How do percentage changes over 100% apply to price reductions—can prices be reduced by 500%?

1. How percentage reductions are defined in everyday math and commerce

The canonical formula for a percent reduction is New Price = Original Price − (Original Price × discount/100), equivalently New = Original × (1 − p/100), and retailers, calculators and teaching sites use that form to compute sale prices and savings ^{[1] [5] [2]}. Worked examples—$100 with 30% off becomes $70, or multiplying by 0.70—illustrate that percent-off discounts scale the original price by the remaining share ^{[6] [5]}.

2. What “more than 100%” means mathematically

If p > 100 in the formula New = Original × (1 − p/100), the multiplier (1 − p/100) becomes negative and the arithmetic final price is negative; calculators and algebraic treatments explicitly show that a decreased value can exceed 100% only by producing a result below zero or by changing the reference point for percent comparison ^{[2] [3] [7]}. Statistical and visualization debates demonstrate that reporting “more than 100 percentage points” can arise from odd baselines or rescaling of axes, not a conventional sale where prices go below zero ^[4].

3. When a >100% “decrease” can be meaningful

Contexts where a decrease exceeding 100% is meaningful include metrics where the baseline is itself an offset or where negative values are valid—for example, switching from a positive asset to a net liability, rebates that exceed purchase amounts and produce net payments to customers, or accounting adjustments that move balances through zero into negative territory ^{[2] [3]}. Separate but related is the case of graphs or indices constructed relative to a shifted baseline: a plotted “decrease” over a nonzero reference can produce numbers that look like >100% even though simple retail discounts would not ^[4].

4. Practical limits in retail and why calculators “clamp” at zero

Retail systems and many discount tools explicitly clamp final prices at zero because customers are not paid to take goods under normal sale rules; discount calculators and libraries therefore apply the percent formula but then enforce a nonnegative final price to reflect business reality ^{[8] [3]}. Consumer-facing examples and calculator help pages explain that a 100% discount yields a free item, while any larger “percent off” would either be treated as a fixed refund, a special rebate, or simply be disallowed in the commerce flow ^{[3] [8]}.

5. Why the idea of impossibly large discounts circulates and how it’s misrepresented

Confusion comes from mixing mathematical outputs with commercial practice and from charts that rescale or shift baselines so the zero line is not the natural zero of price—such presentations can make decreases appear to exceed 100 percentage points and mislead readers ^[4]. Many online calculators and explanatory pages show the raw formula and examples without always explaining the practical clamp at zero or the difference between percent-change as a mathematical operation and what’s allowed in a store transaction ^{[6] [1] [2]}.

6. Straight answer: can prices be reduced by 500%?

No, not in ordinary retail terms: applying a “500% discount” in the standard percent-off formula gives a negative price (Original × (1 − 5.00) = −4×Original), which is not a valid sale price; commerce practice instead treats 100% as the meaningful cap (free) and would handle any excess as special refunds, rebates, or accounting entries that change the reference frame ^{[2] [3] [8]}. Mathematically one can compute “a 500% decrease,” but claiming a price was “reduced by 500%” without clarifying the context is misleading and usually incorrect for consumer pricing ^{[4] [2]}.