Increase or decrease by a %

What it's for

A price-list increase, a discount to apply, a rent going up with inflation, a quantity to adjust, a salary being cut: they're all the same operation, and doing it in your head almost always ends in a rounded-off number. Here you put in the value and the percentage and see both directions at once, plus the difference in absolute terms, which is the number you need when you have to say «how much am I losing».

The trap that catches everyone: you don't get back

Adding 10% and then taking 10% off does not bring you back to where you started. From 100 you go up to 110, and 10% of 110 is 11, so you come down to 99. A piece is always missing, and the higher the percentage the more you lose: with 50%, 100 becomes 150 and then 75, a quarter less. The reason is simple: the second percentage is worked out on a different number from the first.

This is also where the sale-price mistake comes from: two discounts don't add up. A −20% followed by a −10% isn't −30%, it's −28%, because the second applies to the already discounted price. And to really get back to the old price after a 20% discount you need a 25% increase, not 20.

The arithmetic, if you want to redo it by hand

Increase: value × (1 + percentage ÷ 100). Decrease: value × (1 − percentage ÷ 100). The quick way for mental arithmetic is to multiply by the factor instead of adding the part: for +22% multiply by 1.22; for −35% multiply by 0.65. With factors, discounts in a row really do chain together (0.80 × 0.90 = 0.72, that is −28%).

Nearby tools

If you have two numbers and want to know how much the value changed, the page is Percentage change; if you have the full price and the discounted one and want the discount as a percentage, Discount percentage. For the final price of a sale with several discounts there is Discount calculator, and to add or remove VAT VAT calculator.