How to Calculate Percent Change (Formula + Examples)

TL;DR Percent change measures how much a value has increased or decreased relative to its original amount. The formula is: Percent Change = ((New Value - Old Value) / Old Value) x 100. A positive result means an increase; a negative result means a decrease. Plug any two numbers into our free Percent Change Calculator to get the answer instantly.

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What Is Percent Change?

Percent change is a mathematical measure that describes the degree of change over time, expressed as a percentage of the original value. It answers the question: “By what percentage did this number go up or down?” Whether you are tracking a stock price, comparing monthly expenses, measuring population growth, or evaluating a salary raise, percent change puts the shift into context by relating it to where you started.

Without percent change, raw numbers can be misleading. A $5,000 increase in salary sounds great — but it means something very different to someone earning $40,000 (a 12.5% raise) than to someone earning $200,000 (a 2.5% raise). Percent change normalizes the comparison so you can evaluate magnitude relative to scale.

Percent change is one of the most frequently tested concepts in standardized math, and it appears constantly in business, finance, science, and everyday decision-making.

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The Percent Change Formula

The core formula is:

[ \text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 ]

Component	Meaning
New Value	The value after the change occurred.
Old Value	The original value before the change (also called the reference or baseline value).
New - Old	The absolute difference between the two values (positive if increased, negative if decreased).
÷ Old Value	Dividing by the original value expresses the change relative to the starting point.
x 100	Converts the decimal result into a percentage.

Result interpretation:

• A positive percent change means the value increased.
• A negative percent change means the value decreased.
• A result of 0% means no change occurred.

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Percent Change vs Percent Difference

People often confuse these two. They are not the same.

	Percent Change	Percent Difference
Question it answers	”By what % did Value A change to become Value B?"	"How far apart are Value A and Value B, relative to their average?”
Has a direction	Yes — increase or decrease	No — it is always positive
Requires a baseline	Yes — the “old” value is the denominator	No — uses the average of both values
Formula	((New - Old) / Old) x 100	(|A - B| / ((A + B) / 2)) x 100
When to use	Comparing the same thing at two different times	Comparing two different things at the same time

Example: If your rent went from $1,200 to $1,350, you want percent change (12.5% increase). If you are comparing the rent of two different apartments ($1,200 vs $1,350), you want percent difference (11.8%).

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6 Worked Examples

Example 1: Price Increase

A laptop costs $800 last year and $920 this year.

• Old value: $800
• New value: $920
• Change: $920 - $800 = $120
• Percent change: ($120 / $800) x 100 = 15% increase

The laptop’s price went up by 15%.

Example 2: Price Decrease (Sale Discount)

A jacket was $150 and is now on sale for $112.50.

• Old value: $150
• New value: $112.50
• Change: $112.50 - $150 = -$37.50
• Percent change: (-$37.50 / $150) x 100 = -25% (a 25% decrease)

The jacket is 25% off its original price.

Example 3: Salary Raise

Your annual salary increased from $62,000 to $67,000.

• Old value: $62,000
• New value: $67,000
• Change: $67,000 - $62,000 = $5,000
• Percent change: ($5,000 / $62,000) x 100 = 8.06% increase

You received roughly an 8% raise. For context, the average U.S. annual raise in 2025 was 3.5–4%, so this raise is well above average.

Example 4: Stock Price Drop

A stock was trading at $48.00 per share and dropped to $36.00.

• Old value: $48.00
• New value: $36.00
• Change: $36.00 - $48.00 = -$12.00
• Percent change: (-$12.00 / $48.00) x 100 = -25% (a 25% decrease)

The stock lost a quarter of its value. Note: to recover from a 25% loss, the stock would need to increase by 33.3% (from $36 back to $48), not 25%. This asymmetry is important in investing.

Example 5: Website Traffic Growth

Your website had 4,200 visitors last month and 5,460 this month.

• Old value: 4,200
• New value: 5,460
• Change: 5,460 - 4,200 = 1,260
• Percent change: (1,260 / 4,200) x 100 = 30% increase

Traffic grew by 30% month over month.

Example 6: Population Decline

A town’s population was 32,000 in 2020 and 29,440 in 2025.

• Old value: 32,000
• New value: 29,440
• Change: 29,440 - 32,000 = -2,560
• Percent change: (-2,560 / 32,000) x 100 = -8% (an 8% decrease over 5 years)

The town lost 8% of its population over the period, or roughly 1.6% per year on average.

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How to Calculate Percent Increase

Percent increase is simply percent change when the result is positive (the new value is larger than the old value). The formula is identical:

[ \text{Percent Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 ]

If you need a dedicated tool for this, try our Percentage Increase Calculator.

Quick Reference Table

Old Value	New Value	Increase	Percent Increase
50	65	15	30%
100	125	25	25%
200	210	10	5%
1,000	1,500	500	50%
75	90	15	20%

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How to Calculate Percent Decrease

Percent decrease is percent change when the result is negative (the new value is smaller than the old value). Some people prefer to express it as a positive number with the word “decrease” attached:

[ \text{Percent Decrease} = \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \times 100 ]

Note that the numerator is flipped (Old - New instead of New - Old) so the result comes out positive.

Quick Reference Table

Old Value	New Value	Decrease	Percent Decrease
80	60	20	25%
500	425	75	15%
1,200	1,080	120	10%
250	200	50	20%
10,000	9,500	500	5%

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The Asymmetry Problem: Why a 50% Drop Needs a 100% Gain

One of the most counterintuitive aspects of percent change is that a percent decrease and the percent increase needed to recover are not equal.

