Percentage Change Calculator
Compare two numbers, or add or subtract a percentage from one.
How to calculate percentage change
Subtract the starting value from the ending value, divide by the starting value, and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%, a 25% increase.
Increase vs. decrease are not symmetrical
A 25% increase from 80 gives 100, but going back from 100 to 80 is only a 20% decrease. That is because the starting value is different each time. This is why a price that rises 50% and then falls 50% ends up lower than where it started.
Percentage change vs. percentage points
If an interest rate goes from 4% to 5%, it rose by 1 percentage point, but the percentage change is 25%. Use percentage points for the plain difference between two percentages, and percentage change for the relative size of the move.
What if the starting value is 0?
Percentage change cannot be calculated from zero, since dividing by zero is undefined. Describe the change as an absolute amount instead.
Worked examples
- Price increase: a subscription goes from $40 to $52. The change is $12, and $12 ÷ $40 = 0.30, so the price rose 30%.
- Decrease: a monthly bill drops from $200 to $150. The change is −$50, and −$50 ÷ $200 = −0.25, so the bill fell 25%.
- More than 100%: traffic grows from 50 visits to 150. The change is 100, and 100 ÷ 50 = 2, which is a 200% increase.
Why a rise and a fall do not cancel out
Start with 100. A 50% drop takes it to 50. A 50% rise on that new number only adds 25, so you finish at 75, which is 25% below where you started. The same thing happens in reverse: after a 20% drop, you need a 25% rise to get back to the original number. Always check which number the percentage is measured from.
Two increases in a row
A 10% raise followed by another 10% raise is not a 20% raise. The second 10% is taken from the larger amount, so $1,000 becomes $1,100 and then $1,210, a total increase of 21%. To combine changes, multiply the factors (1.10 × 1.10 = 1.21) instead of adding the percentages.
Common uses
- Comparing a salary or rent before and after a change
- Tracking weight, savings or investment balances over time
- Reading sales reports and website traffic month over month
- Working out how much a sale price or a markup really changes a number
Frequently asked questions
Can a percentage decrease be more than 100%?
Not for a quantity that cannot go below zero, such as a price. A 100% decrease means the value reaches zero. A number that can go negative, such as a bank balance or temperature, is a special case where percentage change can be misleading.
Which number goes in the denominator?
The starting value. Dividing by the ending value is a common mistake and gives a different, wrong answer.
What if the starting value is negative?
The usual formula gives a result that is hard to interpret, because a move from −50 to −25 looks like a drop even though the number went up. When values cross zero, describe the change in plain amounts instead.