A stock jumps from $50 to $65. A jacket drops from $100 to $75. The raw dollar amounts tell you what happened, but percentage change tells you how big it was — on a standardized 100-point scale that lets you compare a $5 shift and a $500 shift side by side.
In this guide you’ll master the universal percentage-change formula, work through real-world increase and decrease examples, and learn the classic traps that trip up even careful calculators.
What Is Percentage Change?
Percentage change measures the relative difference between a starting quantity (the original value) and the ending quantity (the new value):
- Percentage increase: the new value is larger — e.g., a stock rising from $50 to $65.
- Percentage decrease: the new value is smaller — e.g., an item marked down from $100 to $75.
If you’re working on fraction-to-percentage problems first, explore our guide on converting fractions to percentages formula. To see how rate changes connect with coordinate graphing, review our tutorial on slope-intercept form explained. You can also verify your steps quickly with the automated CalcSolver calculation tool.
The Universal Percentage Change Formula
One formula handles both directions:
Percentage Change = (New Value – Original Value)/(Original Value) × 100
A positive result means a percentage increase; a negative result means a percentage decrease (the sign shows the direction).
Method 1: Calculating Percentage Increase
- Subtract the original value from the new higher value to find the difference.
- Divide that difference by the original starting value.
- Multiply by 100 and attach the % symbol.
Example: Subscription price increase
A software subscription rises from $40 to $50 per month.
- Numerical change: $50 − $40 = $10
- Divide by the original: 10 / 40 = 0.25
- Convert to a percentage: 0.25 × 100 = 25%
The subscription increased by 25%.
Method 2: Calculating Percentage Decrease
- Find the difference: Original − New.
- Divide by the original starting value.
- Multiply by 100 to get the reduction rate.
Example: Retail discount
A winter coat drops from $120 to $90 on sale.
- Difference: $120 − $90 = $30
- Divide by the original: 30 / 120 = 0.25
- Convert: 0.25 × 100 = 25%
The coat is discounted by 25%.
Worked Example 3: An Increase Followed by a Decrease
A $80 gadget rises 25% in price, then later drops 25%. What’s the net change?
- After the increase: $80 × 1.25 = $100
- After the decrease: $100 × 0.75 = $75
- Net change: (75 − 80) / 80 × 100 = (−5/80) × 100 = −6.25%
You’re down 6.25% overall — proof that equal-and-opposite percentages never cancel. Which brings us to…
The Reversibility Trap: Why +50% and −50% Don’t Cancel
Start with $100 and add 50%: you land at $150. Now subtract 50% — but 50% of $150 is $75, so you land at $75, not $100.
Why it happens: every percentage is computed from its own baseline. Once the first change moves the baseline, the second percentage is measured against a different number. You can’t add, subtract, or reverse percentages without recalculating from the new base.
3 Critical Mistakes to Avoid
- Dividing by the new value: the single most common error. The denominator is always the original starting value — keep the baseline fixed.
- Double-labeling negatives: report “−20%” or “a 20% decrease” — never “a −20% decrease.” That double negative confuses everyone.
- Adding sequential percentages: two consecutive 10% increases don’t make 20%. The second 10% applies to the inflated amount: $100 → $110 → $121, a total increase of 21%, not 20%.
Change over original, times 100: that one formula — applied carefully — covers price adjustments, investment returns, and statistical shifts with total accuracy.