How to compute percentage decreases with worked examples, plus the trick for applying a decrease in one step.
The formula for percentage decrease and how to apply it in one step. Worked examples, plus why this is the same math used for discount calculations.
See also: Percentage calculator · How to calculate percentages
percentage decrease = (old − new) ÷ old × 100Note the order is reversed from percentage increase to keep the result positive when there’s a decrease.
(80 − 60) ÷ 80 × 100
= 20 ÷ 80 × 100
= 25%A 25% decrease took 80 down to 60.
new = old × (1 − P ÷ 100)For 80 with a 25% decrease: 80 × 0.75 = 60. The factor 0.75 is the “keep” ratio — you keep 75% of the value.
A 30% off sale on a $100 item:
$100 × (1 − 0.30) = $100 × 0.70 = $70The same math, just called “discount” instead of “decrease”.
100% decrease takes any value to 0. 50% decrease cuts in half. Decreases above 100% don’t physically make sense for most quantities (you’d be subtracting more than you have).
$60. Calculation: $80 × (1 − 0.25) = $80 × 0.75 = $60.
Generally no for physical quantities. A 100% decrease takes any value to zero. You can't subtract more than the original.
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