Percentage Change Calculator
Calculate the percentage change between two values. Determine whether a value increased or decreased and by what percentage. See also Percentage Difference Calculator and Percentage Calculator.
What Is Percentage Change?
Percentage change measures how much a value has increased or decreased relative to its original value, expressed as a percentage. It is one of the most commonly used calculations in finance, science, and everyday life. Unlike percentage difference (which is symmetric), percentage change is directional — it matters which value is the "old" value and which is the "new" value.
Percentage Change Formula
Percentage Change = ((New Value - Old Value) / |Old Value|) x 100
If result is positive → Increase
If result is negative → Decrease
If result is zero → No change
Example Calculation
Old Value = 80, New Value = 100
Percentage Change = ((100 - 80) / |80|) x 100
Percentage Change = (20 / 80) x 100
Percentage Change = +25.00% (Increase)
Percentage Change vs. Percentage Difference
These two calculations are often confused but serve different purposes:
- Percentage Change is directional. It measures how much a value changed FROM an original value TO a new value. The order matters.
- Percentage Difference is symmetric. It measures how different two values are from each other, regardless of which came first. The order does not matter.
Use percentage change when you have a clear "before" and "after" (e.g., last year's revenue vs. this year's). Use percentage difference when comparing two independent values (e.g., the price of two competing products).
Real-World Examples
- Stock prices: A stock goes from $50 to $62.50 — that is a +25% change.
- Population growth: A city grows from 200,000 to 230,000 residents — a +15% change.
- Weight loss: Weight drops from 180 lbs to 162 lbs — a -10% change.
- Inflation: A product that cost $3.00 now costs $3.24 — a +8% change.
- Test scores: A student improves from 72 to 90 — a +25% change.
Common Percentage Changes Reference Table
| Old Value | New Value | % Change | Direction |
|---|---|---|---|
| 10 | 12 | +20.00% | Increase |
| 100 | 75 | -25.00% | Decrease |
| 50 | 50 | 0.00% | No Change |
| 200 | 250 | +25.00% | Increase |
| 80 | 100 | +25.00% | Increase |
| 500 | 450 | -10.00% | Decrease |
| 1000 | 1500 | +50.00% | Increase |
| 75 | 60 | -20.00% | Decrease |
| 40 | 52 | +30.00% | Increase |
| 300 | 150 | -50.00% | Decrease |
How to Calculate Percentage Change
- Identify the old (original) value and the new (final) value.
- Subtract the old value from the new value to get the absolute change.
- Divide the absolute change by the absolute value of the old value.
- Multiply the result by 100 to convert to a percentage.
- If the result is positive, it is an increase. If negative, it is a decrease.
Frequently Asked Questions
What is the difference between percentage change and percentage point change?
Percentage change is relative (e.g., going from 10% to 12% is a 20% increase). Percentage point change is absolute (going from 10% to 12% is a 2 percentage point increase). These are very different concepts often confused in media reporting.
Can percentage change exceed 100%?
Yes. If a value more than doubles, the percentage change exceeds 100%. For example, going from 50 to 150 is a +200% change. There is no upper limit to percentage increase, but percentage decrease is capped at -100% (the value reaches zero).
Why can't the old value be zero?
The formula divides by the old value. Division by zero is undefined in mathematics. If your starting value is zero, percentage change is not meaningful — you would need to use absolute change instead.
Is a 50% increase followed by a 50% decrease the same as no change?
No. A 50% increase on 100 gives 150. A 50% decrease on 150 gives 75. You end up with less than you started. This asymmetry is a common source of confusion.
How do I calculate percentage change with negative numbers?
The formula uses the absolute value of the old value in the denominator: ((New - Old) / |Old|) x 100. This ensures correct results even when the old value is negative. For example, going from -20 to -10 is a +50% change.
What is the reverse percentage change?
The reverse percentage change tells you what percentage change is needed to go from the new value back to the old value. Due to the asymmetry of percentages, this is always a different number (unless the change is 0%).
When should I use percentage change vs. absolute change?
Use percentage change when you want to understand the relative magnitude of a change. Use absolute change when the actual numeric difference matters more. For example, a $5 increase on a $10 item (50%) feels very different from a $5 increase on a $1000 item (0.5%).