Skip to content
mathbehind

Percentage Change vs Percentage Points, and Why Losses Are Harder to Recover

A rate going from 4% to 5% rose by 1 percentage point, or by 25%. And a 50% drop needs a 100% rise to recover. Here is the math behind both.

By Muhammad Ahmad. Published . 1 min read.

Want to run your own numbers?Percentage Change CalculatorOpen the calculator

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.

A price rising from 80 to 100
  1. Difference

    100 − 80equals20

  2. 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.

Down 50%, then up 50%
  1. After a 50% drop

    100 × (1 − 50%)equals50

  2. 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.