From a pay rise to a price cut, a sale discount to a tax added at the till, percentage increase and decrease is a skill you use constantly, often without noticing. Getting it right, and knowing the one common trap, saves you money and avoids mistakes. The method is quick: to increase, you multiply by a little more than one; to decrease, by a little less. This guide shows both directions with clear worked examples, explains how to find the percentage increase or decrease between two numbers, and reveals why increasing and then decreasing by the same percentage does not return you to the start. For instant results, use our percentage calculator.
Quick answer: To increase a number by a percentage, multiply it by (1 plus the percentage as a decimal). To decrease, multiply by (1 minus the decimal). Increasing 80 by 25% gives 80 x 1.25 = 100; decreasing 80 by 25% gives 80 x 0.75 = 60.
How to increase by a percentage
New value = original x (1 + percentage / 100)
Convert the percentage to a decimal, add 1, and multiply. To increase 80 by 25%: 25% is 0.25, so 80 x (1 + 0.25) = 80 x 1.25 = 100. The single-step multiplier is faster than working out the increase and adding it separately, though both give the same answer.
How to decrease by a percentage
New value = original x (1 – percentage / 100)
This time you subtract the decimal from 1. To decrease 80 by 25%: 80 x (1 – 0.25) = 80 x 0.75 = 60. This is exactly how a sale discount works, which our discount guide covers in more detail.
Finding the percentage between two numbers
If you know the old and new values and want the percentage increase or decrease, use:
Percentage change = ((new – old) / old) x 100
For example, from 80 to 100: (100 – 80) / 80 x 100 = 20 / 80 x 100 = 25% increase. From 80 to 60: (60 – 80) / 80 x 100 = minus 25%, a 25% decrease. A positive result is an increase, a negative one a decrease.
Do it in one click
Our percentage calculator handles increases, decreases, and the change between two numbers instantly. For sale prices specifically, our discount calculator applies the decrease for you.
The increase-then-decrease trap
Here is the mistake almost everyone makes: increasing a number by a percentage and then decreasing it by the same percentage does not return the original value.
Take 80, increase by 25% to get 100, then decrease by 25%: 100 x 0.75 = 75, not 80. The reason is that the second percentage is applied to a different, larger number. The same effect appears with stacked discounts and with prices that go up and then come back down.
Frequently asked questions
How do I increase a number by a percentage?
Convert the percentage to a decimal, add 1, and multiply the original number by the result. To increase 80 by 25%, the decimal is 0.25, so multiply 80 by 1.25 to get 100. Alternatively, work out 25% of 80 (which is 20) and add it to 80. Both methods give the same answer.
How do I decrease a number by a percentage?
Convert the percentage to a decimal, subtract it from 1, and multiply. To decrease 80 by 25%, subtract 0.25 from 1 to get 0.75, then multiply 80 by 0.75 to get 60. You can also calculate 25% of 80 (20) and subtract it. This is exactly how a discount reduces a price.
How do I find the percentage increase between two numbers?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 80 to 100, that is (100 minus 80) divided by 80, times 100, which is 25%. A positive result means an increase and a negative result means a decrease. Always divide by the original value.
Why does increasing and decreasing by the same percentage not give the original?
Because the two percentages are applied to different numbers. Increasing 80 by 25% gives 100, but decreasing 100 by 25% removes 25 (a quarter of 100), leaving 75, not 80. The decrease works on the larger figure, so it takes away more than the increase added. This surprises many people.
How do I add tax as a percentage?
Adding tax is a percentage increase. Multiply the pre-tax amount by 1 plus the tax rate as a decimal. For 8% tax on 50, multiply 50 by 1.08 to get 54. To find a pre-tax price from a taxed total, divide by 1 plus the rate instead. The same multiply-and-divide logic applies both ways.
The bottom line
To increase a number by a percentage, multiply by 1 plus the decimal; to decrease, multiply by 1 minus the decimal, so 80 becomes 100 with a 25% rise and 60 with a 25% cut. To find the change between two numbers, divide the difference by the original and multiply by 100. And remember: a rise then an equal fall never returns the start. Do it all instantly with our percentage calculator.
Further reading
For authoritative background on this topic, see Percentage on Wikipedia.
Note. This article is for general educational purposes.
Last reviewed: July 2026