Percent change formula
Percent change = (new − old) ÷ |old| × 100
A positive answer is a percentage increase; a negative answer is a percentage decrease. Always divide by the old (starting) value.
Worked examples
- Increase: rent goes from $1,200 to $1,320. (1,320 − 1,200) ÷ 1,200 × 100 = 10% increase.
- Decrease: a price falls from $80 to $60. (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
Why a 50% drop needs a 100% rise to recover
Percent changes are measured from different starting points. If $100 falls 50% to $50, getting back to $100 means rising $50 from a base of $50, which is +100%. The same is true for any loss: undoing a 20% drop takes a 25% rise.
Percent difference vs percent change
Use percent change when one value came first (before and after). Use percent difference to compare two values with no natural order, such as two quotes or two test results:
Percent difference = |a − b| ÷ ((a + b) ÷ 2) × 100
Increase a number by a percentage
Multiply by (1 + p ÷ 100): $50 plus 8% is 50 × 1.08 = $54. To decrease, multiply by (1 − p ÷ 100). Choose “Increase or decrease by %” above.
Percent change vs percentage points
If an interest rate goes from 4% to 5%, it rose by 1 percentage point, but by 25% in relative terms (1 ÷ 4). News reports mix these up often; both are correct, they just answer different questions.
Why a drop and a rise don’t cancel out
A price that falls 50% and then rises 50% ends up 25% lower: 100 → 50 → 75. The rise is measured from the smaller number. To get back to where you started after a 50% fall, you need a 100% rise.
Related calculators
- Percentage Calculator: X% of Y, X is what % of Y, and more.
- Discount Calculator: Sale price, savings and stacked discounts.
- Margin & Markup Calculator: Profit margin, markup and selling price.
Questions people ask
Can percent change be more than 100%?
Yes. Going from 20 to 50 is a 150% increase. A decrease, however, can’t go below −100% (that would mean dropping below zero).
What if the old value is zero?
Percent change from zero is undefined, because you can’t divide by zero. Describe the change in absolute terms instead (for example “from 0 to 40 sign-ups”).
How do I calculate percentage growth over several years?
For average yearly growth, use the compound rate: (new ÷ old)^(1 ÷ years) − 1. Growth from 100 to 150 over 5 years is about 8.4% a year, not 10%.
Formula checked October 2026 · How we calculate