How Do I Find Percentage Increase Between Two Numbers?
To find the percentage increase between two numbers, subtract the old number from the new number, divide that result by the old number, then multiply by 100. In formula form: Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100. For example, if a value rises from 50 to 65, the percentage increase is calculated by subtracting 50 from 65, dividing the result by 50, and multiplying by 100, giving a 30% increase.
That’s the short answer. But percentage increase shows up in more places than most people expect – sales reports, salary negotiations, stock portfolios, rent hikes, grades, and grocery receipts – and the formula alone doesn’t cover everything you’ll run into. What happens when the old number is negative? What if it’s zero? Is “percentage increase” the same thing as “percentage change” or “percentage difference”? This guide answers all of that, with worked examples for nearly every situation you’re likely to encounter.
What Percentage Increase Means
Percentage increase measures how much a value has grown, expressed as a percentage of its original (starting) value. It answers the question: “How much bigger is the new number, relative to where it started?”
This is different from just looking at the raw difference between two numbers. A $10 increase means something very different depending on the starting point – a $10 raise on a $20 item is a 50% increase, while a $10 increase on a $10,000 item is just 0.1%. Percentage increase puts every change on the same relative scale, which is exactly why it’s used so widely in business, finance, science, and everyday comparisons.
Percentage Increase vs. Percentage Change vs. Percentage Difference vs. Percentage Growth
These four terms get used interchangeably online, but they aren’t quite the same thing, and mixing them up is one of the most common sources of confusion.
| Term | What It Means | Can Be Negative? | Typical Use Case |
| Percentage Increase | Growth from an old value to a larger new value | No – by definition, it describes growth | Sales growth, raises, price hikes |
| Percentage Decrease | Decline from an old value to a smaller new value | No – expressed as a positive number describing the drop | Discounts, weight loss, depreciation |
| Percentage Change | General term covering both increase and decrease; the result’s sign shows direction | Yes – negative means a decrease | Financial reports, year-over-year comparisons |
| Percentage Difference | Compares two values without treating either as the “original” – typically uses their average as the base | No – usually expressed as an absolute value. | Comparing two independent measurements or estimates (not a before/after relationship) |
| Percentage Growth | Often used interchangeably with percentage increase, especially over time or multiple periods | No | Business growth, population growth, investment growth |
The key distinction: percentage increase and percentage decrease assume a clear “before” and “after” – one number came first. Percentage difference is different: it’s meant for comparing two values that don’t have that before/after relationship (like comparing two competitors’ prices), so it typically divides by the average of the two numbers instead of treating one as the baseline.
If you’re comparing a value over time (last year vs. this year, old price vs. new price), you want percentage increase or decrease. If you’re comparing two unrelated figures side by side, percentage difference is technically the more correct term. However,h many people use “percentage difference” loosely to mean the same thing as percentage change.
The Formula, Explained Step by Step
The percentage increase formula has three parts:
Percentage Increase (%) = (Difference Between the New and Original Value ÷ Original Value) × 100
Here’s what each part does:
- New Value − Old Value finds the raw difference – how much the number actually grew in absolute terms.
- ÷ Old Value converts that raw difference into a proportion of the starting point. This step converts the change into a relative measure, allowing you to compare it fairly regardless of the original value.
- × 100 converts that proportion (a decimal) into a percentage, which is just a more familiar way of expressing the same number.
A useful way to remember the formula: “change over original, times 100.” The “original” number always goes on the bottom of the fraction – that single detail is where most calculation errors happen.
Manual Calculation Walkthrough
Let’s calculate a percentage increase from scratch, one step at a time.
Example: Sales rose from $5,000 to $6,000. What’s the percentage increase?
| Step | Action | Result |
| 1 | Subtract: New − Old | $6,000 − $5,000 = $1,000 |
| 2 | Divide by the old value | $1,000 ÷ $5,000 = 0.2 |
| 3 | Multiply by 100 | 0.2 × 100 = 20% |
Sales increased by 20%.
A second example, with less round numbers: A stock price moved from $47.50 to $52.90.
| Step | Action | Result |
| 1 | Subtract | $52.90 − $47.50 = $5.40 |
| 2 | Divide by old value | $5.40 ÷ $47.50 ≈ 0.1137 |
| 3 | Multiply by 100 | 0.1137 × 100 ≈ 11.37% |
The stock price increased by approximately 11.37%.
