Google Sheets, with the old value in A2 and the new value in B2, =(B2-A2)/A2 gives the percentage change; format the cell as Percentage to show it as 25% instead of 0.25.