The three percentage formulas
X as % of Y = (X ÷ Y) × 100
% change = (new − old) ÷ |old| × 100
Everyday examples
- Tipping: 15% of a $240 dinner bill → 0.15 × 240 = $36.
- Test scores: 36 correct out of 40 questions → 36 ÷ 40 × 100 = 90%.
- Price rises: rent going from $80 to $100 → (100 − 80) ÷ 80 × 100 = a 25% increase.
Quick mental math tricks
10% is one decimal shift. 10% of 240 is 24, so 5% is 12 and 20% is 48 — combine these to build any percentage. x% of y equals y% of x: 8% of 50 feels hard, but 50% of 8 is obviously 4. And to reverse a percentage ("$36 is 15% of what?"), divide instead of multiplying: 36 ÷ 0.15 = 240.
A common trap: percentage points vs percent
If an interest rate moves from 4% to 5%, it rose by 1 percentage point but by 25 percent (1 ÷ 4). News headlines mix these up constantly; knowing the difference keeps your comparisons honest.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply. 15% of 240 = (15 ÷ 100) × 240 = 36. On any basic calculator: 240 × 15 ÷ 100.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. If 36 of 240 units sold are returns, that's 36 ÷ 240 × 100 = 15%.
How is percentage change calculated?
Subtract the old value from the new, divide by the old value, then multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = +25%. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%. Note the answers differ — the base changes.
Why is a 50% loss not fixed by a 50% gain?
Because the base shrinks. Lose 50% of $100 and you have $50; gaining 50% of $50 only brings you to $75. After a 50% loss you need a 100% gain to break even.
How do I add or subtract a percentage from a number?
Multiply by (1 + rate) to add or (1 − rate) to subtract. Adding 8% tax to $50: 50 × 1.08 = $54. Taking 30% off $80: 80 × 0.70 = $56.