Calculator Method
For quick, error-free results – especially with decimals, large datasets, or numbers that don’t divide cleanly – a dedicated percentage increase calculator is the fastest option. You enter the old value and the new value, and it applies the formula instantly, which is especially useful when you’re comparing dozens of rows of data (like monthly sales figures) and don’t want to risk a manual arithmetic slip. If you want to double-check any of the examples in this guide, our Percentage Increase Calculator applies the exact formula above and returns the result in one step.
Spreadsheet Formulas (Excel & Google Sheets)
Both Excel and Google Sheets use the same formula structure, since they both apply the standard percentage increase formula to cell references instead of typed numbers.
If your old value is in cell A2 and your new value is in cell B2:
=(B2-A2)/A2
Format that cell as a percentage (right-click → Format Cells → Percentage in Excel, or Format → Number → Percent in Google Sheets), and it will automatically display as something like 20.00% instead of 0.2.
If you want the formula to output the percent sign without separate formatting:
=((B2-A2)/A2)*100
This returns a plain number (like 20) rather than a formatted percentage, which can be useful if you’re feeding the result into another calculation.
Pro tip: When dragging this formula down a column of monthly or row-by-row data, use absolute references (like $A$1) only if you’re comparing everything back to a single fixed baseline (such as a base year). If each row compares to the row directly above it, relative references (no dollar signs) are what you want, since the formula should shift down with each row.
Special Cases: Negatives, Zero, Decimals, Fractions
The basic formula works cleanly for positive whole numbers, but real-world data isn’t always that tidy. Here’s how to handle the trickier cases.
Negative Numbers
When the old value is negative, the standard formula can produce misleading results, because dividing by a negative number flips the sign of the outcome. For example, going from −$10,000 to −$5,000 (a business loss shrinking) is genuinely an improvement, but plugging it directly into the formula gives:
(−5,000 − (−10,000)) ÷ (−10,000) × 100 = 5,000 ÷ −10,000 × 100 = −50%
Mathematically, that’s correct, but it reads as a 50% decrease when the situation actually improved. This is why financial analysts often avoid using straight percentage increase when the starting value is negative, and instead describe the change in absolute terms (e.g., “losses narrowed by $5,000”) to avoid confusion.
Zero Values
If the old value is zero, the formula breaks down completely, because division by zero is undefined. Going from 0 to any positive number is technically an “infinite” percentage increase, which isn’t a meaningful number to report. In practice, when a metric starts at zero (like a brand-new product with no prior sales), it’s more useful to describe the new value directly (“$4,000 in sales “). Instead, display a clear message such as “No previous data available” or “This is the first month of data” rather than calculating a percentage that would be misleading.
Decimal Values
The formula works the same way with decimals – just carry the decimal places through each step. Example: a value increases from 2.5 to 3.15.
(3.15 − 2.5) ÷ 2.5 × 100 = 0.65 ÷ 2.5 × 100 = 26%
Fractions
If your numbers are fractions, convert them to decimals first, then apply the same formula. Example: an increase from 1/4 to 1/2.
1/4 = 0.25, 1/2 = 0.5
(0.5 − 0.25) ÷ 0.25 × 100 = 0.25 ÷ 0.25 × 100 = 100%
Large Numbers and Small Numbers
The formula scales without changing at all – the process is identical whether you’re working with tiny decimals or numbers in the millions. The only practical difference is being careful with rounding.
Large numbers: A company’s revenue grows from $12,400,000 to $14,100,000.
(14,100,000 − 12,400,000) ÷ 12,400,000 × 100 = 1,700,000 ÷ 12,400,000 × 100 ≈ 13.71%
Small numbers: A measurement increases from 0.004 to 0.0052.
(0.0052 − 0.004) ÷ 0.004 × 100 = 0.0012 ÷ 0.004 × 100 = 30%
Pro tip: With very large numbers, avoid rounding the raw difference too early – round only your final percentage, not the intermediate subtraction step, or small rounding errors can compound into a noticeably inaccurate result.