Starting Value	After Drop	% Drop	Value Needed to Recover	% Gain Required
$100	$90	-10%	$100	+11.1%
$100	$75	-25%	$100	+33.3%
$100	$50	-50%	$100	+100%
$100	$25	-75%	$100	+300%

This happens because after a drop, the base value (the denominator) is smaller. A 50% drop brings $100 to $50. To get back to $100 from $50, you need a $50 gain — which is 100% of $50, not 50%.

This asymmetry is why investors focus so heavily on avoiding large losses. It is also why understanding percent change at a fundamental level matters for personal finance decisions.

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Compound Percent Change (Multiple Periods)

When percent change occurs over multiple periods, you cannot simply add the percentages together. You need to compound them.

Example: A stock gains 20% in Year 1 and loses 15% in Year 2. What is the total change?

Wrong approach: 20% - 15% = 5% gain. (Incorrect.)

Correct approach:

1. After Year 1: $100 x 1.20 = $120
2. After Year 2: $120 x 0.85 = $102
3. Total change: ($102 - $100) / $100 x 100 = 2% gain

The overall formula for compounding multiple period changes:

[ \text{Total Change} = \left[(1 + r_1) \times (1 + r_2) \times \cdots \times (1 + r_n) - 1\right] \times 100 ]

Where each r is the decimal form of that period’s percent change (20% = 0.20, -15% = -0.15).

Using our example: (1.20)(0.85) - 1 = 1.02 - 1 = 0.02 = 2%.

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Real-World Applications

Inflation and Cost of Living

The Consumer Price Index (CPI) uses percent change to measure inflation. When news outlets say “inflation was 3.2% last year,” they mean the CPI increased by 3.2% compared to the prior year. This single number affects wages, rent adjustments, Social Security payments, and monetary policy.

Business KPIs

Virtually every business metric is tracked as a percent change: month-over-month revenue growth, year-over-year customer acquisition, quarter-over-quarter churn rate. Expressing metrics as percent change allows you to compare across time periods and across companies of different sizes.

Academic Grading

Teachers use percent change to track student performance improvement. If a student scored 65 on the midterm and 78 on the final, the percent change is +20% — a concrete way to show progress.

Health and Fitness

Tracking body weight changes, strength progress (e.g., bench press max going from 185 lbs to 215 lbs = 16.2% increase), and calorie intake adjustments all use percent change math.

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Common Mistakes to Avoid

1. Dividing by the wrong value. Always divide by the old (original) value, not the new one. Dividing by the new value gives you a different number and a wrong answer.

2. Forgetting the sign. A negative percent change means a decrease. Do not drop the minus sign or report a decrease as an increase.

3. Adding percentages across periods. As shown in the compound section above, sequential percent changes must be multiplied, not added.

4. Confusing percent change with percentage points. If an interest rate goes from 3% to 5%, the change is 2 percentage points, but the percent change is 66.7% ((5-3)/3 x 100). These are different concepts.

5. Using percent change when you mean percent difference. If you are comparing two different items (not the same item over time), use percent difference instead.

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FAQ

Q: What is percent change? A: Percent change is a mathematical formula that measures how much a value has increased or decreased relative to its original amount, expressed as a percentage. The formula is ((New Value - Old Value) / Old Value) x 100. A positive result indicates an increase, and a negative result indicates a decrease.

Q: Is this calculator free to use? A: Yes. The Percent Change Calculator is completely free, requires no account or signup, and runs entirely in your browser. Your data never leaves your device — no information is sent to any server.

Q: How do I calculate percent change between two numbers? A: Subtract the old value from the new value to get the difference. Divide that difference by the old value. Multiply by 100 to convert to a percentage. For example, going from 80 to 100: (100 - 80) / 80 x 100 = 25% increase.

Q: What is the difference between percent change and percent difference? A: Percent change requires a clear “before” and “after” — it measures how much one value changed over time. Percent difference compares two values without a directional relationship, using their average as the denominator. Use percent change for the same measurement at different times; use percent difference for comparing two different measurements.

Q: Can percent change be more than 100%? A: Yes. If a value more than doubles, the percent change exceeds 100%. For example, if your investment goes from $1,000 to $3,500, the percent change is ((3,500 - 1,000) / 1,000) x 100 = 250%. There is no upper limit on percent increase. However, percent decrease cannot exceed 100% because a value cannot fall below zero (in most real-world contexts).

Q: Why does a 50% loss require a 100% gain to recover? A: Because after a 50% loss, the base value (denominator) is now half of what it was. If $100 drops to $50, you need to gain $50 to get back to $100. But $50 is 100% of $50, not 50%. The smaller your base, the larger the percentage gain needed to return to the original amount. This asymmetry is fundamental to how percentages work.

Q: How do I calculate percent change in Excel or Google Sheets? A: If the old value is in cell A1 and the new value is in cell B1, use the formula: =(B1-A1)/A1*100. Format the cell as a number with one or two decimal places. Alternatively, use =(B1-A1)/A1 and format the cell as a percentage — the multiplication by 100 happens automatically with percentage formatting.

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Callout

Calculate percent change instantly with our free Percent Change Calculator

Enter any two values — get the percent change, percent increase, or percent decrease in one click. No formulas needed.

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Additional Resources

• Percentage Calculator — Calculate increases, decreases, and reverse percentages for any number.
• Percentage Increase Calculator — Focused tool for calculating percentage increase between two values.
• Discount Calculator — Calculate sale prices and savings amounts from percentage discounts.
• Fraction Calculator — Add, subtract, multiply, and divide fractions with step-by-step solutions.

References:

1. Khan Academy. “Percent Change.” https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-percent-word-problems/v/percent-change-word-problem-example-1
2. U.S. Bureau of Labor Statistics. “Consumer Price Index — How BLS Measures Price Change.” https://www.bls.gov/cpi/questions-and-answers.htm
3. Investopedia. “Percent Change.” https://www.investopedia.com/terms/p/percentchange.asp