Percentage change measures how much a value has grown or shrunk relative to its starting point. Whether you’re tracking a stock price, comparing last month’s electricity bill, or figuring out how much a salary raise is really worth, the formula is always the same — and it takes about ten seconds once you know it.
The short answer: Percentage change = ((New Value − Old Value) / |Old Value|) × 100
A positive result is an increase; a negative result is a decrease.
The Percentage Change Formula
$$\text{Percentage Change} = \frac{\text{New Value} - \text{Old Value}}{|\text{Old Value}|} \times 100$$
The absolute value bars around the old value ensure the formula works correctly even when starting from a negative number (see the FAQ section). For most everyday use with positive values, you can ignore the bars.
Use the percentage calculator to run any of these calculations instantly.
Step-by-Step Examples
Example 1: Price Increase
A jacket costs $80 in January and $96 in March. What is the percentage increase?
- New − Old = $96 − $80 = $16
- Divide by old: $16 / $80 = 0.20
- Multiply by 100: 0.20 × 100 = +20%
The jacket’s price increased by 20%.
Example 2: Price Decrease (Sale)
A laptop was $1,200 and is now on sale for $900. What is the percentage decrease?
- New − Old = $900 − $1,200 = −$300
- Divide by old: −$300 / $1,200 = −0.25
- Multiply by 100: −0.25 × 100 = −25%
The laptop is 25% off. For discount math, the discount calculator also calculates the dollar savings and final price in one step.
Example 3: Salary Raise
You earn $52,000 and receive a raise to $56,160. What percentage raise is that?
- $56,160 − $52,000 = $4,160
- $4,160 / $52,000 = 0.08
- 0.08 × 100 = +8%
An 8% raise.
Example 4: Test Score Change
You scored 68 on your first quiz and 85 on your second. What’s the percentage improvement?
- 85 − 68 = 17
- 17 / 68 = 0.25
- 0.25 × 100 = +25%
A 25% improvement in score.
Common Percentage Change Scenarios
| Scenario | Old Value | New Value | Change |
|---|---|---|---|
| Grocery price increase | $3.50 | $4.20 | +20% |
| Gas price drop | $4.00 | $3.40 | −15% |
| Portfolio growth (1 year) | $10,000 | $11,350 | +13.5% |
| Monthly rent increase | $1,500 | $1,575 | +5% |
| Sales decline quarter-over-quarter | 240 units | 204 units | −15% |
Percentage Increase vs. Percentage Decrease
The same formula covers both directions — the sign of the result tells you which:
- Positive result → increase (new > old)
- Negative result → decrease (new < old)
- Zero → no change
Many people confuse percentage change with percentage points. If an interest rate goes from 2% to 3%, that is a change of 1 percentage point (simple subtraction), but it is a 50% increase in the rate (using the percentage change formula). These are different things.
The Reverse Calculation: Finding the Original Value
Sometimes you know the final value and the percentage change, and you need to find the starting value.
Formula: Original = New Value / (1 + (Percentage Change / 100))
Example: A product now costs $126 after a 5% price increase. What was the original price?
- Original = $126 / (1 + 0.05) = $126 / 1.05 = $120
Example: A stock is down 20% from its peak and now trades at $64. What was the peak price?
- Original = $64 / (1 − 0.20) = $64 / 0.80 = $80
The Symmetry Trap: Why +X% Then −X% ≠ 0%
A common misconception: if something increases by 25% and then decreases by 25%, you’d expect to be back where you started. You’re not.
Starting with $100:
- +25%: $100 × 1.25 = $125
- −25% of $125: $125 × 0.75 = $93.75
You end up at $93.75, not $100. The loss of 25% applies to a larger base ($125), so it removes more in absolute terms than the original gain. This asymmetry is important to understand for investments, pricing, and any repeated percent changes.
Percentage Change vs. Percentage Difference
These two terms are often mixed up:
- Percentage change compares a new value to an old value. Direction matters: the “old” is the reference point.
- Percentage difference is used when there is no clear “before” and “after” — for example, comparing the prices of the same item at two different stores. The formula uses the average of the two values as the denominator: |V1 − V2| / ((V1 + V2)/2) × 100.
Fractions and percentages are closely linked — a 1/4 price reduction is the same as a 25% decrease, a 3/8 discount equals 37.5% off. The fraction calculator can help convert fraction-based discounts to their decimal form before plugging into the percentage change formula.
Frequently Asked Questions
What is the percentage change formula? ((New Value − Old Value) / |Old Value|) × 100. A positive result means an increase; a negative result means a decrease.
What if the old value is zero? Percentage change is undefined when the old value is zero, because you cannot divide by zero. If you’re comparing to a starting value of zero (like first-month revenue), describe the change in absolute terms instead (e.g., “grew from $0 to $5,000”) or use a different metric.
Can percentage change be more than 100%? Yes. If a value doubles, that is a 100% increase. If it triples, that’s 200%. There is no upper ceiling on percentage increase.
How do I calculate percentage change in Excel or Google Sheets? Use the formula =(B2-A2)/ABS(A2)*100, where A2 is the old value and B2 is the new value. Format the cell as a number or percentage.
Is a 50% increase followed by a 50% decrease the same as no change? No. Start at 100 → +50% → 150 → −50% → 75. You lose 25% overall. This is the symmetry trap described above.
How is percentage change different from percentage points? Percentage change uses the original value as the base (relative). Percentage points are an absolute difference between two percentages. If inflation rises from 3% to 5%, that’s 2 percentage points but a 66.7% percentage change in the inflation rate.
The Bottom Line
The percentage change formula is straightforward: subtract the old value from the new, divide by the old value, and multiply by 100. A positive number means growth; a negative number means decline.
Keep two things in mind:
- The old (original) value is always the denominator — direction matters.
- Percentage change and percentage points are different things.
For quick calculations, the percentage calculator handles any percentage problem, including change, in seconds. For discount-based scenarios, the discount calculator goes further and shows your total savings and final price in one step.