Percentage change is one of the most practically useful pieces of math in everyday life — and one of the most commonly misunderstood. It shows up in salary negotiations, news headlines, investment returns, test scores, and price comparisons. Knowing exactly how to calculate it (and the traps that trip people up) gives you a real analytical edge.
The Formula
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result is an increase. A negative result is a decrease. Example: A stock goes from $80 to $100. Change = ((100 − 80) ÷ 80) × 100 = +25%. Reverse: from $100 to $80 = ((80 − 100) ÷ 100) × 100 = −20%.
💡 The asymmetry trap: A 25% increase followed by a 20% decrease does not return to the original value. $100 → +25% = $125 → −20% = $100. They cancel here — but only by coincidence. In general, percentage increases and their reversals are never symmetric. A 50% gain followed by a 50% loss leaves you 25% down.
Percentage Points vs Percentage Change
This distinction matters enormously in finance and news. If unemployment rises from 4% to 5%, it has increased by 1 percentage point but by 25% (1÷4×100). Both statements are technically correct. Journalists and politicians frequently choose whichever number serves their narrative — knowing the difference lets you evaluate both claims properly.
Practical Examples
- Salary: Current $55,000, offered $60,500. Change = (5,500÷55,000)×100 = 10% raise
- Price: Item was $120, now $89. Change = (−31÷120)×100 = −25.8% (price drop)
- Test score: Last test 72, this test 81. Change = (9÷72)×100 = +12.5% improvement
- Investment: Bought at $45, sold at $38. Change = (−7÷45)×100 = −15.6% loss
Finding the Original Value
If you know the final value and the percentage change, you can find the original: Original = Final ÷ (1 + Change%/100). An item costs $75 after a 25% increase — original price was 75 ÷ 1.25 = $60. An item costs $60 after a 20% discount — original was 60 ÷ 0.80 = $75.