FIELD NOTE 02 / RATIOS
Percentage change and percentage points
A percentage has a base. If the base changes, the question changes. These examples separate three calculations that are often mixed together.
1. Find a percentage of an amount
To find 15% of 80, multiply the amount by the rate divided by 100: 80 × (15 ÷ 100) = 12. The answer is an amount in the same unit as 80.
2. Find what share one amount is of another
To ask “15 is what percent of 80?”, divide the part by the whole and multiply by 100: (15 ÷ 80) × 100 = 18.75%. State which value is the whole. Swapping the values changes the answer.
3. Calculate relative percentage change
For a move from 80 to 100, subtract the starting value from the ending value, then divide by the starting value: ((100 − 80) ÷ 80) × 100 = 25%. The sign tells direction: a negative result is a decrease. If the starting value is zero, relative percentage change is undefined because division by zero has no finite result.
Percentage points compare rates directly
If a rate moves from 20% to 25%, the difference is 5 percentage points. Relative to the old rate, it is a 25% increase: ((25 − 20) ÷ 20) × 100. Those descriptions answer different questions. Use percentage points to state the absolute gap between two rates; use percentage change to compare the gap with the original rate.
Negative values and context
The standard relative-change formula can be hard to interpret when the baseline is negative or when values cross zero. In that case, show the original values and the absolute difference as well. For business, scientific or policy reporting, follow the metric’s established convention rather than choosing a formula solely because it yields a larger or smaller headline.
Try the calculator
Open the percentage calculator and choose the matching question before entering values.
Formula summary
- A% of B:
(A ÷ 100) × B - A as a percentage of B:
(A ÷ B) × 100 - Change from A to B:
((B − A) ÷ A) × 100, when A is not zero - Percentage-point difference: ending rate minus starting rate