Percentage Decrease Calculator

The most persistent misconception about percentage decreases is that they undo increases of the same size. They do not, because the two percentages are calculated against different bases. Raise 100 by 20% and you reach 120; cut 120 by 20% and you land at 96. To get back to exactly 100 you would need a 16.67% cut, because 100 ÷ 120 = 0.8333.

The general rule is that a rise of p percent is undone by a fall of p ÷ (100 + p) percent. A 25% rise needs a 20% fall; a 100% rise needs a 50% fall; a 400% rise needs an 80% fall. Working in multipliers avoids the arithmetic entirely — if the increase multiplied by 1.25, the reversal divides by 1.25.

A percentage decrease of a positive quantity cannot meaningfully exceed 100%: removing 100% of something leaves nothing, and there is nothing further to remove. Claims of a "120% reduction" in costs almost always mean something else — usually that a cost became a net gain, or that the writer meant percentage points, or that the baseline was itself negative.

This ceiling is why decreases and increases are asymmetric in another way too: an increase has no upper limit, so percentage rises can reach thousands, while percentage falls crowd into the range between 0 and 100. When comparing volatility in both directions, that asymmetry can make declines look smaller than equivalent rises.

Stacked discounts multiply in the same way stacked increases do. A 30% reduction followed by a further 20% off the reduced price leaves 0.70 × 0.80 = 0.56 of the original, a total reduction of 44% — noticeably less than the 50% a shopper might expect from adding them.

Retailers are legally required in many jurisdictions to make the base of each reduction clear for this reason. When you see "extra 20% off sale prices", the extra applies to the already-discounted figure, not the original ticket.

Depreciation is the most systematic use: an asset losing 15% of its value each year retains 0.85 of its value annually, so after five years it is worth 0.85⁵ = 44% of the purchase price. The declining balance depreciation calculator handles that pattern directly.

Weight loss, cost reduction, traffic decline, error-rate improvement and discount pricing all use the same arithmetic. In each case the honest presentation includes the base: "a 40% reduction in defects" means very different things at 10 defects and at 10,000.