Percent Change Calculator
Skip the manual arithmetic and calculate your own numbers.
Percentage increase formula
When a value rises from an old amount to a new amount, first find the increase. Then divide the increase by the original value and multiply by 100.
For example, if a price rises from $80 to $92, the increase is $12. Dividing $12 by the original $80 gives 0.15, so the percentage increase is 15%.
Percentage decrease formula
The process is nearly identical when the value falls. Find the amount of the decrease, divide it by the original value and convert the decimal to a percentage.
If a price falls from $120 to $90, the decrease is $30. Dividing $30 by $120 gives 0.25, so the percentage decrease is 25%.
Why the original value matters
The denominator is the starting value because percentage change measures the change relative to where you began. Reversing the old and new values produces a different result.
This is also why a 20% increase followed by a 20% decrease does not return to the starting value. If 100 increases by 20%, it becomes 120. A 20% decrease from 120 is 24, leaving 96.
Percentage change vs. percent difference
Percentage change is normally used when there is a meaningful starting value and ending value. Percent difference is commonly used when comparing two values without treating one as the original baseline.
For percent difference, the absolute difference is often divided by the average of the two values rather than by the first value.
Reverse percentage questions
Sometimes you know the final number and the percentage change but need to recover the original number. For an increase, divide the final value by 1 plus the percentage expressed as a decimal. For a decrease, divide by 1 minus the percentage expressed as a decimal.
For example, if a price after a 25% increase is $100, the original price was $100 ÷ 1.25 = $80.
Common percentage mistakes
- Dividing by the new value instead of the original value.
- Using 15 instead of 0.15 inside a decimal-based formula.
- Confusing a percentage-point change with a percent change.
- Assuming equal percentage increases and decreases cancel each other out.
- Trying to calculate percentage change from an original value of zero, which makes the standard formula undefined.
Frequently asked questions
What is the formula for percentage increase?
Subtract the old value from the new value, divide the increase by the old value, then multiply by 100.
Can percentage change be negative?
Yes. A negative percentage change indicates that the new value is below the original value.
What happens if the original value is zero?
The standard percentage-change formula divides by the original value, so a starting value of zero makes the usual percentage change undefined.