Percentage Change Calculator
Calculate the percentage change between any two values. Find percentage increase or decrease instantly using the formula with worked examples.
A percentage change calculator finds how much a value has grown or shrunk relative to its starting point. Enter any two numbers and this percentage change calculator returns the exact result instantly. Step-by-step working shows the formula so the result is clear, not just a number.
Finance professionals use percentage change to track stock returns. Retailers apply it to measure discounts. Employers use it to calculate raise percentages. Scientists use it to report experimental results. Because it measures change relative to the original value, it gives meaningful comparisons regardless of scale.
What Is Percentage Change?
Percentage change is a measure of how much a value has increased or decreased relative to its original value, expressed as a percentage. A positive result indicates a percentage increase; a negative result indicates a percentage decrease. Unlike absolute change, percentage change accounts for the size of the starting value. This makes comparisons across different scales meaningful and standardized.
A $10 rise on a $50 item represents a 20% increase. The same $10 rise on a $500 item is only a 2% increase. The dollar amount is identical; the relative change is not. That distinction is why percentage change is the standard unit of comparison across economics, health, and data analysis.
Percentage Change Formula
The standard percentage change formula is:
Percentage Change = ((New Value - Old Value) / |Old Value|) x 100
The vertical bars around Old Value indicate absolute value. This prevents a negative starting point from inverting the direction of the result.
Worked example: A product price rises from $40 to $52.
- Difference: 52 - 40 = 12
- Divide by original: 12 / 40 = 0.30
- Multiply by 100: 0.30 x 100 = 30% increase
If the result is positive, the value increased. If negative, it decreased. The formula is the same in both cases.
Percentage Increase Formula
When the new value is larger than the original, the calculation produces a percentage increase. The percentage increase formula is identical to the general percentage change formula, with a positive result confirming growth:
Percentage Increase = ((New Value - Original Value) / Original Value) x 100
Example: An employee annual salary increases from $48,000 to $54,000. How to calculate percentage increase: (54,000 - 48,000) / 48,000 x 100 = 12.5% salary increase.
This is exactly what a percentage increase calculator computes automatically. A $6,000 raise on a $48,000 salary (12.5%) is a much stronger outcome than the same $6,000 on a $120,000 salary (5%).
Percentage Decrease Formula
When the new value is smaller than the original, the result is a percentage decrease. The percentage decrease formula returns a negative number, and the absolute value of that number is the percentage decrease:
Percentage Decrease = ((Original Value - New Value) / Original Value) x 100
Example: A retailer marks down a jacket from $180 to $135. Percentage decrease: (180 - 135) / 180 x 100 = 25% decrease.
How to Calculate Percentage Change
Follow these four steps to calculate percentage change between any two values:
- Identify the old value — the starting number before the change occurred.
- Identify the new value — the ending number after the change.
- Find the difference: New Value minus Old Value.
- Divide the difference by the absolute value of the old value, then multiply by 100.
A positive result means the value increased. A negative result means it decreased. To learn how to find percentage change for any pair of numbers, follow these four steps above.
How to Calculate Percentage Change Between Two Numbers
To calculate percentage change between two numbers: subtract the first from the second. Then divide by the absolute value of the first number and multiply by 100. Example: percentage change from 80 to 100 is ((100 - 80) / 80) x 100 = 25% increase. From 100 to 80 it is ((80 - 100) / 100) x 100 = negative 20%, meaning a 20% decrease. Always use the original as the denominator when you calculate percentage change between two numbers. To calculate percentage increase between two numbers, ensure the new value is larger than the old value. The result will be positive, confirming an increase.
Percentage Change Examples
Calculate Raise Percentage
Maria earns $3,200 per month. After her review, her employer raises her pay to $3,520. To calculate raise percentage: (3,520 - 3,200) / 3,200 x 100 = 10% raise. Knowing how to calculate raise percentage helps employees compare offers and negotiate, not just focus on the dollar amount.
Calculate Percent Growth in Revenue
A business recorded $85,000 in quarterly revenue last year and $102,000 this year. To calculate percent growth: (102,000 - 85,000) / 85,000 x 100 = 20% revenue growth. Expressing growth as a percentage allows meaningful ratio comparison against benchmarks regardless of company size.
Calculate Percent Improvement
To calculate percent improvement, use the same percentage change formula. If a student test score improves from 60 to 75, the percent improvement is (75 - 60) / 60 x 100 = 25%. An athlete reducing mile time from 8 to 6.5 minutes shows 18.75% improvement: (8 - 6.5) / 8 x 100 = 18.75%. Percent improvement always uses the original value as the base.
