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Everyday math

Percentage Calculator

The three percentage questions in one place: X% of Y, what percent X is of Y, and percentage change, each with the formula shown.

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Quick answer

X% of Y = (X ÷ 100) × Y. What percent is X of Y = (X ÷ Y) × 100. Change = (new − old) ÷ old × 100. The classic trap: a 10% rise then a 10% fall lands at 99%, not 100, percentages of different bases never cancel.

15% of 200
30

Formulas last verified 2026-10-10. Results are estimates, not financial advice. How we calculate.

Three questions, three formulas

Nearly every percentage problem is one of three questions. The calculator handles all three; here is what each one is doing.

QuestionFormulaExample
What is X% of Y?(X ÷ 100) × Y15% of 240 = 36
X is what % of Y?(X ÷ Y) × 100452 of 600 = 75.33%
% change from old to new?(new − old) ÷ old × 10080 → 92 = +15%

The one thing all three share: the base matters. A percentage is always a fraction of something, and identifying that something correctly is the entire game.

Mode 1: X% of Y, tips, tax, commissions

The workhorse. 18% GST on ₹2,500 is 0.18 × 2,500 = ₹450. The mental-math shortcut is to anchor on 10% (move the decimal: 250) and scale from there: 18% is 10% + 5% + 3% ≈ 250 + 125 + 75 = 450. Exact when you need it, estimable when you don't.

Mode 2: X is what % of Y, scores and shares

Part ÷ whole × 100. A student scoring 452 out of 600 has (452 ÷ 600) × 100 = 75.33%. The common slip is dividing the wrong way, the number after "of" goes on the bottom. If your answer exceeds 100% and the part shouldn't exceed the whole, you have them inverted.

Mode 3: percentage change, the one with the trap

Change is always measured against the old value: (new − old) ÷ old × 100. This base-dependence produces the classic trap: start at 100, gain 10% (→ 110), lose 10% (→ 99). You do not return to 100, because the −10% acted on a bigger base than the +10% did. Multiplicatively: 1.10 × 0.90 = 0.99, a guaranteed 1% loss from any symmetric up-down pair. Scaled up, a 30% fall requires a 42.9% rise to break even, and a 50% fall requires a 100% rise. Sequential percentages multiply; intuition adds. Trust the multiplication.

Percentage points vs percent, the news-headline distinction

When a rate itself changes, there are two honest ways to describe it. An interest rate going from 4% to 6% has risen by 2 percentage points, and by 50 percent, since 2 is half of 4. Both are correct; they answer different questions. The blur between them is a favourite tool of headlines and marketing: "risk increases 50%!" may describe a probability moving from 4% to 6%. Whenever a change in a rate is quoted, ask: points, or percent of the rate? The answer often deflates the drama.

Where these formulas show up next

Percentages are the building block behind half the calculators on this site. Discounts are mode 1 with a subtraction, and stacked "extra % off" offers multiply rather than add, which the discount calculator handles correctly. GST adds a twist in reverse: extracting tax from an inclusive price divides by 1.18 rather than subtracting 18%, as the GST calculator shows. And for students, "what do I need on the final?" is a weighted rearrangement of mode 2, solved directly by the final grade calculator.

Frequently asked questions

How do I calculate X% of a number?

Divide the percentage by 100 and multiply: X% of Y = (X ÷ 100) × Y. So 15% of 240 is 0.15 × 240 = 36. A useful mental shortcut: find 10% by moving the decimal point (24), then scale, 15% is 10% plus half of it again (24 + 12 = 36). This is the mode to use for tips, commissions and tax.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100: (X ÷ Y) × 100. Scoring 452 marks out of 600 gives (452 ÷ 600) × 100 = 75.33%. The order matters, the number after "of" is always the divisor. Getting them backwards gives 132.7%, which is a quick sanity check: a part larger than its whole should make you re-check the inputs.

How is percentage change calculated?

Change = (new − old) ÷ old × 100, the old value is always the base. A price going from 80 to 92 is (12 ÷ 80) × 100 = +15%; going from 92 to 80 is −13.04%, not −15%, because the base changed. This asymmetry is why a 50% loss needs a 100% gain to recover, and why up-then-down percentages never cancel exactly.

Why does +10% then −10% not get me back to the start?

Because the second percentage applies to a different base. Start at 100: +10% gives 110, then −10% of 110 removes 11, landing at 99. In multiplication terms, 1.10 × 0.90 = 0.99, a net 1% loss. The same effect makes a stock that drops 30% need a 42.9% rise to break even. Sequential percentages multiply; they never simply add or cancel.

What is the difference between percentage points and percent?

An interest rate moving from 4% to 6% rises by 2 percentage points, but by 50 percent (2 ÷ 4 × 100). Both statements are true; they answer different questions. News reports and marketing routinely blur the two, "50% increase" sounds far bigger than "2-point increase" for the identical change. When reading any claim about a change in a rate, check which one is meant.

How do I calculate my marks percentage?

Total your marks obtained, divide by total maximum marks, multiply by 100. Scoring 452 out of 600 across subjects: (452 ÷ 600) × 100 = 75.33%. When papers carry different maximums, sum the actual marks and actual maximums, do not average the individual percentages, since that weights a 50-mark paper equally with a 100-mark one and gives the wrong answer.

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