Common Mistakes People Make
| Mistake | Why It’s Wrong | The Fix |
| Dividing by the new value instead of the old value | This calculates a different (and smaller) percentage that doesn’t represent true growth from the starting point | Always divide by the original/old value |
| Forgetting to multiply by 100 | Leaves the answer as a decimal (0.2) instead of a percentage (20%) | Multiply the decimal result by 100 |
| Confusing percentage increase with percentage points | A rate moving from 10% to 15% is a 5 percentage point increase, but a 50% percentage increase (5 ÷ 10 × 100) | Be explicit about which one you mean – they are not interchangeable |
| Applying the formula directly to negative starting values without context | Produces a technically correct but misleading result | Describe the change in absolute terms instead, or clearly flag the sign issue |
| Rounding too early in multi-step calculations | Small errors compound across steps | Round only the final answer |
| Mixing up percentage increase and percentage difference | Leads to using the wrong base (average vs. original value) | Use percentage increase only when there’s a clear “before” and “after” |
Percentage Increase vs. Percentage Points: A Closer Look
This mistake deserves its own callout because it’s so common in news and financial reporting. If an interest rate moves from 4% to 6%, that’s a 2 percentage point increase. But expressed as a percentage increase, it’s actually (6 − 4) ÷ 4 × 100 = 50%. Both statements are accurate – they’re just measuring different things, and mixing them up can make a change sound much bigger or smaller than it really is.
Real-World Examples by Category
Business & Sales Growth
A store’s monthly revenue rises from $18,500 to $21,200.
(21,200 − 18,500) ÷ 18,500 × 100 ≈ 14.59% sales growth.
Salary Increase
Your salary goes from $58,000 to $62,000 after a raise.
(62,000 − 58,000) ÷ 58,000 × 100 ≈ 6.90% raise.
Inflation
The Consumer Price Index rises from 300 to 309 over a year (illustrative figures – check the U.S. You can also compare your results with the latest inflation figures published by reliable sources, such as the U.S. Bureau of Labor Statistics (BLS) Consumer Price Index (CPI).
(309 − 300) ÷ 300 × 100 = 3% inflation for that period.
Stock Market
A share purchased at $85 is now worth $110.
(110 − 85) ÷ 85 × 100 ≈ 29.41% gain.
Real Estate Appreciation
A home purchased for $340,000 is now valued at $391,000.
(391,000 − 340,000) ÷ 340,000 × 100 ≈ 15% appreciation.
Budgeting & Personal Finance
Your monthly grocery bill rose from $420 to $470.
(470 − 420) ÷ 420 × 100 ≈ 11.90% increase in grocery spending – useful for spotting budget creep before it becomes a bigger problem.
Retail Discounts vs. Increases
Retail pricing uses this formula in both directions. A jacket’s price increases from $60 to $75 (a 25% increase), while a discount from $75 back down to $60 is a 20% decrease – not the same percentage, since the base number changes depending on direction. This asymmetry trips people up constantly (see the Common Mistakes section above).
Academic Grades
A student’s test score improves from 72 to 90 out of 100.
(90 − 72) ÷ 72 × 100 = 25% improvement.
Mental Math Shortcuts
You don’t always need a calculator. A few shortcuts make percentage increase easier to estimate on the fly:
- 10% shortcut: Move the decimal point one place left. 10% of 250 is 25. Use this as a building block for other percentages (20% is just double the 10% figure).
- 50% shortcut: Just divide by 2. If a number doubles, that’s a 100% increase – a useful anchor point for double-checking larger calculations.
- 1% shortcut: Move the decimal two places left. 1% of 250 is 2.5. Multiply that by any whole number to build up other percentages quickly (7% ≈ 1% × 7).
- Round first, refine after: For a quick estimate, round both numbers to easier figures, calculate roughly, then adjust. Going from $198 to $247? Round to $200 → $250, which is a clean 25% increase – close enough for a fast mental estimate.
Reverse Percentage Calculations
Sometimes you know the new value and the percentage increase, but need to find the original number. This is common with pricing that already includes a markup or tax.
Formula: Old Value = New Value ÷ (1 + (Percentage Increase ÷ 100))
Example: A product now costs $138 after a 15% price increase. What was the original price?
Old Value = 138 ÷ (1 + 0.15) = 138 ÷ 1.15 = $120
This reverse calculation is especially useful for checking receipts, verifying markups, or working backward from a final price that already includes a known percentage change.
Percentage Increase vs. Percentage Decrease
The two formulas are mirror images of each other, but it’s worth seeing them side by side, since the sign and interpretation differ.
| Percentage Increase | Percentage Decrease | |
| Formula | (New − Old) ÷ Old × 100 | (Old − New) ÷ Old × 100 |
| When to use | New value is larger than old | New value is smaller than old |
| Result direction | Always expressed as growth | Always expressed as a decline |
| Example | $50 → $65 = 30% increase | $65 → $50 ≈ 23.08% decrease |
Notice that a 30% increase from $50 to $65 does not reverse into a 30% decrease going back from $65 to $50 – it’s actually about 23.08%. This is because the base (“old value”) changes depending on which direction you’re calculating, which is one of the most counterintuitive but important things to understand about percentage math.
