Percentage Change Between Two Numbers
Formula: (New minus Old) / Old x 100. Percentage change tells you how much a value has moved relative to where it started. A positive answer means it went up; a negative answer means it went down. Order matters: always put the starting value in the denominator.
The Formula in Plain Language
Three steps:
- Subtract the starting value from the ending value to get the raw change.
- Divide that change by the starting value.
- Multiply by 100 to convert to a percentage.
If the result is positive, the value rose. If negative, it fell. The sign is built into the arithmetic.
Worked Examples
Increase: from 400 to 500
(500 minus 400) / 400 x 100 = 100 / 400 x 100 = 25% increase.
Decrease: from 500 to 400
(400 minus 500) / 500 x 100 = (minus 100) / 500 x 100 = minus 20%.
Notice the asymmetry: going from 400 to 500 is a 25% increase, but going from 500 back to 400 is only a 20% decrease. The base is different each time.
Temperature in Celsius
Average January temperature: 5 degrees. Average July temperature: 22 degrees.
(22 minus 5) / 5 x 100 = 17 / 5 x 100 = 340% increase.
That sounds extreme, but it reflects the small starting value (5). Percentage change amplifies when the base is small.
Revenue quarter-on-quarter
Q3: $840,000. Q4: $756,000.
(756,000 minus 840,000) / 840,000 x 100 = minus 84,000 / 840,000 x 100 = minus 10%.
Revenue fell 10% in Q4.
Test scores
A student scored 58 in the first test and 72 in the second.
(72 minus 58) / 58 x 100 = 14 / 58 x 100 = approximately 24.1% improvement.
Why the Starting Value Matters
The denominator anchors the percentage. Gain of 10 from a base of 20 is 50%. Gain of 10 from a base of 1,000 is 1%. Same raw gain, completely different percentage because the context is different.
This is why sports analysts, investors, and epidemiologists all care about what the base is before quoting a percentage change. A 50% increase in rare-disease cases sounds alarming; a 50% increase when starting from 2 cases means you went from 2 to 3.
Quick Reference Table
| Old Value | New Value | Change | % Change |
|---|---|---|---|
| 100 | 130 | +30 | +30% |
| 100 | 80 | -20 | -20% |
| 50 | 75 | +25 | +50% |
| 200 | 150 | -50 | -25% |
| 1,000 | 1,100 | +100 | +10% |
When the Starting Value Is Negative
Say a company reported a loss (minus $30,000) one year and a profit of $15,000 the next. The formula gives: (15,000 minus (minus 30,000)) / |minus 30,000| x 100 = 45,000 / 30,000 x 100 = 150%. But that sign and direction is misleading in financial contexts. When the base is negative, report the absolute change alongside the raw numbers rather than relying on a percentage alone.
When the Starting Value Is Zero
You cannot divide by zero, so standard percentage change is undefined when the old value is zero. Report the absolute change instead: "grew from 0 to 500 units" or "increased by 500 units." Some analysts use a placeholder like "N/A" or "infinity" in a table, with a footnote explaining it.
Chaining Multiple Percentage Changes
A value that rises 20% then falls 20% does not return to its starting point. It lands at 96% of the original. The math: 100 x 1.20 = 120, then 120 x 0.80 = 96. Percentage changes multiply, not add. So "up 20%, down 20%" is a net 4% loss. Keep that in mind when reading year-over-year comparisons.
For more on how individual increases and decreases work, see percentage increase and percentage decrease. For cases where you do not have a clear direction, see percentage difference vs percentage change.
Using the Calculator
The percentage calculator on this site has a dedicated percent change section. Enter the old value and new value; the calculator returns the percentage change with the direction labelled.
Frequently Asked Questions
What is the formula for percentage change?
Percentage Change = (New Value minus Old Value) / Old Value x 100. A positive result is an increase; a negative result is a decrease.
How do I know if the result is an increase or a decrease?
If the result is positive, the value increased. If negative, it decreased. The sign tells you the direction automatically.
What happens when the starting value is zero?
You cannot calculate a standard percentage change from zero because dividing by zero is undefined. Use the raw change or describe it in absolute terms instead.
Does the order of numbers matter?
Yes. The old (starting) value always goes in the denominator. Reversing the order gives a different answer and misrepresents the actual change.