Everyday math
Percentage Change: Formula, Examples and Common Errors
Calculate percentage increase or decrease with the correct baseline, worked examples, edge cases and a free percentage change calculator.
The formula is (new value − old value) ÷ old value × 100. A rise from 40 to 50 is 10 ÷ 40 × 100, or a 25% increase.
The key idea
The old value belongs in the denominator because it is the reference point. A move from 50 to 40 is a 20% decrease, while the move back from 40 to 50 is a 25% increase.
Increase and decrease examples
Suppose a monthly bill rises from $64 to $72. The difference is $8 and the old bill is the baseline, so 8 ÷ 64 × 100 = 12.5% increase. If it later falls from $72 to $64, the decrease is 8 ÷ 72 × 100 = 11.11%. The percentages differ because their starting values differ.
| Old | New | Difference | Percentage change |
|---|---|---|---|
| 50 | 65 | +15 | +30% |
| 200 | 170 | -30 | -15% |
| 80% | 84% | +4 points | +5% relative |
Percentage change versus percentage points
When both values are percentages, choose the language carefully. An interest rate moving from 4% to 5% rises by one percentage point, but its relative percentage increase is 25%. Percentage points describe the direct gap; percentage change describes the gap relative to the old value.
What if the old value is zero?
The standard formula divides by the old value, so a move from zero has no finite percentage change. Describe it as an absolute increase. A move from 0 sales to 10 sales is an increase of 10, not a conventional 100% increase. Negative baselines also need explanation because the mathematical result can be misleading in a business report.
Report a change so it can be checked
Include the old value, new value, time period and direction. “Revenue increased 12.5%, from $64,000 to $72,000, year over year” is auditable; “up 12.5%” is not. When neither measurement is a natural baseline, explain which value you selected as the reference rather than presenting the direction as self-evident.
A practical workflow
Use the percentage-change calculator when you need the direction and size of a movement. Keep unrounded values until the final display when the figures will be used in a report.
Checks and limitations
Do not confuse percentage points with percentage change. A rate moving from 80% to 60% changes by 20 percentage points but by 25% relative to its starting value.
Check the result in the working tool
Open the Percentage change with the same values used in the example. Read the labels and units beside the result, then keep the source information until the output has been checked for its intended use.
Quick answers
Frequently asked questions
What is the percentage change from 100 to 120?
It is a 20% increase.
Can percentage change exceed 100%?
Yes. A value rising from 20 to 50 increases by 150% because the increase of 30 is one and a half times the starting value.
Should I use the old or new number underneath?
Use the old value for change over time. The denominator represents the baseline against which the difference is being measured.
What does a negative percentage change mean?
With a positive starting value, a negative result indicates a decrease. Report the direction in words as well as showing the signed number so the result cannot be misread.
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