Percentage Decrease Calculator

What a percentage decrease measures

A percentage decrease says how much of the starting value went away. It compares the change with where you started rather than with where you ended up, so the original number sits in the denominator.

A jacket marked down from $80.00 to $62.00 fell by $18.00, and 18 / 80 = 0.225, so the decrease is 22.5%. The same sale reads the other way too: $62.00 is 77.5% of $80.00, so 77.5% of the original price survived. Both statements describe one price change, and the two percentages always add to 100%.

That base rule separates a percentage decrease from a dollar decrease. A drop of $18 is large on an $80 item and small on a $1,800 laptop, while 22.5% means the same thing in both cases. Ratios let you compare changes across things with different price tags, which is why stores, budgets and statistics all report them.

The formula and a worked example

Percent decrease = (old value - new value) / old value x 100

For the jacket: (80.00 - 62.00) / 80.00 = 18.00 / 80.00 = 0.225, and 0.225 x 100 = 22.5%. Two checks confirm the sign and the size. The answer is positive when the value fell and negative when the value rose, and the share left should be 100% minus the decrease, so 77.5% here.

The table below runs the same arithmetic on five changes, and the pattern is worth noticing before you use the calculator.

Look at the hours row. A schedule cut from 40 hours to 37.5 hours is a 6.25% decrease, while the people living through it describe it as two and a half hours, which hides how small the percentage is. The last row shows the opposite extreme: a value that falls 75% leaves a quarter, and turning that quarter back into the whole takes a 300% rise.

Percentage points are not a percent decrease

When the thing being measured is itself a percentage, two different numbers can describe the same move. A gross margin that falls from 30% to 24% dropped 6 percentage points, and that drop is a 20% decrease relative to where it started: 6 / 30 = 0.20.

Reports mix the two all the time, and the gap is widest when the starting rate is small. An interest rate that goes from 5.00% to 4.00% fell 1 percentage point, which sounds modest, and it is also a 20% cut in the cost of borrowing. A sales tax that moves from 8.00% to 6.50% is 1.50 points, or 18.75%.

The rule to keep: points describe the gap between two percentages, while a percent decrease describes that gap relative to the first one. When both numbers carry a percent sign, say which one you mean, because a reader can hear either.

Chained decreases multiply, they do not add

Two cuts in a row do not add up to a bigger cut, they multiply. Knock 10% off a price and the new price is 90% of the old one. Knock another 10% off that price and you take 10% of 90, which is 9 points, so the total decrease is 19%.

The order of the cuts does not matter, which is a useful check: 0.90 x 0.95 is the same as 0.95 x 0.90. The size mix does matter. Two 15% cuts are 0.85 x 0.85 = 0.7225, a 27.75% decrease, while a 10% cut and a 20% cut are 0.72, a 28.00% decrease.

This is why a store's extra 20% off the sale price is not a 50% discount when the sale price was already 30% off. The factors are 0.70 and 0.80, so the customer pays 56% of the original, a 44% total decrease. To combine any sequence, multiply the shares that remain and subtract the result from 1.

The rebound: a drop needs a bigger rise

Recovering a loss uses a different base. To get from $62.00 back to $80.00 you need $18.00, and $18.00 is 29.03% of $62.00 rather than 22.5% of $80.00. The formula is (old value - new value) / new value x 100.

The asymmetry grows with the size of the loss, which is why investment losses deserve respect. A portfolio that falls 20% needs a 25% gain to break even, one that falls 50% needs 100%, and one that falls 75% needs 300%. A 10% drop needs 11.11% back, which is close enough that people treat the two as the same number. At 50% they are nowhere near the same.

The same logic explains why a 20% pay cut is not undone by a later 20% raise. On a $50,000 salary, the cut takes $10,000 and leaves $40,000, and a 20% raise on $40,000 adds $8,000, which lands at $48,000. Restoring the original pay takes a 25% raise, because the base shrank.

Reading real declines in the data

Published indexes use the same formula, which makes them a good place to test your reading. The Bureau of Labor Statistics reported that the all items Consumer Price Index rose 2.9% over the 12 months ending December 2024, while the gasoline index fell 3.4% and the index for used cars and trucks fell 3.3% over the same period. Shelter went the other way, up 4.6%.

You can rebuild those numbers from the index values. The all items index was 306.746 in December 2023 and 315.605 in December 2024. The change is 315.605 - 306.746 = 8.859, and 8.859 / 306.746 = 0.0289, so an increase of 2.9%, which matches the release. A decline works the same way, with a negative numerator and the earlier index in the denominator.

Two cautions when you do this by hand. Index values are rounded, so a small change can land a tenth of a point off. And a percent decrease in an index is not a percent decrease in your bill: gasoline fell 3.4% on average, while a household that drives more than average saw a different dollar amount. The CPI tables at BLS carry the detail by category and region, and the EIA retail gasoline prices show the dollar side of the same move.

Five mistakes that flip the number

Most wrong answers come from one of five habits.

Dividing by the new value is the first. For $80.00 to $62.00 that gives 18 / 62 = 29.03%, which is the rebound percentage rather than the decrease. Second, calling a 6 point drop in a 30% margin a 6% decrease understates it, since the relative drop is 20%. Third, adding chained cuts: two 10% cuts are 19%, not 20%. Fourth, mixing time windows, such as a one month drop divided by a twelve month total. Fifth, rounding early, which turns a 22.5% decrease into 22% or 23% depending on where the rounding happens.

One more trap is quiet: a decrease can be good news. A cost that falls 12% is a win, a defect rate that falls from 4% to 2.5% is a 1.5 point improvement, and a store's markdown is a planned decrease rather than a failure. Read the direction and the meaning of the number before deciding how to feel about it.

For the neighbouring steps, the percent increase calculator handles a rise from one value to another, the percentage change calculator covers either direction in one pass, the percent off calculator turns a discount into a final price, and the percentage calculator handles the general arithmetic. The monthly CPI release lists the 12 month changes by category if you want to check a figure.