How to Calculate Percentage Increase (and Decrease): A Simple Guide
Percentage increase and decrease are among the most practical calculations you will ever use. They show up everywhere: salary negotiations, sale prices, investment returns, test scores, and inflation figures. Yet a lot of people either forget the formula or apply it backwards and get the wrong answer.
This guide walks through the formula step by step, covers the most common real-world scenarios, and points out the mistakes that trip people up.
The Core Formula
All percentage change problems use the same basic formula:
A positive result means an increase. A negative result means a decrease. The old value is always the denominator — this is the part most people get wrong.
Example 1: Price increase
A jacket costs $80 last year and $100 this year. What is the percentage increase?
((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25%
Example 2: Salary raise
You earned $55,000 last year and now earn $58,300. What percentage raise did you get?
((58,300 − 55,000) / 55,000) × 100 = (3,300 / 55,000) × 100 = 6%
Example 3: Price decrease (discount)
A laptop drops from $1,200 to $900. What is the percentage decrease?
((900 − 1,200) / 1,200) × 100 = (−300 / 1,200) × 100 = −25%
The negative sign confirms this is a decrease. You can say the laptop is 25% cheaper.
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Open Percentage CalculatorCommon Real-World Scenarios
Calculating a discount at checkout
If something is "30% off" a $75 item, multiply: 75 × 0.30 = $22.50 off. Final price: $75 − $22.50 = $52.50. Alternatively, multiply by what you do pay: 75 × 0.70 = $52.50.
Investment returns
If your portfolio was worth $12,000 and is now worth $15,600, your return is:
((15,600 − 12,000) / 12,000) × 100 = 30%
This is your total return, not annualized. To find an annualized return, you need a different formula (CAGR), but for simple before-and-after comparisons this works fine.
Year-over-year revenue growth
Businesses track revenue changes the same way. If Q1 revenue was $420,000 last year and $483,000 this year:
((483,000 − 420,000) / 420,000) × 100 = 15% growth
Body weight change
If you weighed 195 lbs and now weigh 182 lbs:
((182 − 195) / 195) × 100 = (−13 / 195) × 100 = −6.7%
You lost about 6.7% of your body weight.
Finding the New Value After a Percentage Change
Sometimes you know the starting value and the percentage change and need to find the result. The formula is:
For an increase of 15% on $200:
200 × (1 + 15/100) = 200 × 1.15 = $230
For a decrease of 20% on $200:
200 × (1 − 20/100) = 200 × 0.80 = $160
Working Backwards: Finding the Original Value
If you know the result after a percentage change but need the original, divide by the multiplier:
A shirt is on sale for $68 after a 15% discount. What was the original price?
68 / (1 − 0.15) = 68 / 0.85 = $80
A common mistake here is to add 15% back to $68. That gives you $78.20, not $80 — because 15% of $68 is different from 15% of $80. Always divide by the multiplier, never add or subtract the percentage directly from the sale price.
Percentage Points vs. Percentage Change
This distinction trips up a lot of people, including journalists and politicians.
| Scenario | Percentage Points | Percentage Change |
|---|---|---|
| Interest rate: 3% → 5% | +2 percentage points | +66.7% |
| Approval rating: 60% → 54% | −6 percentage points | −10% |
| Tax rate: 22% → 24% | +2 percentage points | +9.1% |
| Conversion rate: 4% → 6% | +2 percentage points | +50% |
When someone says "the interest rate went up 2%," they almost certainly mean 2 percentage points. The actual percentage increase in the rate could be much larger. Context matters, and the two measures can tell very different stories about the same data.
Sequential Percentage Changes Do Not Add Up
If a stock rises 50% and then falls 50%, you do not break even. You lose money.
Starting value: $1,000
After +50%: $1,500
After −50% of $1,500: $750
You are down $250, or 25%. This is because the second percentage is calculated on a larger base. Percentage changes are multiplicative, not additive.
Similarly, a 10% raise followed by a 10% raise is not a 20% total raise. It is:
1.10 × 1.10 = 1.21, or a 21% total increase
| Two Sequential Changes | Naive Sum | Actual Combined Change |
|---|---|---|
| +10%, +10% | +20% | +21% |
| +50%, −50% | 0% | −25% |
| +20%, −20% | 0% | −4% |
| −10%, +10% | 0% | −1% |
Quick Reference: Percentage Change Formula Summary
| What You Want to Find | Formula |
|---|---|
| Percentage change between two values | ((New − Old) / Old) × 100 |
| New value after % increase | Old × (1 + %/100) |
| New value after % decrease | Old × (1 − %/100) |
| Original value before % increase | New / (1 + %/100) |
| Original value before % decrease | New / (1 − %/100) |
| What % is X of Y? | (X / Y) × 100 |
Calculate Any Percentage Instantly
Our free percentage calculator handles all six types of percentage problems above. No formulas to remember — just enter your numbers and get the answer.
Try the Percentage CalculatorFrequently Asked Questions
What if the old value is zero?
You cannot calculate a percentage change from zero — dividing by zero is undefined. In practice, if something went from zero to any positive number, you describe it as a new entry rather than a percentage change. Some analysts use a placeholder like 0.001 to avoid division errors, but that produces a meaningless number.
How do I calculate percentage increase in Excel or Google Sheets?
Use the formula =(B1-A1)/A1 where A1 is the old value and B1 is the new value, then format the cell as a percentage. Excel multiplies by 100 automatically when you apply percentage formatting.
Is a 100% increase the same as doubling?
Yes. A 100% increase means the value grew by an amount equal to itself, which doubles it. A 200% increase means it tripled. This is a common source of confusion: "200% more" means three times as much, not twice as much.
How do I express a percentage change as a multiplier?
Add the percentage to 100 and divide by 100. A 35% increase is a 1.35 multiplier. A 20% decrease is a 0.80 multiplier. Multipliers are useful when chaining multiple percentage changes together, since you can simply multiply them: 1.10 × 1.10 = 1.21 (two 10% raises = 21% total).