The percentage increase formula
A percentage increase tells you how much something grew compared with where it started. Take the difference between the new and old values, divide by the old value, then multiply by 100.
If the answer is positive, it is an increase. If it is negative, it is a decrease. The bars around “old” mean you use its size without the minus sign, so the direction still reads correctly when you start from a negative number, such as a loss turning into a smaller loss.
Example: a monthly bill goes from 50 to 65. The difference is 15, and 15 ÷ 50 × 100 = 30% increase.
Example: a laptop drops from 1,200 to 900. The difference is −300, and −300 ÷ 1,200 × 100 = 25% decrease.
Increasing a number by a percentage
To add a percentage, multiply by 1 plus the percentage written as a decimal. To take one off, use a negative percentage.
A salary of 80,000 with a 6% raise becomes 80,000 × 1.06 = 84,800. A price of 400 cut by 12.5% becomes 400 × 0.875 = 350.
Watch out: a rise and a fall of the same percentage do not cancel. 100 up 20% is 120, but 120 down 20% is 96. To undo a 20% rise you need a fall of about 16.67%. The calculator shows this “to undo it” figure for you.
Reverse percentages: finding the original
This is where most people slip. If a price is 115 after a 15% increase, the original is not 115 minus 15% of 115 (that gives 97.75). The 15% was worked out on the original, so you divide instead.
115 ÷ 1.15 = 100. The same idea removes sales tax or VAT from a price that already includes it: a 120 bill with 20% VAT was 100 before tax. For tax-specific help, see the VAT calculator.
Average percentage increase over several periods
When something grows over several years, dividing the total change by the number of years overstates the yearly rate, because each year’s growth builds on the last. Use the compound average instead.
Example: sales grow from 100,000 to 150,000 over 3 years. The total increase is 50%. The simple average is 50 ÷ 3 = 16.67% a year, but the compound average is (1.5)^(1/3) − 1 = 14.47% a year. Check it: 100,000 × 1.1447³ ≈ 150,000. Investors call this the CAGR (compound annual growth rate). It needs a positive start and end value; it has no meaning if the value crosses zero.
The same field in “Increase by %” mode does the opposite: it applies a fixed rate several times. 10% a year for 2 years turns 100 into 121, not 120.
Percent vs percentage points
When the values themselves are percentages, such as interest rates or exam pass rates, there are two ways to describe a change:
| From | To | Percentage points | Percent change |
|---|---|---|---|
| 4% | 5% | +1 point | +25% |
| 10% | 8% | −2 points | −20% |
| 50% | 75% | +25 points | +50% |
| 2.5% | 3% | +0.5 points | +20% |
Both numbers are true, but they answer different questions. News reports often say “rates rose 1%” when they mean 1 percentage point. Tick the box under the inputs and the calculator shows both, so you can say exactly what you mean.
Tips and edge cases
- Starting from zero. Percentage change from 0 is undefined, because you would divide by zero. Say “up from 0 to 25” instead.
- More than 100%. A 100% increase doubles a value; 200% triples it. From 40 to 100 is a 150% increase.
- Decreases stop at −100%. You cannot lose more than everything, so a decrease is never below −100% when both values are positive.
- Negative values. From −50 to −25 is a 50% increase, because the value moved up by half of its size. Results with negative values can surprise people, so explain them in words when you share them.
- Rounding. Round only the final answer. Rounding the multiplier early (for example using 1.14 instead of 1.1447) adds visible errors over many periods.
For the other everyday percentage questions, such as “what is 15% of 200”, use the percentage calculator. To see how rising prices eat into money over time, try the inflation calculator. Everything is worked out in your browser, and nothing you type is sent anywhere.