Percentage of a Percentage Calculator
Effortlessly learn how to calculate a percentage of a percentage with our precise calculator. Simplify complex calculations now. Try it!
The formula
result = a ÷ 100 × b ÷ 100 × 100
Percentages of percentages compound
Taking 50% of 40% gives 20%, not 90% and not 10% — you multiply the decimal factors rather than adding or subtracting the percentages. This is the arithmetic behind stacked discounts: 20% off, then a further 10% off, leaves 0.8 × 0.9 = 0.72, a 28% saving rather than 30%.
What a percentage is
"Per cent" means "per hundred", so a percentage is just a fraction with 100 on the bottom. 15% is 15/100, which is 0.15 as a decimal. Every percentage calculation is therefore multiplication or division by a decimal — the percent sign is bookkeeping, not a new operation.
The three questions
Almost every percentage problem is one of three:
- What is P% of N? Multiply:
N × P/100 - A is what percent of B? Divide:
A/B × 100 - A is P% of what? Divide the other way:
A ÷ (P/100)
Recognising which one you have is most of the work; the arithmetic is straightforward once you do.