Calculate percent decline instantly — discounts, depreciation, and reductions with full steps. Free, fast, and mobile-friendly.
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Sales, depreciation, weight loss, shrinking budgets — decreases are everywhere, and they are quoted as percentages: 25% off, a 10% pay cut, 30% less sugar. Computing the percent decrease tells you how large the drop is relative to the starting point, which is far more informative than the raw difference. Our free Percentage Decrease Calculator finds the percent decline between any two values and shows every step.
The formula mirrors percentage increase: subtract the new value from the old, divide by the old value, multiply by 100. A price falling from $80 to $60 dropped $20, and $20/$80 = 25% — a 25% decrease. The calculator frames the result as a decrease and notes when the inputs actually describe an increase instead.
Whether you are evaluating a discount’s true size, tracking asset depreciation, or measuring any reduction, this tool gives the decline as a clean percentage with the derivation visible.
A percentage decrease expresses the drop as a share of what you started with. The $20 markdown on an $80 item is 25% because 20 is one quarter of 80. The same $20 off a $200 item is only 10%. The percent rescales the drop so deals at any price can be compared — which is exactly why retailers advertise the percent, not just the dollars.
Decrease has a natural floor: 100%. An item cannot drop more than 100% of its price (that would be negative pricing — paying you to take it). Unlike increases, which are unbounded, decreases live in the 0–100% range for positive quantities. If your computed decrease exceeds 100%, either the new value went negative or the inputs are swapped.
Repeated decreases compound. Two successive 10% markdowns do not total 20% off: $100 → $90 → $81, which is 19% off overall. Each cut applies to a smaller base. The calculator handles single changes; for chains, apply them sequentially or multiply the retention factors (0.9 × 0.9 = 0.81).
Framing matters: “25% off” and “pay 75%” describe the same deal. The decrease percent (25%) and the remaining percent (75%) always sum to 100%. Shoppers fluent in both framings verify sale claims instantly.
Percent decrease = ((Old − New) / |Old|) × 100%
If the result is negative, the value actually increased — the calculator will tell you.
From 80 to 60: drop = 20. Divide: 20 ÷ 80 = 0.25 → 25% decrease. Check: 80 × 0.75 = 60 ✓ (pay 75% after 25% off).
A $120 jacket marked down to $90: drop = 30; 30 ÷ 120 = 0.25 → 25% off. The sale price is 75% of original.
From 200 to 100: drop = 100; 100 ÷ 200 = 0.5 → 50% decrease. Halving is always a 50% decrease, just as doubling is a 100% increase.
From 60 to 80: drop = −20; −20 ÷ 60 ≈ −33.3%. The negative signals a 33.3% increase — the calculator reports this framing automatically.
Black Friday math: a TV listed at $800 selling for $600 is (800−600)/800 = 25% off. Comparing that 25% against a competitor’s “30% off $900” ($630) shows the first deal wins despite the smaller percent — percents compare rates, but dollars decide.
Car depreciation is quoted in percent: a $30,000 car worth $24,000 after a year lost (30,000−24,000)/30,000 = 20%. Insurers and accountants track this annual percent to model value curves.
Diet and fitness goals use percent decrease: from 180 lb to 162 lb is (180−162)/180 = 10% down. Trainers prefer the percent because a 10% loss means the same relative achievement at any starting weight.
Repeated percent decreases model depreciation and decay. A car losing 15% of its value yearly follows: value × 0.85^n after n years. After 5 years: 0.85^5 ≈ 0.444 — the car keeps ~44% of its value. This exponential decay is the same mathematics as radioactive half-life (just framed as decrease rather than remaining), connecting car lots to nuclear physics.
The “half-life” of a decrease rate is handy: at p% decrease per period, halving takes about 72/p periods (Rule of 72 again). At 10% annual depreciation, value halves in ~7.2 years. Dealers, insurers, and accountants use exactly this to schedule replacements and reserves.
A subtle framing: successive equal percent decreases shrink the absolute drops over time ($100 → $90 → $81: drops of $10, then $9), while successive equal dollar decreases are accelerating percents. Knowing which pattern applies — percent-based or dollar-based — determines whether a projection is exponential or linear.