Calculate Percentage Increase in Price
A streaming subscription rises from $9.99 to $12.99 per month. To calculate percentage increase in price: (12.99 - 9.99) / 9.99 x 100 = approximately 30% price increase. This number frames the decision more accurately than the $3.00 absolute difference.
How to Work Out Percentage Increase in Investments
An investor buys shares at $42 each. The price rises to $63. How to work out the percentage increase: (63 - 42) / 42 x 100 = 50% gain. This growth rate measure is also called return on investment (ROI) when expressed as a percentage of the entry price.
Percentage Change Reference Table
Common percentage change scenarios with old value, new value, and the calculated result:
| Old Value | New Value | Absolute Change | Percentage Change |
|---|---|---|---|
| 50 | 75 | +25 | +50.0% |
| 100 | 80 | -20 | -20.0% |
| 200 | 250 | +50 | +25.0% |
| 1,000 | 1,200 | +200 | +20.0% |
| 500 | 350 | -150 | -30.0% |
| 25 | 30 | +5 | +20.0% |
| 80 | 64 | -16 | -20.0% |
| 150 | 225 | +75 | +50.0% |
| 400 | 300 | -100 | -25.0% |
| 60 | 90 | +30 | +50.0% |
| 1,500 | 1,800 | +300 | +20.0% |
| 10 | 7 | -3 | -30.0% |
Percentage Change vs Percentage Difference
Percentage change and percentage difference measure related but distinct things. Percentage change measures directional movement over time using the old value as the base. Percentage difference compares two values with no implied direction. It uses the average of both values as the base, producing a symmetric result for comparing two unordered items.
Use a percentage difference calculator when comparing two unordered items. Percentage difference formula: |Value A - Value B| / ((Value A + Value B) / 2) x 100. Comparing 80 and 100: percentage change from 80 to 100 = 25%. Percentage difference = 20 / 90 x 100 = approximately 22.2%.
Percentage Change vs Percentage Points
Percentage points and percentage change are frequently confused. A percentage point is the arithmetic difference between two percentages. Percentage change is the relative change using the original as the base and shows the percent increase or percent decrease from the starting point.
Example: An interest rate rises from 2% to 5%. That is a 3 percentage point increase. But expressed as percentage change: (5 - 2) / 2 x 100 = 150% increase. The two numbers describe the same event but look dramatically different.
Why a 50% Loss Requires a 100% Gain to Break Even
Percentage changes cannot be added or averaged because the base shifts after every step. A 50% loss on $1,000 leaves $500. To return to $1,000 requires a 100% gain because the base has changed. This asymmetry explains why investment losses are harder to recover from than they appear. The sequence of returns matters as much as the average growth rate.
Calculating Percentage Change with Negative Numbers
When the old value is negative, the percentage change formula still applies. The absolute value in the denominator prevents the sign from inverting incorrectly. Example: net income shifts from -$50,000 to -$30,000. The result: 20,000 divided by 50,000 times 100 = 40% improvement. When the old value is zero, how to calculate the formula has no solution — there is no meaningful base.
Limitations of the Percentage Change Calculator
The percentage change calculator handles most real-world scenarios accurately. Specific edge cases require careful interpretation:
- Old value of zero: Division by zero is undefined. Percentage change cannot be calculated when the original value is 0.
- Negative starting values: Results are mathematically correct but can seem counterintuitive. A move from -$100 to -$50 shows as a 50% improvement because the value is less negative.
- Chaining percentage changes: A 20% increase followed by a 20% decrease leaves you at 96% of the original — not 100%. Percentage changes cannot be simply added because the base changes each time.
- Very small starting values: A change from $0.01 to $0.02 is technically 100%. The practical significance is near zero.
For mathematical computation standards, DigiCalc follows methodology aligned with the Institute of Electrical and Electronics Engineers (IEEE).
Real-World Uses of Percentage Change
Percentage change applies wherever data changes over time:
- Finance: Stock returns, portfolio performance, and revenue growth are reported as percentage changes for ratio comparison across companies and time periods.
- Employment: Calculating raise percentages, wage growth, and compensation benchmarks use the percentage change formula to give context to dollar figures and show percent increase clearly.
- Retail: Discount percentages, price changes, and seasonal sales performance are measured as percentage changes for planning and consumer decisions.
- Health: Weight loss progress, blood pressure changes, and lab results are expressed as percentage changes to account for individual baseline differences.
- Science: Experimental results, population growth rates, and environmental measurements use percentage change for standardized cross-study comparison of the relative change over time.
- Education: Test score improvements and enrollment trends are reported as percentage changes to track progress meaningfully across student populations.
For related tools, use DigiCalc percentage calculator to find what percentage one number is of another. For growth-only calculations, try the percentage increase calculator. To measure reductions, use the percentage decrease calculator.