Math Formula • Published on July 30, 2026 • Last updated July 30, 2026
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The portion or quantity being expressed as a fraction of the whole
The total or base amount that the part is being compared against
The original or starting value before a change
The updated or resulting value after a change
A known percentage value used to work backward to the original whole amount
A percentage expresses a number as a fraction of 100, making it easy to compare proportions across different scales.
This page covers four related but distinct calculations that are often confused with one another: finding what percentage one number is of another (basic percentage), finding how much a value has grown (percentage increase), finding how much a value has shrunk (percentage decrease), and working backward from a known percentage and part to find the original whole (reverse percentage).
Each uses a different arrangement of the same core relationship between a part, a whole, and 100.
"Percentage change" is a general term that can be positive (an increase) or negative (a decrease). "Percentage increase" specifically refers to a positive change, where the New value is greater than the Old value.
Mathematically it is the same underlying formula, but percentage decrease is conventionally expressed as a positive number describing the size of the drop (e.g., "a 20% decrease") rather than as a negative percentage increase, to avoid confusion in everyday use.
Reverse percentage is useful when you know a resulting amount and the percentage it represents, but need to find the original total — for example, finding the pre-tax price when you only know the tax amount and tax rate.
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