How to Calculate Percentage Increase and Decrease
Percentage change is one of the most useful pieces of everyday maths. It tells you how much a price, a salary, a bill or a set of sales figures has grown or shrunk, in a way that you can compare across different amounts. A rise of 10 means a lot on a price of 20 and very little on a price of 2,000. A percentage puts both on the same scale. This guide explains the formula, walks through examples and covers the mistakes that catch people out most often.
The percentage change formula
To find the percentage change from an old value to a new value:
Percentage change = (new value − old value) ÷ old value × 100
If the answer is positive, it is a percentage increase. If it is negative, it is a percentage decrease. The key point is that you always divide by the old (starting) value, because the change is measured relative to where you started.
Worked examples
Example 1: a price increase
A product used to cost 80 and now costs 100. The difference is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25. Multiply by 100 to get 25%. The price has increased by 25%.
Example 2: a price decrease
A monthly bill falls from 120 to 90. The difference is 90 − 120 = −30. Divide by the old value: −30 ÷ 120 = −0.25. That is a 25% decrease.
Example 3: sales growth
A small shop made 42 sales in March and 57 in April. The change is 57 − 42 = 15, and 15 ÷ 42 ≈ 0.357, so sales grew by about 35.7%. Rounding to one decimal place is usually enough for business reporting.
You can check any of these in seconds with our percentage calculator, which also shows the plain difference alongside the percentage.
Why going up 25% and down 20% can be the same change
From 80 to 100 is a 25% increase. From 100 back to 80 is a 20% decrease. The gap is 20 both times, but the starting value changes, so the percentage changes too. This "asymmetry" is the source of many surprises:
- A price that rises by 10% and then falls by 10% ends up lower than it started. 100 rises to 110, then 10% of 110 is 11, so it falls to 99.
- If an investment loses 50%, it needs to gain 100% to get back to where it was. 100 falls to 50, and 50 has to double to reach 100 again.
- A discount of 20% followed by an extra 10% off is not 30% off. It is 100 × 0.8 × 0.9 = 72, which is 28% off.
The rule behind all three: successive percentage changes multiply, they do not add. Convert each change into a multiplier (a 10% increase is ×1.10, a 10% decrease is ×0.90), multiply the multipliers together, and turn the result back into a percentage.
Increasing or decreasing a number by a percentage
Sometimes you know the percentage and want the new value. Use a multiplier:
- Increase by X%: new value = old value × (1 + X ÷ 100). For example, 50 increased by 20% is 50 × 1.2 = 60.
- Decrease by X%: new value = old value × (1 − X ÷ 100). For example, 50 decreased by 20% is 50 × 0.8 = 40.
Reverse percentages: finding the original value
A common mistake is trying to "undo" a percentage by applying the same percentage the other way. Suppose a price is 120 including 20% tax. Taking 20% off 120 gives 96, but that is wrong. The 20% was added to the original price, not to 120. Instead, divide by the multiplier: 120 ÷ 1.2 = 100. Check it: 100 plus 20% is 120.
The same method works for discounts. If something costs 63 after 30% off, the original price was 63 ÷ 0.7 = 90.
Percent vs percentage points
When the thing that is changing is itself a percentage, such as an interest rate, a conversion rate or a tax rate, be precise with words. If a rate moves from 4% to 5%:
- It has risen by 1 percentage point (5 − 4).
- It has risen by 25% in relative terms (1 ÷ 4 × 100).
Both statements are true, but they sound very different. In reports, say "percentage points" when you mean the simple difference between two percentages.
When the starting value is zero or negative
If the starting value is zero, percentage change cannot be calculated, because you cannot divide by zero. Going from 0 sales to 5 sales is a real change, but it is not a percentage of anything. Report the plain difference instead.
Negative starting values, such as a loss that becomes a smaller loss, are also tricky. Our calculator divides by the size of the starting value, so a move from −50 to −25 shows as a 50% increase (the number went up). In finance, though, people often describe this in words ("the loss halved") because percentages of negative numbers confuse readers.
Spreadsheet formulas
In Excel, Google Sheets or LibreOffice, put the old value in A2 and the new value in B2, then use:
- Percentage change:
=(B2-A2)/A2, then format the cell as a percentage. - Increase A2 by the percentage in C2:
=A2*(1+C2), where C2 is formatted as a percentage (for example 20%). - Original value before a percentage was added:
=B2/(1+C2).
Formatting a cell as a percentage multiplies the displayed value by 100, so do not multiply by 100 in the formula as well, or you will get 2500% instead of 25%.
Averaging percentage changes
If sales rose 10% one month and 30% the next, the overall change is not 20% per month on average in a simple sense. Using multipliers, the total is 1.10 × 1.30 = 1.43, a 43% rise over two months. The steady monthly rate that gives the same result is the square root of 1.43, about 1.196, or roughly 19.6% a month. For long periods, this "compound" average is the honest way to describe growth.
Quick checklist
- Subtract old from new to get the difference.
- Divide by the old value.
- Multiply by 100 and keep the sign: positive means increase, negative means decrease.
- For several changes in a row, multiply the multipliers.
- To reverse a percentage, divide by the multiplier rather than subtracting.
Sellers can apply the same ideas to prices and discounts with our sale and discount calculator, which shows how a percentage off changes your profit, not just your price.
This guide is general information for sellers and is not financial, tax or legal advice. Marketplace rules and fees change, so always confirm in your own seller account. DailyToolLab is not affiliated with Etsy Inc., Shopify Inc. or eBay Inc.