Percentage Decrease: How to Work It Out
Formula: (Old minus New) / Old x 100. Percentage decrease measures how much something has fallen, expressed as a share of the original value. This guide covers the formula, five worked examples, how to apply a known decrease, and how to reverse it to find the original.
The Percentage Decrease Formula
The structure mirrors the increase formula, with one change: you subtract the new value from the old, keeping the result positive:
Percentage Decrease = (Old Value minus New Value) / Old Value x 100
If the result comes out negative, you actually have an increase, not a decrease. That is just arithmetic being helpful.
Five Worked Examples
Example 1: Sale price
A jacket was $120. It is now on sale for $90.
(120 minus 90) / 120 x 100 = 30 / 120 x 100 = 25%.
The jacket is 25% off. That matches the "25% off" tag in the window.
Example 2: Employee headcount
A department had 40 people. After a restructure, it has 32.
(40 minus 32) / 40 x 100 = 8 / 40 x 100 = 20% reduction.
Example 3: Blood pressure reading
A patient's systolic pressure dropped from 160 to 136 mmHg after medication.
(160 minus 136) / 160 x 100 = 24 / 160 x 100 = 15% decrease.
Example 4: Energy use
Monthly electricity use fell from 850 kWh to 680 kWh after installing better insulation.
(850 minus 680) / 850 x 100 = 170 / 850 x 100 = 20% reduction.
Example 5: Project budget
A project budget was cut from $500,000 to $375,000.
(500,000 minus 375,000) / 500,000 x 100 = 125,000 / 500,000 x 100 = 25% cut.
Applying a Known Decrease
If you know the percentage decrease and want to find the new value, multiply by (1 minus the decimal):
New Value = Old Value x (1 minus Percentage / 100)
A 30% decrease on $200: 200 x (1 minus 0.30) = 200 x 0.70 = $140.
A 15% decrease on 480: 480 x 0.85 = 408.
The "multiply by the complement" trick works for any percentage. Want 12% off $95? 95 x 0.88 = $83.60.
Quick Reference
| Decrease % | Multiply by | Example on $300 |
|---|---|---|
| 5% | 0.95 | $285 |
| 10% | 0.90 | $270 |
| 20% | 0.80 | $240 |
| 25% | 0.75 | $225 |
| 33.3% | 0.667 | $200 |
| 50% | 0.50 | $150 |
Reversing a Decrease: Finding the Original Value
You see a sale price and want to know the original. The sale price is what remains after the decrease was applied, so:
Original = Sale Price / (1 minus Percentage / 100)
A coat costs $84 after a 30% discount. Original: 84 / 0.70 = $120. Check: 120 x 0.70 = 84. Correct.
A pair of shoes at $68 after a 15% sale. Original: 68 / 0.85 = $80.
This matters in reverse-tax calculations too. If a price of $107 includes 7% sales tax, the pre-tax price is 107 / 1.07 = $100.
Percentage Decrease vs. Subtraction
Subtracting 20% is not the same as subtracting a fixed $20. Twenty percent of $200 is $40; twenty percent of $50 is $10. The decrease scales with the base. That is the whole point of expressing change as a percentage rather than a raw number.
For more on how increases and decreases relate to each other, the article on percentage increase is a natural companion. And if you want to compare two values without a clear "old" and "new," see percentage difference vs percentage change.
Use the Calculator
The percentage calculator handles percentage decrease through the percent change section. Enter the old value first, then the new (lower) value, and it returns the percentage decrease automatically.
Frequently Asked Questions
What is the formula for percentage decrease?
Percentage Decrease = (Old Value minus New Value) / Old Value x 100. A price drop from $80 to $60 is (80 minus 60) / 80 x 100 = 25%.
How do I apply a percentage decrease to find the new price?
Multiply the original by (1 minus the percentage as a decimal). A 30% decrease on $200 is 200 x 0.70 = $140.
Can a percentage decrease exceed 100%?
No. A 100% decrease brings the value to zero. You cannot decrease something by more than its total value.
How do I find the original price before a percentage decrease?
Divide the reduced price by (1 minus the percentage as a decimal). A sale price of $70 after a 30% discount: 70 / 0.70 = $100 original.
Is a percentage decrease the same as subtracting a percentage?
Yes, in practical terms. A 20% decrease means you keep 80% of the original. Multiply by 0.80 or subtract 20% of the value for the same result.