Percentage Change Calculator
Use this free Percentage Change Calculator to calculate the percentage increase or decrease between an original value and a new value. The calculator also shows the absolute change and supports applying or reversing a known percentage change.
Calculate Percentage Change
Enter the original value and the new value to calculate the percentage increase or decrease.
Apply a Percentage Change
Enter an original value and a known percentage increase or decrease to calculate the resulting new value.
Enter a positive percentage for an increase and a negative percentage for a decrease.
Find Original Value From Percentage Change
If you know the final value and the percentage increase or decrease, use this calculator to find the original value.
What Is Percentage Change?
Percentage change measures how much a value has increased or decreased compared with its original or starting value. It is commonly used to compare prices, salaries, revenue, sales, populations, measurements, scores and other values over time.
A positive result indicates that the new value is higher than the original value. A negative result indicates that the new value is lower than the original value.
Percentage Change Formula
The standard percentage change formula is:
The original value is the reference point. This is why the order of the values matters.
Percentage Increase Formula
When the new value is greater than the original value, the result represents a percentage increase.
Example: a value increases from 80 to 100.
Percentage Increase = (20 ÷ 80) × 100
Percentage Increase = 25%
Percentage Decrease Formula
When the new value is lower than the original value, the result is a percentage decrease.
Example: a value decreases from 100 to 80.
Percentage Decrease = (20 ÷ 100) × 100
Percentage Decrease = 20%
Why 80 to 100 Is Not the Same as 100 to 80
Percentage change depends on the starting value. Therefore, reversing the values does not simply change the sign of the same percentage.
| Change | Absolute Change | Percentage Change |
|---|---|---|
| 80 → 100 | +20 | +25% |
| 100 → 80 | -20 | -20% |
The numerical difference is the same in magnitude, but the percentage uses a different starting value.
Percentage Change vs Percentage Difference
Percentage change and percentage difference answer different questions.
| Feature | Percentage Change | Percentage Difference |
|---|---|---|
| Starting value | Has a defined original value | No specific baseline |
| Direction | Can show increase or decrease | Normally expressed as a positive value |
| Reference | Original value | Average of the two values |
| Typical use | Before-and-after comparisons | Comparing two independent values |
Percentage Change vs Percentage Points
Percentage points and percentage change are not the same thing.
Suppose an interest rate changes from 5% to 6%.
Relative percentage change = (1 ÷ 5) × 100 = 20%
Therefore, the rate increased by 1 percentage point but by 20% relative to its original value.
Common Percentage Change Examples
| Original | New | Absolute Change | Percentage Change |
|---|---|---|---|
| 100 | 120 | +20 | +20% |
| 100 | 80 | -20 | -20% |
| 200 | 250 | +50 | +25% |
| 500 | 400 | -100 | -20% |
| 1,000 | 1,250 | +250 | +25% |
| 1,000 | 750 | -250 | -25% |
How to Calculate Percentage Change
- Identify the original or starting value.
- Identify the new or ending value.
- Subtract the original value from the new value.
- Divide the change by the original value.
- Multiply the result by 100.
- Interpret a positive result as an increase and a negative result as a decrease.
Percentage Change in Price
Percentage change is commonly used to compare an old price with a new price.
For example, if a product increases from $80 to $100, the percentage change is 25%.
Percentage Change in Salary
Salary increases can be expressed as a percentage change from the previous salary.
For example, if a salary increases from 4,000 to 4,600:
Percentage Increase = (600 ÷ 4,000) × 100
Percentage Increase = 15%
Percentage Change in Revenue and Sales
Businesses frequently use percentage change to compare revenue, sales, orders, customers and other performance metrics between two periods.
A positive result indicates growth, while a negative result indicates a decline compared with the previous period.
Percentage Change in Weight
Percentage change can also be used to compare measurements such as weight before and after a change.
The same mathematical formula applies as long as the original measurement is used as the baseline.
Applying a Percentage Increase
To increase a value by a known percentage, use:
Example: increase 200 by 15%.
New Value = 200 × 1.15
New Value = 230
Applying a Percentage Decrease
To decrease a value by a known percentage, use:
Example: decrease 200 by 15%.
New Value = 200 × 0.85
New Value = 170
How to Find the Original Value
If you know the new value and the percentage change, the original value can be calculated using:
A negative percentage can be used when the known change represents a decrease.
Why a Percentage Increase Is Not Reversed by the Same Percentage
Percentages use a reference value. If a number increases by 25%, the resulting number is larger than the original. A subsequent 25% decrease is calculated from that larger number, so it does not return to the starting value.
125 − 25% = 93.75
To return from 125 to 100, the required decrease is 20%, not 25%.
What Happens When the Original Value Is Zero?
Percentage change from zero is mathematically undefined because the original value appears in the denominator of the formula.
In this situation, report the absolute change or use another appropriate measure rather than presenting an ordinary percentage change.
Negative Values and Percentage Change
Percentage change involving negative values requires additional care because the interpretation can depend on the context. A formula using the absolute value of the original value can preserve the direction of the numerical movement, but a sign change can make percentage interpretation misleading.
For financial losses, temperatures, accounting values or other measurements that can cross zero, consider reporting both the absolute change and the percentage result.
Common Uses of Percentage Change
- Price increases and decreases
- Salary and wage changes
- Business revenue growth
- Sales growth and decline
- Population growth
- Website traffic changes
- Investment performance comparisons
- Exam score changes
- Weight changes
- Production volume changes
- Inventory changes
- Monthly and yearly financial comparisons
- Before-and-after measurements
Percentage Change Calculation Tips
- Always identify which value is the original or starting value.
- Do not divide by the new value when calculating ordinary percentage change.
- Keep the sign when you need to identify whether the value increased or decreased.
- Do not confuse percentage points with percentage change.
- Remember that percentage change from zero is undefined.
- For important business or financial reports, retain the unrounded calculation and round only the displayed result.
Frequently Asked Questions
How do I calculate percentage change?
Subtract the original value from the new value, divide the result by the original value, and multiply by 100.
What is the percentage change from 80 to 100?
The percentage change from 80 to 100 is a 25% increase. The difference is 20, and 20 divided by 80 equals 25%.
What is the difference between percentage increase and percentage decrease?
Both compare the new value with the original value. A higher new value produces a positive percentage change, while a lower new value produces a negative percentage change.
Why is percentage change not the same when values are reversed?
Percentage change uses the starting value as the reference. Therefore, reversing the values changes the denominator and produces a different percentage.
What happens if the original value is zero?
Percentage change from an original value of zero is undefined because division by zero is not mathematically valid.
What is the difference between percentage change and percentage difference?
Percentage change uses a defined original value as the reference. Percentage difference is generally used when neither value is the designated baseline and uses their average as the reference.
What is the difference between percentage change and percentage points?
Percentage points show the direct difference between two percentages, while percentage change measures the difference relative to the original percentage.
Can I calculate percentage change for prices and salaries?
Yes. Percentage change can be used for prices, salaries, revenue, sales, population, scores, measurements and many other before-and-after comparisons.
How do I calculate a new value after a percentage increase?
Multiply the original value by 1 plus the percentage increase divided by 100.
How do I find the original value after a percentage change?
Divide the new value by 1 plus the percentage change divided by 100.
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