The percentage decrease formula
Percentage decrease measures how much a value has dropped relative to its starting point. The formula is nearly identical to percentage increase, but it subtracts the new value from the original to keep the result positive when values fall.
Percentage Decrease = (Original Value - New Value) / Original Value x 100
Three steps: subtract the new value from the original, divide that difference by the original value, then multiply by 100. The result tells you the reduction as a percentage of the starting amount.
Step-by-step example: price drop
A jacket originally priced at $120 is marked down to $78. What is the percentage decrease?
- Find the difference: $120 - $78 = $42
- Divide by the original: $42 / $120 = 0.35
- Multiply by 100: 0.35 x 100 = 35%
The jacket is 35% off.
Example: weight loss
A person weighing 210 pounds loses 21 pounds and now weighs 189 pounds. What is the percentage decrease?
(210 - 189) / 210 x 100 = 21 / 210 x 100 = 0.10 x 100 = 10%
Body weight decreased by 10%.
Example: stock portfolio decline
An investment portfolio drops from $15,000 to $12,300 during a market downturn. What is the percentage decrease?
- Difference: $15,000 - $12,300 = $2,700
- Divide: $2,700 / $15,000 = 0.18
- Multiply: 0.18 x 100 = 18%
The portfolio declined by 18%.
Notice that to recover from an 18% loss, you need more than an 18% gain. If the portfolio then grew from $12,300 back to $15,000, the percentage increase would be ($15,000 - $12,300) / $12,300 x 100 = 21.95%. This asymmetry is why percentage decrease and percentage increase produce different magnitudes for the same absolute change.
Example: expense reduction
A company reduces its monthly utility bill from $4,500 to $3,600 after energy-saving upgrades. What is the percentage decrease?
(4500 - 3600) / 4500 x 100 = 900 / 4500 x 100 = 0.20 x 100 = 20%
Utility costs fell by 20%.
When percentage decrease is misleading
- Small denominators exaggerate changes. A drop from 2 customers to 1 is a 50% decrease, but the absolute change is trivial. Always report the absolute numbers alongside the percentage.
- Decreases over 100% are impossible for positive values. You cannot decrease by more than 100% unless the result drops below zero. A claim of "150% reduction" is mathematically meaningless for things like prices or weights.
- Percentage-point confusion. An interest rate dropping from 6% to 4% is a 2 percentage-point decrease, but a 33.3% relative decrease. In finance and policy, the distinction matters.
Related calculators
Verify the examples above or calculate your own decreases.