Last updated: September 2026
Percentages show up everywhere: the tip on a restaurant bill, the discount tag on a jacket, the raise in your paycheck, the interest on a loan. A percentage is simply a way of talking about a part of a whole, scaled so that the whole is always 100. Once you understand the three basic percentage formulas, you can handle almost any everyday situation without reaching for your phone in a panic.
The word "percent" comes from the Latin per centum — "per hundred." So 25% literally means 25 out of every 100. If a store says a $200 television is 25% off, it means you save $25 for every $100 of the price, or $50 total. Thinking of percentages as "parts per hundred" makes every formula below feel like common sense instead of math-class magic.
Nearly every percentage question in daily life is one of these three. Learn them and you're covered.
Formula: (X ÷ 100) × Y, or equivalently (X × Y) ÷ 100.
Example — the restaurant tip: Your bill is $46.50 and you want to leave a 20% tip. Multiply 20 × 46.50 = 930, then divide by 100: 930 ÷ 100 = $9.30. Your total is $55.80. Quick mental shortcut: 10% of anything is just the number with the decimal moved one place left ($4.65), and 20% is double that ($9.30).
Formula: (X ÷ Y) × 100.
Example — the sale discount: A jacket was $80 and now costs $60. How big is the discount? The savings are $20. Divide 20 ÷ 80 = 0.25, then multiply by 100 to get 25%. That's a 25%-off sale. This formula is also how you check sale claims: if a store advertises "40% off" but the price only dropped from $80 to $55, that's $25 ÷ $80 = 31.25% — the claim doesn't hold up.
Formula: ((New value − Old value) ÷ Old value) × 100.
Example — the pay raise: Your hourly wage goes from $22.00 to $23.50. Subtract: 23.50 − 22.00 = 1.50. Divide by the old value: 1.50 ÷ 22.00 ≈ 0.0682. Multiply by 100: about a 6.8% raise. If the new value is smaller than the old one, the same formula gives a negative number — that's a percent decrease, like a stock portfolio dropping from $10,000 to $9,200 (an 8% decrease).
Sometimes you know the sale price but not the original. If an item costs $60 after a 25% discount, the $60 represents 75% of the original price (100% − 25%). So divide the sale price by the remaining percentage as a decimal: $60 ÷ 0.75 = $80. The original price was $80, and you saved $20. The same trick works in reverse for taxes and markups: a $108 total after 8% sales tax means the pre-tax price was $108 ÷ 1.08 = $100.
This one trips up news headlines regularly. If a poll shows a candidate's support rising from 5% to 7%, that's an increase of 2 percentage points — but it's a 40% relative increase (2 ÷ 5 × 100). When someone says "interest rates went up 2%," do they mean from 5% to 7% (2 percentage points) or from 5% to 5.1% (a 2% relative increase)? Always ask which one is meant when money is involved.
Try these, then check your answers. A calculator is allowed — the point is knowing which formula to reach for.
| Question | Answer |
|---|---|
| What is 15% of 200? | 30 |
| 45 is what percent of 180? | 25% |
| A price rises from $50 to $65. What is the percent increase? | 30% |
| A $90 coat is marked 30% off. What do you pay? | $63 |
| You pay $72 after a 10% discount. What was the original price? | $80 |
| Support rises from 40% to 46%. How many percentage points is that? | 6 percentage points |
Percentages stop being intimidating the moment you see them as "parts per hundred" and match each question to one of the three formulas. Practice with real numbers from your own life — your bills, your paycheck, the sale tags you pass in stores — and the math becomes second nature.