The percent change is:
Table of Contents
Percentage change, instantly
Enter an old value and a new value and this calculator returns the percentage change between them. Use it for tracking growth, inflation, revenue swings, stock returns, weight loss, traffic deltas — any time you need to compare two numbers in proportional rather than absolute terms.
The formula
Percentage change is the signed difference between two values, expressed as a percent of the original:
% change = (new − old) / |old| × 100
- old — the original (baseline) value. Must not be zero.
- new — the updated value.
- |old| — the absolute value of the original, so the sign of the result reflects increase/decrease rather than the sign of the base.
Positive = increase. Negative = decrease.
Worked example
Using the defaults old = 100, new = 125:
- Subtract: 125 − 100 = 25.
- Divide by the original: 25 / 100 = 0.25.
- Multiply by 100: 0.25 × 100 = 25.
So the percentage change is +25% — a 25% increase.
Reference table
| Old | New | Change | Note |
|---|---|---|---|
| 100 | 110 | +10% | tenth-up |
| 100 | 125 | +25% | quarter-up (default) |
| 100 | 150 | +50% | half-up |
| 100 | 200 | +100% | doubled |
| 100 | 300 | +200% | tripled |
| 100 | 90 | −10% | tenth-down |
| 100 | 75 | −25% | quarter-down |
| 100 | 50 | −50% | halved |
| 50 | 100 | +100% | same absolute jump, double the percent |
| 200 | 100 | −50% | reverse of doubling is halving, not −100% |
Pitfalls people get wrong
- Percentage vs percentage points. A mortgage rate moving from 4% to 6% is a 2 percentage-point rise, but a 50% percentage change. Headlines confuse the two regularly.
- Asymmetric reversal. A 20% gain followed by a 20% loss is not break-even — it’s a 4% net loss (1.20 × 0.80 = 0.96). To reverse a +X% move you divide by (1 + X/100), not subtract.
- Averaging is wrong. Average of +50% and −50% is not zero. Use the geometric mean of growth factors (1.5 and 0.5) to get the true compounded result.
- Zero or negative bases. If the original is 0 the percent change is undefined. If old and new have opposite signs (e.g. −10 → +10), the formula returns +200%, which is mathematically correct but rarely the most readable framing — quote the absolute change too.
Common applications
- Inflation. The US Bureau of Labor Statistics publishes year-over-year CPI changes — the canonical percentage-change measurement of price levels.
- Stock returns. A share that closes at $125 versus an open of $100 is up 25% on the day.
- Marketing & analytics. “Conversions are up 18% week-over-week” is a percentage change on the prior week’s base.
- Weight loss. Losing 10 kg from a 100 kg starting weight is a 10% body-weight reduction; the same 10 kg from 80 kg is 12.5%.
- Year-over-year reporting. Most financial statements show this period vs the same period last year as a percentage change.
Limitations & gotchas
- The base matters. Without quoting it, “up 25%” is ambiguous.
- Single-period percentage changes do not compound additively across periods.
- For very small bases, percent changes look dramatic but say little — report the absolute change alongside.
- This calculator returns one period’s change. For multi-period growth use a compound interest calculator or compute a compound annual growth rate (CAGR).
Sources & references
- Weisstein, Eric W. “Percent.” Wolfram MathWorld.
- Investopedia, “Percentage Change.”
- US Bureau of Labor Statistics, “How the CPI is calculated.”
FAQs
Subtract the original value from the new value, divide by the original (absolute) value, then multiply by 100. Formula: %change = (new − old) / |old| × 100. A positive result is an increase; a negative result is a decrease.
Percentage points measure the arithmetic difference between two percentages; percentage change measures the proportional difference. If a mortgage rate moves from 4% to 6%, that’s 2 percentage points, but a 50% percentage change (because 2 is half of 4). Misusing the two is one of the most common errors in financial reporting.
Because the denominator is the original value. Going from 10 to 20 is +100% (10 is the base). Going from 20 back to 10 is −50% (20 is the base). The two moves are the same in absolute terms but proportionally different. To reverse a 20% gain you don’t apply a 20% loss — you apply ≈16.67% loss (1 ÷ 1.20 − 1).
Yes. A value that triples (1 → 3) is a +200% change. A tenfold growth is +900%. Percent change is unbounded on the upside but bounded by −100% on the downside — you can’t lose more than everything.
Because they multiply, not add. A +50% gain followed by a −50% loss is not zero — it’s a 25% net loss (1.5 × 0.5 = 0.75). For compounded changes, use the geometric mean of the growth factors, not the arithmetic mean of the percent changes.
The new value equals the old value — no movement. Common in benchmark or stable-state contexts. A 0% change is different from ‘no data’: it means you measured and the result was flat.