Percent Change Formula & Calculator
Enter an old and a new value to get the percent change, with every step of the working shown.
Change = 65 − 50 = 15Divide by |old value| = 15 ÷ 50 = 0.3× 100 = +30%
How to calculate percent change
Percent change tells you how much a value has grown or shrunk relative to where it started. Three steps:
- Find the change: subtract the old value from the new value.
- Divide by the old value (use its absolute value if it is negative).
- Multiply by 100 to turn the decimal into a percentage.
A positive answer is a percent increase; a negative answer is a percent decrease.
Worked examples
| Situation | Old | New | Working | Percent change |
|---|---|---|---|---|
| Test score | 50 | 65 | (65 − 50) ÷ 50 × 100 | +30% |
| Monthly visitors | 80 | 60 | (60 − 80) ÷ 80 × 100 | −25% |
| Share price | $120 | $96 | (96 − 120) ÷ 120 × 100 | −20% |
| Loss narrowing | −40 | −10 | (−10 − (−40)) ÷ 40 × 100 | +75% |
Percent change with negative numbers
When the starting value is negative, such as a company loss, divide by the absolute value of the old number. A loss that narrows from −40 to −10 is an improvement of 30, and 30 ÷ 40 = +75%. If you divided by −40 instead, you would get −75% and wrongly report a worsening. Spreadsheets need the same fix: see percent change in Excel.
Percent change vs. percent difference
Percent change has a direction: there is an old value and a new value, and the old value is the base. Percent difference compares two values with no “before” and “after”, so it divides by their average instead. From 50 to 65 is a 30% change, but the percent difference between 50 and 65 is 26.087%. Use the percent difference calculator when neither value is the starting point.
Percent change vs. percentage points
When the values are already percentages, say an interest rate going from 3% to 4%, the change is 1 percentage point but a 33.33% relative increase. Mixing the two up is one of the most common errors in news reports. See percentage points vs. percent.
Common mistakes
- Dividing by the new value. The base is always the old (starting) value.
- Adding percentages across periods. +10% then −10% is not 0%: 100 → 110 → 99, a net −1%. For multi-year growth use the CAGR calculator.
- Reversing a percentage the wrong way. If a price rose 20% to 90, the original was 75, not 72. The reverse percentage calculator does this for you.
- Starting from zero. Percent change from 0 is undefined; say “from 0 to 12” instead.
Frequently asked questions
What is the formula for percent change?
Percent change = (new value − old value) ÷ |old value| × 100. A positive result is an increase and a negative result is a decrease.
How do I calculate percentage change between two numbers?
Subtract the old number from the new number, divide the result by the old number, then multiply by 100. For example, from 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.
Is percentage change the same as percent change?
Yes. 'Percent change' and 'percentage change' are two names for the same calculation.
Can percent change be more than 100%?
Yes. Any value that more than doubles has a percent change above 100%. Going from 20 to 50 is a 150% increase. A decrease, however, can't go below −100% for positive numbers.
What is the percent change from 0?
It is undefined, because the formula divides by the old value and you can't divide by zero. Describe the change in absolute terms instead, for example 'up from 0 to 12'.
Why do I divide by the absolute value of the old number?
So the sign of the answer always matches the direction of the change. When the old value is negative, dividing by it directly would flip the sign and report an increase as a decrease.