What is Percentage Change?
Percentage change measures how much a value has increased or decreased relative to its original amount. It's expressed as a percentage and helps compare changes across different scales.
This is commonly used in finance, business, science, and everyday life to track growth, compare prices, analyze performance, and understand trends.
Percent Increase
When the new value is higher than the original
Percent Decrease
When the new value is lower than the original
Absolute Change
The actual difference between values
Multiplier
How many times the original value
Common uses for percentage change:
- Stock prices — Track daily/yearly performance
- Sales & revenue — Compare month-over-month or year-over-year
- Price comparisons — How much more or less something costs
- Population growth — Census changes over time
Percentage Change Formula
Percentage Change = ((New Value - Original Value) / |Original Value|) × 100
The absolute value in the denominator ensures correct calculation when dealing with negative original values.
Calculation Examples
Example: Price Increase
Original: $80, New: $100
Change = ((100 - 80) / 80) × 100
= (20 / 80) × 100
= 25% increase
Example: Price Decrease
Original: $200, New: $150
Change = ((150 - 200) / 200) × 100
= (-50 / 200) × 100
= 25% decrease
Quick Reference
Double (2x): = 100% increase
Triple (3x): = 200% increase
Half (0.5x): = 50% decrease
Quarter (0.25x): = 75% decrease
Use our percentage change calculator above to quickly calculate the change between any two values.
Percentage Change vs. Percentage Points
These two phrases get mixed up constantly, and the gap between them is large enough to change how a headline reads. Say a savings rate moves from 4% to 5%. The rise of one point is a 1 percentage point increase, but as a percentage change it is (5 - 4) / 4 × 100 = 25%. Percentage difference is different again: it compares two values against their average, so 4% and 5% differ by (5 - 4) / 4.5 × 100 ≈ 22.2%.
| Term | 4% → 5% gives | What it answers |
|---|---|---|
| Percentage change | 25% increase | Growth relative to the starting value |
| Percentage points | +1 point | Raw gap between two percentages |
| Percentage difference | ≈ 22.2% | Gap relative to the average of both |
Edge Cases Worth Knowing
- Original value of 0: dividing by zero is undefined, so going from 0 to any number has no finite percentage change. The calculator returns no result here rather than a made-up figure.
- Negative to positive: moving from -50 to 25 is a change of 75 over |−50|, which is 75 / 50 × 100 = 150% increase. Using the absolute value of the original keeps the direction of the change correct.
- A 50% drop then a 50% gain: this does not return you to the start. 100 falls to 50, then a 50% gain adds only 25, leaving 75. Equal-sized percentage moves in opposite directions never cancel out.
Reversing a Percentage Change
When you know the result and the percentage but need the starting figure, divide instead of multiply. If an item costs $144 after a 20% increase, the original was 144 / 1.20 = $120, not 144 × 0.80. Multiplying by 0.80 would undershoot to $115.20 because the 20% was taken on the smaller original, not the larger new price.
Repeated Change and Growth Rates
Percentage changes compound when they stack over several periods. Growing 10% a year for three years is not 30% overall. Each year multiplies by 1.10, so the total factor is 1.10 × 1.10 × 1.10 = 1.331, which is a 33.1% total increase. Working backward from a known total gives the compound annual growth rate (CAGR), the steady yearly rate that would produce the same end value.
Worked Comparison Table
| Item | Original | New | Absolute change | % change |
|---|---|---|---|---|
| Dozen eggs | $3.00 | $4.50 | +$1.50 | +50% |
| Gallon of gas | $3.80 | $3.42 | −$0.38 | −10% |
| Share price | $120.00 | $138.00 | +$18.00 | +15% |
| Monthly rent | $1,600 | $1,520 | −$80 | −5% |