You have a starting figure and a rate, and you want to know what is left after the cut. Take 20% off a $150 jacket. Reduce a 4,000-word draft by 25%. Trim a $12,000 budget line by 8%. The answer is the original minus the reduction, and as with increases there is a single multiplication that gets you there directly.
Multiply by 1 minus the rate as a decimal. A 20% reduction is × 0.8. A 25% reduction is × 0.75. A 5% reduction is × 0.95. The factor is what remains, which is a useful way to think about it: taking 20% off leaves 80%, so multiply by 0.8 and you have the answer in one step.
When you need this
Applying a discount. The most common use by far, and if that is what you are doing the discount calculator shows you the amount saved alongside the final price.
Cutting a budget or a target. “Reduce this line by 8%” — the factor method gives you the new figure immediately without a separate subtraction.
Depreciation and decay. An asset losing 15% of its value each year is × 0.85 annually. After three years it is at 0.85³ = 61.4% of its original value, not 55%.
Worked examples
$150 reduced by 20%. Multiply 150 by 0.8 to get $120. Check it the long way: 20% of 150 is 30, and 150 − 30 = 120.
4,000 reduced by 25%. 4,000 × 0.75 = 3,000.
$12,000 reduced by 8%. 12,000 × 0.92 = $11,040, a saving of $960.
Two reductions in a row. A 20% cut followed by a further 10% cut is × 0.8 × 0.9 = × 0.72, so a total reduction of 28%, not 30%. The second cut applies to an already-reduced figure, so it takes less off than its headline rate suggests. Retailers rely on this; how stacked discounts work explains the pattern in full.
Where people go wrong
Subtracting the percentage from 100 incorrectly. A 7% reduction is × 0.93, not × 0.97 or × 0.7. It is a small slip that produces a plausible-looking wrong answer, which makes it particularly dangerous.
Assuming a matching increase restores the original. Cut $100 by 20% to get $80, then add 20% back and you have $96. To undo a 20% cut you need a 25% rise. The reverse percentage calculator handles this properly, and the guide on why rises and falls don’t cancel explains why the asymmetry exists.
Adding stacked reductions together. “30% off, then a further 20% off” is not 50% off. It is 0.7 × 0.8 = 0.56, so 44% off. The difference on a $200 item is $12 — small enough to go unnoticed, consistent enough to matter across a whole basket.
Reductions over 100%. You cannot reduce something by more than 100%; the factor would go negative, which means you have handed money back rather than merely reduced a price. If a calculation produces this, something upstream is wrong.
Applying a cut to the wrong figure. Whether a discount comes off before or after tax changes the final amount. Most jurisdictions apply the discount to the pre-tax price and then tax the reduced figure, but not all, and not for every kind of charge. If it matters, check rather than assume — and see the sales tax calculator for the tax side.
Doing it in your head
Think in terms of what remains rather than what goes. 25% off leaves three quarters. 10% off leaves nine tenths. 33% off leaves about two thirds. Reframing the cut as the remainder turns a two-step subtraction into a one-step multiplication, and it is much harder to get backwards. More of the same in percentages in your head.