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Percentage change measures how much a value has increased or decreased relative to the original value. The formula is: Percentage Change = ((New − Old) / |Old|) × 100. A positive result means an increase; a negative result means a decrease.
This is one of the most widely used calculations in finance (stock returns, revenue growth), science (population change, measurement error), and everyday life (price changes, grade improvements). Knowing how to calculate and interpret percentage change is a core quantitative skill.
For example, if sales go from $4,000 to $5,200, the change is +$1,200 and the percentage change is (1,200 / 4,000) × 100 = +30%. If they drop to $3,200, the change is −$800 and the percentage change is (−800 / 4,000) × 100 = −20%.
Percentage Change = ((New − Old) / |Old|) × 100
Enter the original (old) and new value.
| Scenario | Old Salary | New Salary | % Change | Raise Amount |
|---|---|---|---|---|
| Standard 3% raise | $50,000 | $51,500 | +3.0% | +$1,500 |
| Standard 5% raise | $50,000 | $52,500 | +5.0% | +$2,500 |
| Strong 10% raise | $50,000 | $55,000 | +10.0% | +$5,000 |
| Job switch 20% bump | $60,000 | $72,000 | +20.0% | +$12,000 |
| Job switch 30% bump | $70,000 | $91,000 | +30.0% | +$21,000 |
| 3% raise — $80K base | $80,000 | $82,400 | +3.0% | +$2,400 |
| 5% raise — $80K base | $80,000 | $84,000 | +5.0% | +$4,000 |
| 5% raise — $100K base | $100,000 | $105,000 | +5.0% | +$5,000 |
| 10% raise — $100K base | $100,000 | $110,000 | +10.0% | +$10,000 |
| 20% raise — $100K base | $100,000 | $120,000 | +20.0% | +$20,000 |
| Salary cut 10% | $80,000 | $72,000 | -10.0% | $-8,000 |
| Salary cut 20% | $100,000 | $80,000 | -20.0% | $-20,000 |
| Scenario | Old Price | New Price | % Change |
|---|---|---|---|
| Gas: $3.00 → $3.50 | $3.00 | $3.50 | +16.7% |
| Gas: $3.50 → $2.80 | $3.50 | $2.80 | -20.0% |
| Groceries: $200 → $230 | $200 | $230 | +15.0% |
| Rent: $1,500 → $1,650 | $1,500 | $1,650 | +10.0% |
| Stock: $100 → $115 | $100 | $115 | +15.0% |
| Stock: $150 → $120 | $150 | $120 | -20.0% |
| Stock: $50 → $75 | $50 | $75 | +50.0% |
| Stock: $200 → $160 | $200 | $160 | -20.0% |
| House: $350K → $420K | $350,000 | $420,000 | +20.0% |
| House: $500K → $450K | $500,000 | $450,000 | -10.0% |
| iPhone: $999 → $1,099 | $999 | $1,099 | +10.0% |
| Coffee: $4.50 → $5.25 | $4.50 | $5.25 | +16.7% |
Using 100 as the base value — shows intuition for common percent changes.
| Old Value | New Value | Change | % Change |
|---|---|---|---|
| 100 | 101 | +1 | +1.0% |
| 100 | 105 | +5 | +5.0% |
| 100 | 110 | +10 | +10.0% |
| 100 | 115 | +15 | +15.0% |
| 100 | 120 | +20 | +20.0% |
| 100 | 125 | +25 | +25.0% |
| 100 | 130 | +30 | +30.0% |
| 100 | 150 | +50 | +50.0% |
| 100 | 175 | +75 | +75.0% |
| 100 | 200 | +100 | +100.0% |
| 100 | 99 | -1 | -1.0% |
| 100 | 95 | -5 | -5.0% |
| 100 | 90 | -10 | -10.0% |
| 100 | 85 | -15 | -15.0% |
| 100 | 80 | -20 | -20.0% |
| 100 | 75 | -25 | -25.0% |
| 100 | 50 | -50 | -50.0% |
| 100 | 25 | -75 | -75.0% |
| 200 | 150 | -50 | -25.0% |
| 500 | 400 | -100 | -20.0% |
❌ Using the new value as the denominator
50 → 75: Wrong: (25/75)×100 = 33.3% | Correct: (25/50)×100 = 50%
Fix: Always divide by the original (old) value, not the new one.
❌ Confusing percentage change with percentage points
Interest rate rises from 3% to 5%: that's a 2 percentage point increase, but a +66.7% percentage change.
Fix: Percentage points = arithmetic difference. Percentage change = relative difference ÷ original × 100.
❌ Thinking +50% then −50% returns to start
100 × 1.5 = 150; 150 × 0.5 = 75. A +50% increase followed by a −50% decrease gives −25%, not zero.
Fix: Percentage changes compound multiplicatively, not additively. Use (1 + r₁)(1 + r₂) − 1 for chained changes.
❌ Averaging percentages to get overall change
Stock +100% one year, −50% next year: average = +25%, but net = 0%.
Fix: For multi-period returns, use CAGR = (End/Start)^(1/n) − 1, not the arithmetic average of period returns.
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This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.