Percentage Change Calculator
Enter an original value and a new value to instantly find the percentage increase or decrease between them. The tool shows the direction of change, the absolute difference and the exact formula used, so you can verify the result yourself.
Enter values
Enter original and new values, then press Calculate change.
The percentage change formula
percentage change = ((new − original) / |original|) × 100
The numerator is the absolute change; the denominator is the original value. Using the absolute value of the original in the denominator ensures the sign of the result describes the direction of movement, not the sign of the original number. This matters when the original value is negative — for example, going from −50 to −40 is a 20% increase, not a 20% decrease.
| Symbol | Meaning |
|---|---|
original | The starting value (must be non-zero) |
new | The ending value |
new − original | The absolute change (positive = increase, negative = decrease) |
|original| | The magnitude of the starting value, ignoring sign |
Interpreting the result
- Positive percentage — the value increased.
- Negative percentage — the value decreased.
- Zero percentage — the value did not change.
- Magnitude tells you how big the change is relative to the original. A 5% change on a large base may be a bigger absolute difference than a 50% change on a small base — percentage and absolute change tell different stories.
Worked examples
Example 1 — Simple increase
Original = 80, new = 100.
((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25%
Result: +25% (increase)
Example 2 — Simple decrease
Original = 250, new = 200.
((200 − 250) / 250) × 100 = (−50 / 250) × 100 = −20%
Result: −20% (decrease)
Example 3 — Negative original value
Original = −50, new = −40.
((−40 − (−50)) / |−50|) × 100 = (10 / 50) × 100 = 20%
Result: +20% (increase)
Even though both values are negative, the value moved toward zero — an increase of 20%.
Common mistakes
- Dividing by the new value. Percentage change always uses the original value as the denominator. Using the new value gives a different number, and a common source of error in financial reporting.
- Assuming symmetry. A 20% increase followed by a 20% decrease does not return you to the original value. Starting at 100: +20% → 120, then −20% → 96. The net change is −4%.
-
Adding percentages across sequential changes. Two
sequential changes of +10% each are equivalent to a single change
of +21%, not +20%:
1.10 × 1.10 = 1.21. - Confusing percentage points with percentages. A rate going from 4% to 6% is a rise of 2 percentage points, but a 50% relative increase. Which measure is appropriate depends on the question being asked.
Related calculators
Frequently asked questions
Percentage change = ((new − original) / |original|) × 100. A positive result is an increase; a negative result is a decrease.
No. A 20% increase followed by a 20% decrease leaves you at 96% of the original value, because each percentage is calculated on a different base. Starting at 100: +20% → 120, then −20% → 96.
Negative values are accepted. Zero is not, because division by zero is undefined — the calculator will show a clear error message.
Percentage change uses the original value as the denominator and is directional. Percentage difference uses the average of the two values and is symmetric — swapping the two inputs gives the same result.
Results use IEEE-754 double-precision arithmetic and are displayed rounded to six decimal places. The underlying calculation always uses full precision.