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Percentage change
Measure how much a value rose or fell relative to where it started.
Formula: subtract the old value from the new, divide by the absolute old value, then multiply by 100.
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Percentage Change Calculator
Percentage change tells you how far a number moved relative to where it started — the language of price hikes, pay raises, and growth stats. Enter the old and new values; a positive result is growth, a negative one is decline.
How the percentage change calculator works
Percentage change tells you how far a number moved relative to where it started — the language of price hikes, pay raises, and growth stats. Enter the old and new values; a positive result is growth, a negative one is decline.
The formula
(new − old) ÷ |old| × 100
Worked example
A stock rises from $40 to $46. Subtract: 46 − 40 = 6. Divide by the starting value: 6 ÷ 40 = 0.15. Multiply by 100: a 15% increase.
Where this comes in handy
- Investments: track how much a portfolio gained or lost since purchase.
- Pay raises: a move from $22 to $24 an hour is a 9.09% raise.
- Business: compare this month's revenue with last month's.
- Fitness: measure weight or performance changes over time.
Percentage Change Calculator — frequently asked questions
What is the formula for percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. The sign of the answer tells you whether it rose or fell.
How is percentage change different from percentage difference?
Percentage change uses the starting value as its reference, so direction matters. Percentage difference compares two values symmetrically with no "before" and "after."
Can percentage change be more than 100%?
Yes — increases have no upper limit. Doubling is a 100% increase; tripling is a 200% increase. Decreases, though, cannot pass −100% for values that cannot go below zero.
What if the starting value is zero?
Percentage change from zero is undefined, because you cannot divide by zero. In that case describe the move in absolute terms instead.
Why do a 20% rise and a 20% fall not cancel out?
They apply to different bases. A 20% rise turns 100 into 120; a 20% fall then removes 24 from 120, leaving 96 — not 100.