Percentages
How do you calculate a percentage of a number?
What is X% of Y, what percent is X of Y, percentage change between two numbers.
Quick answer
X% of Y = (X ÷ 100) × Y. Example: 20% of 150 = 0.20 × 150 = 30. To find what percent X is of Y: (X ÷ Y) × 100 — 30 is 20% of 150 because 30 ÷ 150 × 100 = 20%.
20% of 150
30
How it works
Percentage change from A to B = ((B − A) ÷ |A|) × 100. Price rising from 80 to 100 is a 25% increase (20 ÷ 80 × 100), not 20%. The calculator handles all three modes: of, what percent, and change — switch mode before entering numbers so the right formula applies.
Supermarket labels mix tricks: “30% extra free” is not the same as “30% off” — always convert to €/kg or €/unit before deciding. A scientific calculator handles tax and discount stacks without rounding errors; a pocket calculator in your bag beats guessing at market stalls. Teaching kids? Have them write worked examples in a notebook until the “divide by 1.20” rule sticks.
One distinction is worth more than the arithmetic: a percentage and a percentage point are not the same thing. A rate moving from 5% to 7% has risen by two percentage points and by forty per cent — both statements are true, they describe the same move, and headlines pick whichever is more dramatic. It matters most on things already expressed as percentages: interest rates, unemployment, commissions, tax bands, conversion rates. When someone says a fee "went up two per cent", ask whether they mean from 5 to 5.1 or from 5 to 7, because the difference between those two answers is the whole story.
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Frequently asked questions
How do I add 20% to a price?+
Multiply by 1.20. €100 + 20% = €120. To remove included markup, divide by 1.20 — do not subtract 20%. Reverse VAT and stacked discounts use the same multiply/divide logic, not subtraction.
Percentage vs percentage points?+
Rate rising from 2% to 5% is +3 percentage points but +150% relative increase. Headlines often confuse the two — always check which base the journalist used before reacting.
How do I calculate a tip?+
Tip = bill × (percent ÷ 100). €45 at 15%: 45 × 0.15 = €6.75. Ten percent is bill ÷ 10. Splitting the bill? Apply the same percent to each person’s share, not to the total twice.
Can percentages exceed 100%?+
Yes when comparing to a smaller base. Revenue doubling is +100%; tripling is +200%. A stock falling from €50 to €25 is a −50% change, not −125%.
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