Quick answer: percent change = (new value − old value) ÷ old value × 100. A positive answer is a percentage increase, and a negative answer is a percentage decrease.
The percent change equation
You see it in price changes, salary offers, website traffic and investment returns. The method is the same every time.
How to calculate a percentage increase
A subscription goes from $40 to $46 a month.
- Difference: 46 − 40 = 6
- Divide by the old value: 6 ÷ 40 = 0.15
- Multiply by 100: 15% increase
How to calculate a percentage decrease
Website visits drop from 8,000 to 6,000 a month.
- Difference: 6,000 − 8,000 = −2,000
- Divide by the old value: −2,000 ÷ 8,000 = −0.25
- Multiply by 100: 25% decrease
Percent change between two numbers
Whenever you have two numbers, decide which is the "before" and which is the "after". The before number is the old value and goes in the denominator. If there is no before and after, and you are simply comparing two things, use percentage difference instead: |a − b| ÷ ((a + b) ÷ 2). For 80 and 100, the change from 80 to 100 is 25%, while the percentage difference is 22.2%.
Percent change over last year
To find year-over-year (YoY) change, use last year's figure as the old value. Revenue of 84,000 last year and 96,600 this year gives (96,600 − 84,000) ÷ 84,000 = 0.15, or 15% growth. To go the other way, multiply last year's figure by 1.15 to predict this year's, or divide this year's by 1.15 to recover last year's.
Common mistakes
- Dividing by the wrong number. Always divide by the starting value. Dividing by the new value understates increases and overstates decreases.
- Averaging percentages. If something rises 50% and then falls 50%, you are not back to even: 100 × 1.5 × 0.5 = 75, a 25% loss overall. Multiply growth factors instead of adding percentages.
- Mixing up percent and percentage points. Unemployment moving from 4% to 5% is a 1 percentage point rise, which is a 25% relative increase.
Spreadsheet formula
If the old value is in A2 and the new value is in B2:
Format the result cell as a percentage. ABS keeps the sign meaningful when the old value is negative.
When percent change does not work
A percentage change from zero is undefined, because you would divide by zero. Report the plain difference instead.
For a quick answer, use the percentage change calculator. For "what is X% of Y", use the percentage calculator.