Three common percentage questions, answered instantly.
1. X% of Y — multiply Y by X, then divide by 100: (X ÷ 100) × Y. Example: 15% of 200 = (15 ÷ 100) × 200 = 30.
2. X is what percent of Y — divide X by Y, then multiply by 100: (X ÷ Y) × 100. Example: 30 is what percent of 150 → (30 ÷ 150) × 100 = 20%.
3. Percentage change from X to Y — subtract X from Y, divide by X, then multiply by 100: ((Y − X) ÷ X) × 100. Example: going from 80 to 100 → ((100 − 80) ÷ 80) × 100 = +25%. A negative result means a decrease.
Discounts: Use "X% of Y" to find out how much you save — 20% off a $60 item saves $12, so you'd pay $48.
Tips and splitting bills: Use "X% of Y" with your desired tip percentage against the bill total.
Test scores and grades: Use "X is what percent of Y" to convert raw scores (like 42 out of 50) into a percentage.
Salary raises, price changes, growth rates: Use "percentage change" to see how much something has increased or decreased relative to its starting point.
Why isn't a 20% increase followed by a 20% decrease back to the original number?
Because each percentage is calculated against a different base. A $100 item that rises 20% becomes $120; a 20% decrease from $120 is $24, bringing it to $96 — not back to $100.
What does a negative percentage change mean?
It means the value decreased. Going from 100 to 80 gives a change of −20%.
Can percentages go above 100%?
Yes — if X is larger than Y in "X is what percent of Y," or if a percentage increase more than doubles the original value.
Percentage = (part ÷ whole) × 100.
((new value − old value) ÷ old value) × 100, with the sign showing increase or decrease.
Multiply the whole by the percentage expressed as a decimal (e.g. 20% of 50 = 0.20 × 50 = 10).