Percentage Decrease Formula with Examples
What Is Percentage Decrease?
Percentage decrease measures how much a value has fallen compared to its original value, expressed as a percentage. It tells you not just by how much something went down, but by how much it went down relative to where it started.
This makes percentage decrease far more meaningful than a raw number. For example, a price drop of $50 means something very different if the original price was $100 versus $500. The percentage decrease captures that context clearly.
Percentage decrease is used in almost every field — finance, economics, science, health, business, and everyday life. Whether you are tracking price drops, population decline, weight loss, or cost reductions, this formula gives you the answer.
The Percentage Decrease Formula
The standard formula for percentage decrease is:
Percentage Decrease = [(Old Value − New Value) / Old Value] × 100
Where:
- Old Value = the original value before the decrease
- New Value = the value after the decrease
The result is always expressed as a percentage (%). A positive result confirms a decrease. If your result is negative, the value actually increased — use the percentage increase formula instead.
Step-by-Step Examples
Example 1 — Price Decrease (Discount)
Problem: The price of a product decreased from $120 to $90. What is the percentage decrease?
Old Value = 120, New Value = 90
Percentage Decrease = [(120 − 90) / 120] × 100
= [30 / 120] × 100
= 0.25 × 100
Answer: 25% decrease
Example 2 — Population Decline
Problem: A town's population decreased from 8,000 to 7,200 over three years. What is the percentage decrease in population?
Old Value = 8000, New Value = 7200
Percentage Decrease = [(8000 − 7200) / 8000] × 100
= [800 / 8000] × 100
= 0.10 × 100
Answer: 10% decrease
Example 3 — Weight Loss
Problem: A person's weight dropped from 200 pounds to 170 pounds. What is the percentage decrease in weight?
Old Value = 200, New Value = 170
Percentage Decrease = [(200 − 170) / 200] × 100
= [30 / 200] × 100
= 0.15 × 100
Answer: 15% decrease
Example 4 — Stock Price Decline
Problem: A stock's value fell from $80 to $64 per share. What is the percentage decrease?
Old Value = 80, New Value = 64
Percentage Decrease = [(80 − 64) / 80] × 100
= [16 / 80] × 100
= 0.20 × 100
Answer: 20% decrease
Example 5 — Finding the New Value After a Percentage Decrease
Problem: A laptop costs $1,000. Its price decreases by 15%. What is the new price?
Old Value = 1000, Percentage Decrease = 15%
Decrease Amount = (15 / 100) × 1000 = 150
New Value = Old Value − Decrease Amount
New Value = 1000 − 150
Answer: $850
Or using the direct formula:
New Value = Old Value × (1 − Percentage Decrease / 100)
New Value = 1000 × (1 − 15/100)
New Value = 1000 × 0.85
Answer: $850
Example 6 — Finding the Original Value Before a Decrease
Problem: After a 20% decrease, the price of an item is $80. What was the original price?
New Value = 80, Percentage Decrease = 20%
Old Value = New Value / (1 − Percentage Decrease / 100)
Old Value = 80 / (1 − 20/100)
Old Value = 80 / 0.80
Answer: $100
Percentage Decrease vs Percentage Increase
It is important to know when to use which formula.
Percentage Decrease is used when the new value is less than the old value.
Formula: [(Old − New) / Old] × 100
Percentage Increase is used when the new value is greater than the old value.
Formula: [(New − Old) / Old] × 100
Percentage Change is the general formula that works for both. A positive result means increase. A negative result means decrease.
Formula: [(New − Old) / Old] × 100
| Situation | Old Value | New Value | Result |
|---|---|---|---|
| Price goes down | $200 | $150 | −25% decrease |
| Price goes up | $200 | $250 | +25% increase |
| No change | $200 | $200 | 0% change |
Common Mistake to Avoid
Many people accidentally calculate the percentage decrease based on the new value instead of the old value. This gives a wrong answer.
Wrong: [(Old − New) / New] × 100
Correct: [(Old − New) / Old] × 100
Always divide by the original (old) value — not the new one.
Quick Reference — Percentage Decrease Formulas
| What to Find | Formula |
|---|---|
| Percentage Decrease | [(Old − New) / Old] × 100 |
| New Value | Old Value × (1 − % / 100) |
| Old Value | New Value / (1 − % / 100) |
| Decrease Amount | (Percentage / 100) × Old Value |
Related Formulas
Percentage decrease connects directly to several other important formulas:
- Percentage Increase Formula — Used when a value rises instead of falls. The reverse of percentage decrease. [See Percentage Increase Formula →]
- Percentage Formula — The foundation of all percentage calculations including decrease. [See Percentage Formula →]
- Discount Formula — Discount percentage is a type of percentage decrease from the marked price. [See Discount Formula →]
- Profit and Loss Formula — Loss percentage is a percentage decrease from the cost price. [See Profit and Loss Formula →]
Related Calculators and Pages
Percentage Decrease Calculator
Percentage Increase Formula with Examples
Frequently Asked Questions (FAQ)
Q1. What is the percentage decrease formula?
The percentage decrease formula is: Percentage Decrease = [(Old Value − New Value) / Old Value] × 100. It measures how much a value has fallen relative to its original amount, expressed as a percentage.
Q2. How do you calculate percentage decrease in price?
Subtract the new price from the old price, divide the result by the old price, then multiply by 100. For example, if a price goes from $80 to $60: [(80 − 60) / 80] × 100 = 25% decrease.
Q3. What is the difference between percentage decrease and percentage change?
Percentage change is the general formula that works for both increases and decreases. A negative result is a percentage decrease. The formula is the same: [(New − Old) / Old] × 100. For a decrease, this gives a negative number.
Q4. How do you find the new value after a percentage decrease?
Multiply the old value by (1 − percentage / 100). For example, if the original price is $200 and it decreases by 15%: New Value = 200 × 0.85 = $170.
Q5. How do you find the original value before a percentage decrease?
Divide the new value by (1 − percentage / 100). For example, if a price after a 20% decrease is $80: Old Value = 80 / 0.80 = $100.
Q6. Can percentage decrease be more than 100%?
No. A percentage decrease greater than 100% would mean the value became negative, which is not possible for quantities like price, population, or weight. A 100% decrease means the value fell to zero. Anything above 100% is not meaningful in standard percentage decrease calculations.
Summary
The percentage decrease formula — [(Old Value − New Value) / Old Value] × 100 — is one of the most widely used calculations in mathematics, finance, and everyday life. It tells you exactly how much a value has fallen in percentage terms relative to where it started.
Always remember to divide by the old value, not the new one. Use the rearranged versions of the formula to find the new value, the original value, or the amount of decrease when needed.
Paired with the percentage increase formula and the general percentage change formula, you have a complete toolkit for analyzing any change in value — whether it is a price drop, population decline, weight loss, or cost reduction.