Percentage Change Calculator – Increase & Decrease
Calculate the percentage increase or decrease between two values. Find percentage change, difference, and ratio. Free math tool with instant solution.
The Percentage Change Formula
Percentage change measures how much a value increases or decreases relative to its starting point:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result = percentage increase. A negative result = percentage decrease.
Examples:
- Price rises from $80 to $100: ((100 − 80) ÷ 80) × 100 = +25% increase
- Temperature drops from 20°C to 15°C: ((15 − 20) ÷ 20) × 100 = −25% decrease
- Running pace improves from 6:00 to 5:30 min/km: ((5.5 − 6.0) ÷ 6.0) × 100 = −8.3% (faster = negative % change in time)
Percentage Increase vs Decrease: Asymmetry
A critical insight: percentage changes are not symmetric. A 50% decrease followed by a 50% increase does not return you to the starting value.
Example: Start at $100 → decrease 50% → $50 → increase 50% → $75 (not $100)
This asymmetry matters in investing, business, and fitness:
- A stock that drops 50% needs to rise 100% to recover
- If your race time increases by 10%, you need to improve by 9.1% to return to baseline (not 10%)
- A salary cut of 20% requires a raise of 25% to fully restore earnings
Recovery multiplier formula: To recover from an X% loss, you need a (X ÷ (100 − X)) × 100% gain. For a 20% loss: 20 ÷ 80 × 100 = 25%.
Real-World Applications of Percentage Change
Percentage change appears in nearly every domain:
| Domain | Old value | New value | % Change | Interpretation |
|---|---|---|---|---|
| Running | 5K in 30:00 | 5K in 27:00 | −10% | 10% faster |
| Weight | 90 kg | 81 kg | −10% | 10% weight loss |
| Salary | $50,000 | $55,000 | +10% | 10% raise |
| Heart rate | 75 bpm (rest) | 68 bpm (after training) | −9.3% | 9.3% lower resting HR |
| VO2max | 42 ml/kg/min | 47 ml/kg/min | +11.9% | 11.9% aerobic improvement |
Compound vs Simple Percentage Change
When applying percentage changes repeatedly, the order and compounding matter:
Simple (non-compounding): A 10% increase applied once: $100 × 1.10 = $110.
Compound (applied repeatedly): 10% increase applied for 3 years: $100 × 1.10³ = $133.10 — not $130.
In fitness training, this compounding effect is called supercompensation. A 2% improvement in running economy each month compounds to roughly 27% over 12 months (1.02¹² = 1.268), not the 24% you'd get from simple addition.
To calculate the average percentage change per period from a total change, use the geometric mean: Average rate = (New/Old)^(1/n) − 1, where n is the number of periods.
Frequently Asked Questions
What is the formula for percentage change?
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100. Positive result = increase, negative = decrease.
How do I calculate percentage increase from 50 to 75?
((75 − 50) ÷ 50) × 100 = (25 ÷ 50) × 100 = 50% increase.
Is a 10% loss followed by a 10% gain a net zero change?
No. If you lose 10% from $100 you get $90, then gain 10% on $90 gives $99. The net result is a 1% loss. Percentage changes are not symmetric.
How is percentage change different from percentage points?
Percentage change is relative to a starting value. Percentage points are absolute differences in percentages. If your vote share goes from 40% to 50%, that's a 10 percentage point increase but a 25% relative increase ((50−40)/40 × 100 = 25%).
How do I calculate the percentage change in my running pace?
Use the formula with pace values in the same unit. If you went from 6:30/km to 5:50/km, convert to seconds: 390s to 350s. Change = ((350−390)/390) × 100 = −10.3%. You're running 10.3% faster.
How to Calculate Percentage Change
Percentage change measures how much a value has increased or decreased relative to its starting point. Formula: ((New − Old) ÷ Old) × 100. A positive result indicates an increase; negative indicates a decrease.
| Old Value | New Value | Change | % Change |
|---|---|---|---|
| 100 | 120 | +20 | +20% |
| 100 | 80 | −20 | −20% |
| 50 | 75 | +25 | +50% |
| 200 | 150 | −50 | −25% |
| 1000 | 1350 | +350 | +35% |
Common mistakes: Percentage change is not symmetric — a 50% decrease followed by a 50% increase does not return to the original value (100 → 50 → 75, not 100). To reverse a percentage change: if a price dropped 20%, the original was 25% higher than the current price, not 20%.
What is the formula for percentage change?
((New Value − Old Value) ÷ Old Value) × 100. Example: price went from 80 to 96 → ((96−80)÷80)×100 = 20% increase.
What is the difference between percentage change and percentage points?
If interest rates go from 2% to 3%, that is 1 percentage point increase, but a 50% percentage change. Confusing these two is a common error in financial reporting.