Math
Percentage Change Calculator
Enter the starting value and the new value to see how much it changed, in percent.
The formula
change % = (new − old) ÷ old × 100
multiplier = new ÷ old
Worked example
Rent going from $1,200 to $1,560 a month
- 1560 − 1200 = 360
- 360 ÷ 1200 = 0.30
- 0.30 × 100 = 30% increase
Where this goes wrong
Dividing by the new value instead of the old one
Change is measured against where you started: (new − old) ÷ old. Divide by the new value and 40 to 50 becomes 20% instead of 25%. The error is invisible because both answers look reasonable — which is exactly why it survives into reports.
Questions
- Is percentage change the same in both directions?
- No. Going from 100 to 150 is a 50% increase, but going from 150 back to 100 is a 33.3% decrease. The starting value is the reference, and it changes.
- Why can I not calculate a change from zero?
- The formula divides by the starting value. Dividing by zero has no answer, and no percentage describes growth from nothing. Report the absolute difference instead.
- What does the multiplier tell me?
- It is the single number your starting value is multiplied by. A 30% increase is a multiplier of 1.30 — useful when you need to apply the same change repeatedly.