How percentage change works (including the awkward cases)

The direct answer

For a positive starting value, percentage change is the difference divided by the starting value, multiplied by 100. A positive result means an increase; a negative result means a decrease.

From 80 to 100

The difference is 20. Divide 20 by 80 to get 0.25, then multiply by 100: a 25% increase. The reverse trip from 100 to 80 is a 20% decrease. Percent changes depend on the starting value.

Zero is a special case

There is no defined percentage change from zero because division by zero is undefined. Describe the absolute difference instead. A change from 0 to 10 is an increase of 10 units.

Negative starting values

Our calculator divides by the absolute starting value when it is negative, so the sign follows the direction of change. From −50 to −25, it reports a 50% increase. Other conventions exist; state the denominator when comparing results.

Percentage points are different

Moving from a 10% rate to a 15% rate is a rise of 5 percentage points, or a 50% relative increase. Do not interchange those descriptions.

Use the percentage change calculator to check your example. These formulas are explained through arithmetic rather than external factual claims.