📈 Percentage Change Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Percentage change = (new - old) ÷ |old| × 100.
This percentage change calculator tells you how much a value has gone up or down in percentage terms. Enter the old (starting) value and the new (ending) value, and it shows the percentage change, whether it is an increase or a decrease, and the raw difference between the two numbers. It is handy for prices, salaries, test scores, traffic figures, or any before-and-after comparison.
What is the Percentage Change Calculator?
Percentage change measures how much a number has grown or shrunk relative to where it started, expressed as a percentage rather than a raw amount. The formula is (new value minus old value) divided by the absolute value of the old value, then multiplied by 100. A positive result means the value increased, a negative result means it decreased, and zero means it stayed the same. Because the change is measured against the starting value, the same absolute jump can be a big percentage or a small one depending on the base you start from.
The reason percentage change is so useful is that it puts changes of different sizes on a common scale. A $5 rise on a $10 item is a 50% increase, while the same $5 rise on a $500 item is only a 1% increase. Raw differences alone cannot capture that, but percentages can, which is why they show up everywhere from inflation reports to stock prices to website analytics. Whenever you want to compare growth or decline fairly across items of different sizes, percentage change is the tool.
One important detail is that the result is not symmetric. Going from 100 to 150 is a 50% increase, but going back from 150 to 100 is only about a 33% decrease, because the starting value (the denominator) is different in each direction. This is why a value can drop by, say, 50% and then need a 100% rise just to recover. It is also why percentage change is undefined when the old value is 0: you cannot divide by zero, and there is no meaningful percentage for going from nothing to something.
When to use it
- Working out how much a price rose or fell between two dates, such as a stock, a salary, or a grocery item.
- Comparing this month to last month for website traffic, sales, or sign-ups to see real growth or decline.
- Checking how much a test score, weight, or any measurement changed from a baseline.
- Reporting results clearly, for example "revenue is up 12% on last quarter" instead of just a raw dollar figure.
How to use the Percentage Change Calculator
- Enter the old (starting) value in the first field.
- Enter the new (ending) value in the second field.
- Read the percentage change, which is labelled as an increase or a decrease.
- Check the difference (new minus old) to see the raw amount of the change.
- Use Swap values to reverse the comparison, or Clear to start over.
Formula & method
Worked examples
A price rises from 50 to 75.
- difference = 75 − 50 = 25
- divide by the old value: 25 ÷ 50 = 0.5
- multiply by 100: 0.5 × 100 = 50
Result: +50% (a 50% increase)
A figure falls from 80 to 60.
- difference = 60 − 80 = −20
- divide by the old value: −20 ÷ 80 = −0.25
- multiply by 100: −0.25 × 100 = −25
Result: −25% (a 25% decrease)
A value goes from 200 down to 150.
- difference = 150 − 200 = −50
- divide by the old value: −50 ÷ 200 = −0.25
- multiply by 100: −0.25 × 100 = −25
Result: −25% (a 25% decrease)
Example percentage changes from an old value of 100
| Old value | New value | Difference | Percentage change |
|---|---|---|---|
| 100 | 150 | +50 | +50% |
| 100 | 125 | +25 | +25% |
| 100 | 100 | 0 | 0% |
| 100 | 75 | −25 | −25% |
| 100 | 50 | −50 | −50% |
| 100 | 0 | −100 | −100% |
Why percentage change is not symmetric
| Move | Percentage change |
|---|---|
| 100 → 150 | +50% increase |
| 150 → 100 | about −33.3% decrease |
| 50 → 100 | +100% increase |
| 100 → 50 | −50% decrease |
Common mistakes to avoid
- Dividing by the new value instead of the old one. Percentage change always divides the difference by the original (old) value, not the new value. Using the new value as the denominator gives the wrong percentage.
- Assuming a rise and the matching fall are equal percentages. A 50% increase from 100 to 150 does not reverse with a 50% decrease. Falling from 150 back to 100 is only about a 33% decrease, because the starting point changed.
- Mixing up percentage change with percentage points. If a rate goes from 10% to 12%, that is a 2 percentage point rise but a 20% increase. Confusing the two overstates or understates the change badly.
- Trying to compute a percentage change from zero. When the old value is 0 the result is undefined, because dividing by zero is not allowed. Going from 0 to any positive number is treated as an infinite increase, so report it as such rather than a number.
Glossary
- Old value
- The starting or original number, used as the baseline you measure the change against. It is the denominator in the formula.
- New value
- The ending or final number after the change. The difference is measured from the old value to this one.
- Percentage increase
- A positive percentage change, meaning the new value is larger than the old value.
- Percentage decrease
- A negative percentage change, meaning the new value is smaller than the old value.
- Percentage point
- The simple arithmetic difference between two percentages, such as 10% to 12% being a 2 percentage point change. It is different from the percentage change of the rate itself.
Frequently asked questions
How do you calculate percentage change?
Subtract the old value from the new value, divide the result by the absolute value of the old value, then multiply by 100. For example, going from 50 to 75 gives (75 − 50) ÷ 50 × 100 = 50%, a 50% increase.
What is the difference between percentage increase and percentage decrease?
A percentage increase is a positive change where the new value is larger than the old one, and a percentage decrease is a negative change where the new value is smaller. The same formula gives both: the sign of the result tells you the direction.
Why is the percentage change undefined when the old value is zero?
The formula divides by the old value, and division by zero is undefined. There is no meaningful percentage for going from nothing to something, so a move from 0 to a positive number is described as an infinite or undefined increase.
Why is a 50% increase not cancelled by a 50% decrease?
Because each percentage is measured against a different starting value. Rising 50% from 100 gives 150, but a 50% decrease from 150 lands at 75, not 100. To return from 150 to 100 you need only about a 33% decrease.
What is the difference between percentage change and percentage points?
Percentage change measures the relative change between two numbers, while percentage points measure the plain difference between two percentages. A move from 10% to 12% is a 2 percentage point rise but a 20% percentage change.
Can percentage change be more than 100%?
Yes. Any time the new value is more than double the old value, the increase is over 100%. For example, going from 40 to 120 is a 200% increase, because the value tripled.