Math Calculators
Percentage Change Calculator
Percentage change is the difference between two values divided by the original value, times one hundred: a salary rising from 100 to 120 is a 20% increase, and a price falling from 80 to 60 is a 25% decrease. Enter the old and the new figure to get the change, its direction, and the difference between them.
Calculator
Formula Used
((New Value − Old Value) ÷ |Old Value|) × 100
About This Calculator
What It Does
This calculator measures the percentage increase or decrease between an old value and a new value. Enter two numbers and it instantly shows the change as a percentage, plus whether it's an increase or decrease. Useful for tracking growth, decline, or change over time in any context.
Worked Example
Example 1 — Increase: Old salary was 100 units, new salary is 120 units. ((120 − 100) ÷ 100) × 100 = +20%. A 20% increase. Example 2 — Decrease: An item priced at 80 units is now 60 units. ((60 − 80) ÷ 80) × 100 = −25%. A 25% decrease. Example 3 — Zero to positive: A value goes from 0 to 50. Since division by zero is undefined, percentage change from zero is treated specially — any positive result from zero is a 100% increase by convention.
Real-World Usage
Track salary raises and negotiate pay increases. Measure investment returns and portfolio performance. Monitor price changes in goods, services, or stocks. Calculate year-over-year business growth or decline. Weight loss or gain expressed as a percentage of starting weight. Compare population changes, test scores, or any metric over time.
Local Context
Percentage change works consistently across all currencies and regions. The formula is the same worldwide. When comparing financial metrics across countries, pair this with the currency converter to standardize values in the same currency before calculating the percentage change.
Percent Increase Formula
A percentage increase answers "by how much did it grow?". Divide the difference by the original value, then multiply by 100: (new − old) ÷ old × 100. From 100 to 120 that is (120 − 100) ÷ 100 × 100 = +20%. A shortcut to the final value is old × (1 + rate); to return to the starting value, divide the final value by 1 + rate. Two checks every time: the result is positive only when the new value is larger, and doubling a value is always +100% — 100 to 200, 3 to 6 and 0.5 to 1 all score the same.
Percent Decrease Formula
A percentage decrease answers "by how much did it fall?". The arithmetic is identical to an increase — (new − old) ÷ |old| × 100 — and the sign carries the direction, so a fall from 80 to 60 reads −25%. The absolute value in the denominator keeps the sign meaningful when the starting value is negative. Percentages do not add up: a 25% fall is not undone by a 25% rise, because 100 → 75 → 93.75. Recovering a loss takes a larger percentage than the loss itself — 100 → 80 → 100 is a 20% fall and a 25% rise.
Last reviewed: September 2026.
Frequently Asked Questions
What does a negative percentage change mean?
A negative result means the value has decreased. For example, going from 100 to 80 is a 20% decrease.
How is percentage change different from percentage difference?
Percentage change compares an old value to a new value over time. Percentage difference compares two values without regard to direction or time.
Can this calculator handle negative old values?
Yes, but the result becomes less intuitive. We use the absolute value of the old value as the denominator to avoid misleading results.