How to Calculate Percentage Increase (and Why Decrease Isn't Symmetric)
How to calculate percentage increase with the (new − old) ÷ old formula, worked examples both ways, and the asymmetry that makes a 50% loss need a 100% gain.
The formula is one line, and almost everyone gets it right. The part that catches people is what happens on the way back down — because a percentage increase and the decrease that undoes it are never the same number.
The formula
Percentage change = (new − old) ÷ old × 100
A positive result is an increase, a negative one a decrease. The critical detail is the denominator: always divide by the starting value, not the ending one.
*Increase:* a salary moves from $62,000 to $68,000. (68,000 − 62,000) ÷ 62,000 = 6,000 ÷ 62,000 = 0.0968 → 9.7% increase
*Decrease:* a stock falls from $84 to $57. (57 − 84) ÷ 84 = −27 ÷ 84 = −0.3214 → 32.1% decrease
The asymmetry trap
Lose 50% and you need a 100% gain to break even. This is not a trick of framing — it follows directly from the changed base. After a 50% fall, the recovery is measured against the smaller number.
Recovery required = 1 ÷ (1 − loss) − 1
| Loss | Gain needed to break even |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 30% | 42.9% |
| 40% | 66.7% |
| 50% | 100% |
| 60% | 150% |
| 75% | 300% |
| 90% | 900% |
The practical reading: deep drawdowns are disproportionately expensive. Avoiding a 50% loss is worth far more than capturing an extra 50% gain, which is why risk control dominates return chasing in portfolio design.
The same asymmetry shows up in retail. A price marked up 25% and then discounted 25% does not return to the original: $100 → $125 → $93.75. You end 6.25% below where you started.
Percentage points vs percent
If an interest rate moves from 4% to 5%, that is a 1 percentage point increase and a 25% relative increase. Both statements are true and they describe the same event. Headlines that mix them are usually trying to make a change sound larger or smaller than it is — always check which one is meant.
Percent difference
When neither value is the natural baseline — comparing two independent measurements, say — use percent difference against the average:
Percent difference = |a − b| ÷ ((a + b) ÷ 2) × 100
For 180 and 220: 40 ÷ 200 = 20%, symmetric in either direction. Use this in lab work and A/B comparisons, not for before-and-after changes.
Worked example: three sequential changes
A product price starts at $80, rises 15%, falls 10%, then rises 5%.
- 80 × 1.15 = $92.00
- 92 × 0.90 = $82.80
- 82.80 × 1.05 = $86.94
Total change: (86.94 − 80) ÷ 80 = 8.7% — not the 10% you get by adding 15 − 10 + 5. Percentage changes multiply; they never add.
FAQ
What's the difference between percentage increase and percentage difference? Increase uses the original value as the denominator and has a direction. Difference uses the average of the two values and is symmetric.
How do I calculate a percentage increase in reverse? Divide by the growth factor. If a price is $138 after a 15% increase, the original was 138 ÷ 1.15 = $120 — not 138 × 0.85.
Why doesn't a 20% discount cancel a 20% markup? The discount is applied to the larger, marked-up number. $100 → $120 → $96, leaving you 4% below the start.
Handle both directions with the Percent Change Calculator or the general Percentage Calculator. For the underlying arithmetic, see how to calculate percentages.
---
*Skip the denominator mistakes: run it through the Percent Change Calculator.*