Percentages sound precise, but two common mix-ups make them easy to misread: confusing percentage change with percentage points, and forgetting that increases and decreases are measured from different starting points.
How percentage change works
Percentage change compares the difference between two numbers with the starting number. Subtract the old value from the new one, divide by the old value, and multiply by 100.
Difference
100 − 80equals20
Percentage change
20 ÷ 80 × 100equals25%
Percentage points
When the numbers are already percentages, there are two ways to describe a change. If an interest rate goes from 4% to 5%, it rose by 1 percentage point, which is the simple difference. As a percentage change, it rose by 25%, because 1 is a quarter of 4.
Both are correct, but they sound very different. A headline saying a rate "rose 25%" and one saying it "rose 1 point" are describing the same thing.
Why a drop is harder to recover from
Each change is measured from wherever you are at the time. That makes losses and gains lopsided.
After a 50% drop
100 × (1 − 50%)equals50
After a 50% rise
50 × (1 + 50%)equals75
You end up 25% below where you started. To get from 50 back to 100, you need a 100% rise. The same applies to the price example: going from 80 to 100 is a 25% rise, but falling from 100 back to 80 is only a 20% drop.
When percentage change is misleading
- Small starting numbers: growing from 2 customers to 6 is a 200% increase, but it is still only 6 customers.
- Starting from zero: percentage change from 0 cannot be calculated at all.
- Crossing zero: a loss turning into a profit gives percentages that are hard to interpret. Use the plain difference instead.
Tip: When you report a change, give the before and after numbers alongside the percentage. It removes any doubt about what was measured.