Math
Percentage Change Calculator
Enter the starting value and the new value to see how much it changed, in percent.
The link carries your figures, so it reopens on exactly these numbers.
Why a rise and a fall of the same percentage do not cancel
A fixed reference, not your figures — the point is the pattern. Each pair is the same two numbers read in both directions.
| From → to | Change | Absolute difference | Multiplier |
|---|---|---|---|
| 100 → 150Up 50%. | 50% | 50 | 1.5 |
| 150 → 100Back down is only 33.3%, not 50%. | -33.33% | -50 | 0.6667 |
| 100 → 200Doubling is +100%; halving back is −50%. | 100% | 100 | 2 |
| 100 → 50A 50% fall needs a 100% rise to undo it. | -50% | -50 | 0.5 |
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.