Percentage Increase and Decrease

Percentage change measures a difference relative to the starting value. The starting value is essential because the same numerical difference can represent very different percentage changes.

The percentage-change formula

A positive answer is an increase, a negative answer is a decrease and zero means no change. For ordinary positive prices, measurements and counts, this formula behaves as most people expect.

Why increases and decreases are not symmetrical

Going from 80 to 100 adds 20 relative to a base of 80. Returning from 100 to 80 removes the same 20, but now the base is 100. The different base values produce 25% and 20%.

This also explains why a 20% rise followed by a 20% fall does not return to the starting value. Starting at 100, a 20% rise gives 120. A 20% fall from 120 removes 24, leaving 96.

Percentage change versus percentage points

Percentage points describe the simple difference between two percentages. Percentage change compares that difference with the original percentage.

What happens when the old value is zero?

The standard percentage-change formula divides by the old value. Division by zero is undefined, so a percentage change from zero cannot be expressed by this formula. You can report the numerical increase instead, such as “an increase of 10 units.”

Negative starting values

Changes involving negative values require context. Moving from −10 to −5 is an improvement of 5 units, but conventional percentage descriptions can be confusing. The calculator uses the absolute old value in the denominator, yet financial statements or scientific reports may follow a specific convention. State both values and the numerical difference when clarity matters.