Guide
Calculating Percentage Change Correctly
Compute percent increase and decrease, and tell a percent change apart from a percentage-point difference.
Percent change compares a new value with an older one: (new − old) ÷ |old| × 100. The sign gives the direction and the magnitude gives the size. Two mistakes cause most wrong answers: dividing by the wrong base, and confusing percent with percentage points.
01The formula
percent change = (new - old) / |old| × 10002Worked example
- A price rises from 80 to 100: (100 − 80) ÷ 80 × 100 = +25%.
- The same price falls from 100 to 80: (80 − 100) ÷ 100 × 100 = −20%.
03Limitations
Percent change is undefined when the starting value is zero, and it is not symmetric: a 25% rise is undone by a 20% fall, not by another 25% fall.
Frequently asked questions
- Why is a 25% rise not cancelled by a 25% fall?
- Percent change is relative to the current base, which changed after the rise.
Sources
- NIST Special Publication 811: Guide for the Use of the International System of Units (SI) — NIST (accessed 2026-09-27)