Rule of thumb · MathematicsNº 189 / 238

Percent of means multiply by hundredths

How do you work out a percentage of a number?

X% of Y is (X/100) times Y — and "Y plus X%" is Y times (1 + X/100).

Why it works

Percent just means per hundred. The same algebra powers tips, discounts, VAT-style add-ons, and reverse "what percent is A of B".

When it fails

Percentages do not commute across a sequence. Up 20% then down 20% leaves you at 96%, not 100% — and a change from 3% to 5% is two percentage points but a 67% increase, which is the ambiguity most misleading statistics are built on.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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