Percentage Change Calculator
Type an old and a new value to get the percentage change, positive for a rise and negative for a fall, with the steps behind it.
What’s the % change from to ?
Percentage change
+20%
From 2.35 to 2.82 is a rise of 20%.
How this works: Method, 1 source, Checked against 1 worked example,
How this works
Method
Percentage change is one formula for both directions: (new − old) ÷ old × 100. A positive result is a rise and a negative result is a fall. A loaf going from $2.35 to $2.82 changed by +$0.47, and 0.47 ÷ 2.35 = 0.2, so the price rose 20%. Full method
Sources
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
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Changes
- Added eight pages for common questions, from percent of a number to percent error and reverse percentages, each with its own method, examples and table.
- Added key facts with a worked example of each formula.
- Redesigned: type the numbers straight into a sentence, with bars on one scale that picture the answer.
- Results now update as you type, with no Calculate button.
- First published.
How to calculate percentage change
Percentage change is one formula for both directions: (new − old) ÷ old × 100. A positive result is a rise and a negative result is a fall. A loaf going from $2.35 to $2.82 changed by +$0.47, and 0.47 ÷ 2.35 = 0.2, so the price rose 20%.
When the old value is negative (a temperature, a bank balance, a loss), divide by its size rather than its signed value. From −10 to −5 is a rise of 5, and 5 ÷ 10 is +50%, which matches the direction the number moved. This calculator always divides by the size of the starting value.
Changes in a row multiply, so they don’t simply add up. +10% followed by −10% leaves you 1% down, because the fall is 10% of a larger amount. The table shows how pairs of changes combine.
% change = (new − old) ÷ |old| × 100
- A change between two percentages, such as an interest rate going from 4% to 5%, is better given in percentage points (1 point) than as a percent change (25%), to avoid confusing the two. Source: Wikipedia, Percentage point.
How two changes in a row combine
Apply the first change, then the second to the result; the overall change is exact.
| First change | Then | Overall change |
|---|---|---|
| +10% | −10% | −1% |
| +20% | −20% | −4% |
| +50% | −50% | −25% |
| +25% | −20% | 0% |
| +100% | −50% | 0% |
| −10% | +10% | −1% |
| −50% | +100% | 0% |
| +10% | +10% | +21% |
| +5% | +5% | +10.25% |
| +30% | −30% | −9% |
Show all 12 rowsShow fewer
| −20% | −20% | −36% |
| +3% | −3% | −0.09% |
Frequently Asked Questions
Is percentage change the same as percentage difference?
No. Change has a direction and divides by the old value. Difference compares two values with no starting point and divides by their average, so it is the same whichever order you put them in.
Why does +50% and then −50% not get back to the start?
The fall is half of a bigger number. 100 up 50% is 150, and 150 down 50% is 75, which is 25% below where you began.
What is the percentage change from 0?
It is undefined: any rise from 0 is an infinite percentage of 0. Report the change itself (up 12 units) instead, or compare with the percentage difference.