$$\begin{aligned} \text{Percentage} &= \frac{\text{Part}}{\text{Whole}} \times 100 \\ \text{Percentage Increase} &= \frac{\text{New} - \text{Old}}{\text{Old}} \times 100 \\ \text{Percentage Decrease} &= \frac{\text{Old} - \text{New}}{\text{Old}} \times 100 \\ \text{Reverse Percentage} &= \frac{\text{Part}}{\text{Percentage} / 100} \end{aligned}$$
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.
