Percentage Change
Relative change between two values.
Formula
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Example
$50 to $60: +20%
How it works
Percentage change tells you how much a value has increased or decreased compared with where it started. You subtract the old value from the new value to find the actual change, then divide by the old value so the change is measured relative to the starting amount. Multiplying by 100 turns that ratio into a percentage, which makes it easy to compare changes across different-sized numbers.
When to use it
Use this when you want to describe growth, decline, or comparison in everyday contexts like prices, scores, population, sales, or lab measurements. It is especially useful when the starting value matters, because the same absolute change can be a small or large percentage depending on the original amount.
Worked example, step by step
Original price of a jacket = $80 New price of the jacket = $68 Change = new - old = 68 - 80 = -12 Divide by the old value: -12 / 80 = -0.15 Convert to a percentage: -0.15 × 100 = -15% Final answer: the price changed by -15%, so it decreased by 15%
Common mistakes to avoid
- dividing by the new value instead of the old value
- forgetting that a decrease gives a negative result
- mixing up percentage change with the simple difference in units
Did You Know?
A 50% drop needs a 100% rise to recover.
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