Percentage Decrease Calculator
Pick what you have — two numbers, a number and a percentage, or a sale price you want to reverse — and the calculator shows the answer with the arithmetic written out.
The formula
Percentage decrease is (original − new) ÷ original × 100.
The part people get wrong is which number goes in the denominator. It is always the original value, because the percentage describes how much of the starting amount was lost. Dividing by the new value instead gives a different — and wrong — answer.
Going from 250 to 180 is a 28% decrease: 70 ÷ 250 = 0.28. Going from 180 to 250 is a 38.9% increase, because the base changed.
A decrease and its reversing increase are never equal
This is the single most useful thing on this page, and it surprises people constantly.
A 50% decrease requires a 100% increase to get back. A 28% decrease requires a 38.9% increase. A 20% decrease needs a 25% increase.
The reason is that the second percentage is applied to a smaller base. Drop $100 by 50% and you have $50; to get back to $100 you must add $50, which is 100% of $50.
This is why a stock that falls 50% needs to double before you break even, and why two "20% off" discounts applied in sequence give 36% off rather than 40% — the second is taken from an already-reduced price. The "increase needed to undo it" output shows this for whatever figure you enter.
Working backwards from a sale price
The reverse mode answers "this is $180 after 28% off — what was it originally?"
Divide by (1 − 28/100), not multiply by 1.28. Multiplying gives $230.40, which is wrong; the correct answer is $250. It is the same base problem as above.
This matters when you are checking whether a "50% off" sign is honest, or reconstructing a pre-discount price for an expense report or tax record.
When the original is negative or zero
If the original value is zero, percentage change is undefined — there is nothing to take a percentage of.
If the original is negative, the result becomes ambiguous and different fields handle it differently. This calculator divides by the absolute value, which keeps the sign meaningful, but if you are working with negative numbers — temperatures below zero, losses, deficits — state your convention explicitly rather than assuming the reader shares it.
Frequently asked questions
How do you calculate percentage decrease?
Subtract the new value from the original, divide by the original, and multiply by 100. Going from 250 to 180 is (250 − 180) ÷ 250 × 100 = 28 percent. The denominator is always the original value, never the new one.
Why does a 50% decrease need a 100% increase to reverse?
Because the second percentage applies to a smaller base. Dropping $100 by half leaves $50, and adding $50 back is a 100 percent increase of $50. This is why a stock that falls 50 percent must double to break even.
How do I find the original price before a discount?
Divide the sale price by one minus the discount as a decimal. A $180 item after 28 percent off was originally 180 ÷ 0.72 = $250. Multiplying by 1.28 instead gives $230.40, which is a common and costly mistake.
Do two 20% discounts equal 40% off?
No — they give 36 percent off. The second discount is applied to the already-reduced price, so 100 becomes 80 and then 64. Stacked discounts always total less than their sum.
What is the difference between percentage decrease and percentage points?
A rate falling from 8 percent to 6 percent is a decrease of 2 percentage points, but a 25 percent decrease. Both are correct and they describe different things, which is why interest rates and unemployment figures are quoted in percentage points to avoid ambiguity.