How to calculate percentage increase and decrease
Percentage change tells you how much a number went up or down compared with where it started. You need it for a raise, a rent increase, a sale price or your monthly sales report. The formula is short, and one detail trips most people up.
The percentage change formula
Subtract the old number from the new number, divide by the old number, then multiply by 100.
Percentage change = (new − old) ÷ old × 100
A positive answer is an increase. A negative answer is a decrease. The old number always goes on the bottom, because you are measuring the change against the starting point.
Example: a percentage increase
Your rent goes from $1,200 to $1,290 a month.
- New − old: 1,290 − 1,200 = 90
- Divide by the old number: 90 ÷ 1,200 = 0.075
- Multiply by 100: 7.5
Your rent went up by 7.5%.
Example: a percentage decrease
A jacket was $250 and now costs $200.
- New − old: 200 − 250 = −50
- Divide by the old number: −50 ÷ 250 = −0.2
- Multiply by 100: −20
The price dropped by 20%.
The mistake almost everyone makes
An increase and a decrease of the same size in dollars are not the same size in percent. Going from 80 to 100 is a 25% increase. Going back from 100 to 80 is only a 20% decrease. The dollar change is 20 both times, but the starting number is different.
This is why a stock that falls 50% has to rise 100% to get back to where it was.
Percent versus percentage points
If an interest rate goes from 4% to 5%, it rose by 1 percentage point. As a percentage change, it rose by 25%, because 1 ÷ 4 × 100 = 25. News stories often mix these up, so check which one is meant.
Three related calculations
- What is X% of Y? Multiply Y by X and divide by 100. 15% of $80 is $12.
- X is what percent of Y? Divide X by Y and multiply by 100. 45 out of 60 is 75%.
- Add a percentage to a number: multiply by 1 plus the rate. $80 plus 8% tax is 80 × 1.08 = $86.40.
You can do all of these in seconds with the Percentage Calculator. Type your two numbers and the answer appears as you type. If you are working out a sale price, the Discount Calculator shows the final price and how much you save.