Drop 150; 150 ÷ 1000 = 0.15 → 15% decrease. Verify: 1000 × 0.85 = 850 ✓. The retention factor (1 − 0.15) = 0.85 reconstructs the new value directly.
First: 100 × 0.9 = 90. Second: 90 × 0.9 = 81. Total decrease: (100−81)/100 = 19%, not 20%. Retailers stacking discounts rely on shoppers adding the percents — the true total is always less.
Percent decrease frames the “shrinkflation” phenomenon: a cereal box dropping from 20 oz to 18 oz at the same price is a (20-18)/20 = 10% quantity decrease – a hidden 11.1% unit-price increase (price per oz rises by 1/0.9 – 1). Consumers watching only the sticker price miss it; the percent decrease on quantity exposes it. Unit rates and percent decrease together defeat shrinkflation.
A price drops from $45 to $36. Decrease: (45-36)/45 = 9/45 = 0.2 -> 20% off. Verify: 45 x 0.80 = 36.
Weight drops from 200 lb to 170 lb. Decrease: 30/200 = 0.15 -> 15%. Verify: 200 x 0.85 = 170.
A cereal box shrinks from 20 oz to 18 oz at the same price. Quantity decrease: 2/20 = 10%. The hidden unit-price increase: 20/18 – 1 = 11.1%.
A stock falls from $80 to $60, then rises back to $80. The fall: 20/80 = 25% decrease. The recovery: 20/60 = 33.3% increase. Asymmetric round trip.
A buyer tracks her car: purchased $32,000, worth $27,200 after year one – a (32,000-27,200)/32,000 = 15% decrease. Year two: $27,200 -> $23,120, another 15%. Two-year total: (32,000-23,120)/32,000 = 27.75% – not 30%. The retention factors multiply: 0.85 x 0.85 = 0.7225, so 72.25% retained, 27.75% lost. She budgets the third year the same way: 23,120 x 0.85 = $19,652.
The dealer offers a guaranteed trade-in of $20,000 after year three – slightly above her $19,652 projection. She takes it: the dealer’s actuaries computed the same curve. Percent-decrease modeling is how both sides of the car market price the future.
Depreciation curves, radioactive decay, and equipment wear all follow this exponential pattern. The percent decrease is the parameter; compounding does the rest.
Her three-year projection uses the same exponential model insurers use for reserves, physicists use for decay, and accountants use for depreciation schedules. The percent decrease is always the parameter; time does the compounding. Recognizing this pattern – constant percent change over equal periods means exponential behavior – is one of the most transferable insights in quantitative thinking. Linear intuition (“15% a year for 3 years is 45%”) fails everywhere this pattern appears.
The Percentage Decrease Calculator computes ((old−new)/|old|)×100%, reporting the decline magnitude with a plain-words verdict (decrease/increase/no change). A zero original value is rejected as undefined; steps show the drop amount and the division.
Subtract the new value from the old, divide by the old value, multiply by 100. From 80 to 60: (20/80)×100 = 25% decrease. The calculator shows the drop and the division.
25%. Drop of 25 ÷ 100 = 0.25 → 25%. A quarter of the value removed.
The value halved: new = old × 0.5. A 50% decrease always means half remains. Halving is the landmark 50% decrease.
Not for positive quantities — 100% decrease reaches zero. Going further means the new value is negative. 100% decrease is the floor for positive quantities.
Multiplicatively: 20% then 10% off gives 0.8 × 0.9 = 0.72, i.e., 28% off total — not 30%. Multiply retention factors: 0.8 × 0.9 = 0.72.
Nothing — they describe the same transaction. Decrease percent + remaining percent = 100%. Decrease + remaining = 100% always.
Divide the sale price by (1 − discount rate). A $60 item at 25% off: 60 ÷ 0.75 = $80 original. Invert with 1 − rate: sale ÷ 0.75.
Percent decrease is the magnitude of a downward change; percent change is the signed version (negative for decreases). This calculator reports the decrease framing explicitly. Signed change generalizes the decrease framing.
Cite this page as: Percentage Decrease Calculator. Sigma Calculator. Retrieved October 9, 2026, from https://sigmacalculator.net/math-calculators/percentage-decrease-calculator/
Last updated: October 9, 2026