Calculate a percentage increase or percentage decrease between any two numbers. Enter the original value (the starting measurement or price) and the new value (the ending measurement or price). The result shows the relative change, the numerical difference, and the ratio of new to original. This free percentage change calculator also explains why switching the values changes the answer.
## Percentage increase formula. For a positive original value, subtract the original from the new value, divide by the original, and multiply by 100. For example, a price rising from $50 to $75 changes by $25. The percentage change is ($75 − $50) ÷ $50 × 100 = +50%. The original value is the denominator, not the final price, because percentage change measures the difference relative to where you started.
## Percentage decrease formula. The same calculation gives a negative answer when the new value is smaller. For example, $75 reduced to $50 is ($50 − $75) ÷ $75 × 100 = −33.33%. Notice that a rise from $50 to $75 is +50%, but the reverse movement from $75 to $50 is −33.33%. Percentage movements are not symmetric because the starting amounts are different.
## Why zero matters. When the original is zero, the percentage increase formula would require division by zero. The relative percentage change is undefined, even if the new value is also zero. The tool therefore displays a clear warning instead of treating the result as a zero-percent increase or as infinity. If the goal is comparing two totals that include zero, consider reporting the absolute numerical difference instead.
Signed percentage change (relative to the original)
Change (%) = ((New − Original) ÷ |Original|) × 100, Original ≠ 0
For positive original values, this reduces to the standard percentage increase or decrease formula ((new − old) / old) × 100. For negative starting values, this calculator consistently uses |original| to retain the direction of the signed difference; the original cannot be zero.
An item rises in price from $50 to $75. Find its percentage increase.
Result: The new price is $25 higher, representing a 50% increase.
Subtract the original amount from the new amount, divide by the original (when positive), and multiply by 100. A rise from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%.
It is (50 − 75) ÷ 75 × 100 = −33.33%. The minus sign indicates a decrease, with magnitude about 33.33%.
The second percentage uses the larger, new starting amount. Starting at 100, a 50% rise gives 150; a 50% fall from 150 gives 75, which is 25% below the original 100.
It is undefined because the percentage formula divides by the original amount. For an original amount of zero, report the absolute numerical difference instead.
Yes, but choose a convention. This tool divides the signed difference by the magnitude of the negative original value, preserving the direction of the numerical change. Conventional financial growth rates generally require positive starting amounts.
Moving from 5% to 6% is a rise of one percentage point, but a relative increase of (6 − 5) ÷ 5 × 100 = 20%. These describe different quantities.