Did you know that misreading a percentage change can cost you real money — or a failed exam? Percentage increase and decrease are two of the most used calculations in everyday life: from understanding a salary raise to comparing prices, reading stock reports, or scoring well on standardized tests.
In this complete guide, you will learn exactly how to calculate percentage increase and decrease using a simple formula, see step-by-step worked examples, understand how to apply it in Excel, and avoid the common mistakes that trip up students and professionals alike.
Percentage change measures how much a value has grown or shrunk relative to its original value, expressed as a percentage. It answers the question: "By what percent did this change?"
There are two types of percentage change:
Both use the same core formula — only the interpretation differs. The result tells you the relative size of the change, not the absolute amount. This distinction matters enormously in real life.
A $10 price increase on a $20 item is a 50% increase. The same $10 on a $1,000 item is only 1%. The absolute amount is identical; the relative impact is completely different. That is what percentage change captures.
When a value grows from an old amount to a new (larger) amount, use the percentage increase formula:
Let's break down each part:
The result is always compared to the original value — not the new one. This is a critical detail many people get wrong.
When a value shrinks from an old amount to a new (smaller) amount, apply the percentage decrease formula:
Notice that the numerator is flipped — Old Value minus New Value — so the result is positive even though the value went down. You can also use one unified formula and interpret the sign:
Theory makes sense only when you see it applied to real numbers. Here are five fully worked examples across different real-world contexts.
A number line helps you understand what percentage change looks like spatially. In this visual, we show the relationship between an original value, the new value, and the percentage change.
| Scenario | Old Value | New Value | Change | % Change |
|---|---|---|---|---|
| Price rise | $80 | $100 | +$20 | +25% |
| Salary raise | $55,000 | $62,700 | +$7,700 | +14% |
| Sale discount | $150 | $112.50 | −$37.50 | −25% |
| Population | 240,000 | 276,000 | +36,000 | +15% |
| Test score | 85 | 68 | −17 | −20% |
Percentage change is used constantly in everyday contexts. Understanding it helps you make smarter decisions:
When a store advertises "25% off," knowing the original price lets you immediately calculate the final price. If something was $200 and is 25% off, the discount is $50 and the final price is $150. Our percentage discount calculator does this instantly — enter the original price and discount percentage to get the final price and savings amount.
When negotiating a raise, always think in percentages, not absolute dollars. A $3,000 raise on a $50,000 salary is a 6% increase. On a $100,000 salary, the same dollar amount is only 3%. Percentages reveal the real value of a raise relative to your current compensation.
If you invest $10,000 and it grows to $13,500, that is a 35% return. If it drops to $8,500, that is a 15% loss. Investment platforms always display returns as percentages because they allow you to compare investments of different initial sizes fairly.
Teachers use percentage change to track student progress. A student improving from 60 to 78 has improved by 30% — a significant gain worth recognizing. Tracking percentage change over time reveals learning trajectories more clearly than raw score changes.
Excel makes percentage calculations fast once you know the right formula. Here is exactly how to set it up:
Put your old values in column A and new values in column B. For example: A2 = 80 (old price), B2 = 100 (new price).
In cell C2, type: =(B2-A2)/A2 and press Enter. This gives you the decimal result (e.g., 0.25).
Select column C, press Ctrl+Shift+% (or use Format Cells → Percentage). Excel will display 25% automatically. Set decimal places to 1 or 2 for cleaner results.
Click the small square at the bottom-right of cell C2 and drag it down to apply the formula to all rows at once. Excel adjusts references automatically.
For a quick percentage increase in one cell without setting up columns, use: =(100-80)/80 which returns 0.25. Format as % to get 25%.
| Mistake | Example of Error | Correct Approach |
|---|---|---|
| Dividing by the new value | 20 ÷ 100 = 20% ❌ | Always divide by the old value: 20 ÷ 80 = 25% ✅ |
| Confusing % and % points | 20% → 30% is "a 10% increase" ❌ | It's 10 percentage points, but a 50% relative increase ✅ |
| Adding percentages directly | +20% then −20% = 0% net change ❌ | +20% then −20% = −4% net (order matters) ✅ |
| Forgetting the ×100 | Answer: 0.25 (not a percentage) ❌ | Multiply by 100: answer is 25% ✅ |
| Wrong sign for decrease | Reporting a decrease as positive ❌ | Use the unified formula; negative = decrease ✅ |
Use this embedded calculator to instantly find any percentage increase or decrease. Enter your original and new values — the result updates immediately.
Enter your values below. Works for both increase and decrease.
For more advanced percentage calculations — including percentage of a number, discount price, markup, tip, and compound growth — visit our full Math Calculator.
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. Always divide by the original (old) value, not the new one. The result is positive for an increase and negative for a decrease.
Percentage decrease = ((Old Value − New Value) ÷ Old Value) × 100. Alternatively, use the unified formula ((New − Old) ÷ Old) × 100 — a negative result indicates a decrease.
In Excel, if A2 holds the old value and B2 the new value, enter =(B2-A2)/A2 in cell C2 and format it as a Percentage. Excel will display the percentage change automatically.
A percentage increase is relative (e.g., 20% to 30% is a 50% increase). Percentage points measure absolute change (the same example is a 10 percentage point increase). These two measures are very different and are frequently confused in news reports.
Yes. If a value doubles, that is a 100% increase. Tripling is a 200% increase. There is no ceiling on percentage increase. However, a percentage decrease cannot exceed 100% in most real-world contexts (a value can't go below zero).
Calculating percentage increase and decrease is straightforward once you apply the right formula consistently. The key takeaways are: always divide by the old value, multiply by 100, and remember that a negative result simply means a decrease — not an error.
Whether you're comparing prices, understanding a pay raise, analyzing data in Excel, or preparing for an exam, percentage change is a tool you'll use for life. Bookmark this guide and our free calculator for quick reference.