Formula Cheat Sheet
| What You Want to Find | Formula |
| Percentage Increase | (New − Old) ÷ Old × 100 |
| Percentage Decrease | (Old − New) ÷ Old × 100 |
| Percentage Change (either direction) | (New − Old) ÷ Old × 100 (negative result = decrease) |
| Percentage Difference (no clear “before/after”) | |Value 1 − Value 2| ÷ ((Value 1 + Value 2) ÷ 2) × 100 |
| Original Value (reverse calculation) | New Value ÷ (1 + (Percentage Increase ÷ 100)) |
| Percentage Points Difference | New % − Old % (not divided – a direct subtraction) |
Frequently Asked Questions
1. How do I find the percentage increase between two numbers?
Subtract the old number from the new number, divide the result by the old number, then multiply by 100. The formula is (New − Old) ÷ Old × 100.
2. How do you calculate the percentage increase?
To find the percentage increase, subtract the original value from the new value, divide the result by the original value, and then multiply by 100.
3. What’s the difference between percentage increase and percentage change?
Percentage increase specifically describes growth (a positive change). Percentage change is a broader term that covers both increases and decreases, with a negative result indicating a decrease.
4. What’s the difference between percentage increase and percentage difference?
Percentage increase assumes a clear starting point and ending point (a “before” and “after”). Percentage difference compares two values that don’t have that relationship, typically dividing by their average instead of treating one as the original.
5. How do you calculate percentage increase with negative numbers?
The formula still works mathematically, but the result can be misleading when the old value is negative, since dividing by a negative number flips the sign. In these cases, it’s often clearer to describe the change in absolute terms instead of as a percentage.
6. Can you calculate a percentage increase if the old value is zero?
No – dividing by zero is undefined, so the formula doesn’t produce a meaningful result. When the starting value is zero, it’s better to state the new value directly rather than express it as a percentage increase.
7. How do I calculate percentage increase in Excel or Google Sheets?
Use the formula =(B2-A2)/A2, where A2 is the old value, and B2 is the new value, then format the result as a percentage. Both Excel and Google Sheets use the identical formula structure.
8. What is the difference between a percentage increase and a percentage point increase?
A percentage point increase is a simple subtraction between two percentages (like 4% to 6% being a 2 percentage point increase). A percentage increase measures that same change relative to the original percentage (2 ÷ 4 × 100 = a 50% increase).
9. How do I reverse a percentage increase to find the original number?
Divide the new value by (1 + the percentage increase expressed as a decimal). For a 15% increase, divide the new value by 1.15 to find the original number.
10. Is a 20% decrease the opposite of a 20% increase?
No. Because the “old value” changes depending on the direction of the calculation, increasing a number by 20% and then decreasing the result by 20% does not bring you back to the original number.
11. How do you find percentage increase over multiple years?
Calculate the percentage increase between the starting year and ending year using the standard formula, or calculate year-over-year increases individually if you need to see the rate of change for each specific period.
12. What’s a good percentage increase for sales growth?
This varies significantly by industry, company size, and economic conditions, so there’s no single universal benchmark – comparing your growth rate to your own historical performance and industry averages is generally more useful than a fixed target.
Key Takeaways
- Percentage increase is calculated as (New Value − Old Value) ÷ Old Value × 100, always dividing by the original number.
- Percentage increase, percentage change, and percentage difference are related but distinct terms – increase/decrease need a clear before-and-after, while difference compares two unrelated values.
- The formula behaves predictably with positive numbers and decimals, but negative old values and zero values require extra care or a different way of describing the change.
- A percentage increase and percentage point change are not the same thing, and mixing them up is one of the most common (and misleading) mistakes in reporting.
- Increasing a number by X% and then decreasing it by the same X% does not return you to the original value, because the base changes between the two calculations.
- Spreadsheet formulas in Excel and Google Sheets use the identical structure: =(New-Old)/Old, formatted as a percentage.
Conclusion
Finding the percentage increase between two numbers comes down to one formula: subtract, divide by the original, multiply by 100. Where people usually get tripped up isn’t the formula itself – it’s the edge cases: negative starting values, zero baselines, confusing percentage increase with percentage points, or mixing it up with percentage difference. Once you know the difference between these concepts, you can use the percentage increase formula with confidence for salary increases, investment returns, rent adjustments, or business performance without any confusion.
If you’d rather skip the manual steps entirely – especially for larger datasets or numbers that don’t divide evenly – our Percentage Increase Calculator applies this exact formula instantly and helps you double-check your work in seconds.
