How to calculate percentage increase and decrease

Percentage change compares a new value with an old one: (new − old) ÷ old × 100. A positive result is an increase and a negative result is a decrease.

From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%, a 25% increase. From 100 back to 80 is (80 − 100) ÷ 100 × 100 = −20%, a 20% decrease.

The base is always the starting value. After a 25% rise, the new value is larger, so the same drop in absolute terms is a smaller percentage of it.

This is why a share price that falls 50% needs to rise 100% to get back to where it began.

To increase a number by a percentage, multiply by 1 plus the decimal. Raising 200 by 15% is 200 × 1.15 = 230. To decrease it, multiply by 1 minus the decimal: 200 × 0.85 = 170.

Do the same for repeated changes, one after another. A 10% rise followed by a 10% fall leaves you at 99% of the start, not 100%.

Use percentage change for price rises, pay rises, website traffic, sales growth and inflation. Always state the starting value, so readers know what the percentage is measured against.

Do not confuse percentage change with percentage points. If a rate moves from 4% to 5%, it rises by one percentage point, but by 25% in relative terms.