Find the percent increase or decrease between two numbers.
Percentage change = (new − old) ÷ old × 100
The denominator is always the starting value. Going from 80 to 100 is a 25% increase; going from 100 to 80 is a 20% decrease. Same absolute movement, different percentages, because the base changed.
This asymmetry is the source of most confusion around percentage change, and it has practical consequences: a portfolio that falls 20% needs to rise 25% to recover, and one that halves needs to double.
When the values being compared are themselves percentages, the language has to be precise. A conversion rate moving from 2% to 3% has risen by one percentage point and by 50 percent.
Reporting the second figure without saying which one you mean is a classic way to make a small change sound dramatic. Both are true; only one is informative in most contexts. When you see an eye-catching percentage in a headline, checking the absolute numbers underneath is usually worthwhile.
Consecutive growth rates cannot be averaged arithmetically. A year of +20% followed by a year of −10% does not average to +5%: 100 becomes 120, then 108, so the two-year growth is 8% and the annualised rate is about 3.92%.
The correct measure is the compound annual growth rate, which uses the geometric mean.
CAGR = (final ÷ initial)1 ÷ years − 1
Arithmetic averages always overstate compounded performance when there is any volatility, and the gap widens as volatility increases. This is why fund performance is quoted as annualised return rather than the average of yearly figures.
Small bases produce enormous percentages. A product going from two sales to six is a 200% increase and remains four sales. Reporting the percentage without the base is technically accurate and practically useless.
Percentage change is also undefined when the starting value is zero, since dividing by zero has no meaning. In that case, report the absolute change and say so.