Percentages show up everywhere — sales tax, tips, discounts, grades, interest rates. Once you understand the three core percentage formulas, you can solve almost any real-world percentage problem in your head or with a basic calculator.
The three percentage formulas
Every percentage problem fits one of these three patterns:
- Find the percent of a number: "What is 18% of $50?"
- Find what percent one number is of another: "$9 is what percent of $50?"
- Find percent change: "Price went from $50 to $60 — what percent increase?"
Each has a one-line formula. Memorise these and most percentage questions become arithmetic.
Formula 1: Percent of a number
Result = number × (percent ÷ 100)
Or just: convert the percentage to a decimal and multiply.
Worked example: What is 18% of $50?
- Convert 18% to decimal: 0.18
- Multiply: $50 × 0.18 = $9
This is the formula you use for tips, sales tax, and most discount calculations.
Mental shortcut: 10% of any number is just that number with the decimal moved one place left. So 10% of $50 = $5, and 18% is roughly 10% + 8% ≈ $5 + $4 = $9. Useful for tip math.
Formula 2: What percent is X of Y?
Percent = (X ÷ Y) × 100
Worked example: $9 is what percent of $50?
- Divide: 9 ÷ 50 = 0.18
- Multiply by 100: 18%
This is what you use to figure out test scores ("I got 72 out of 90, what's my percentage?") or compare proportions.
Worked example: 72 ÷ 90 × 100 = 80%
Formula 3: Percent change
Percent change = ((New − Old) ÷ Old) × 100
Positive number = increase. Negative = decrease.
Worked example: Price went from $50 to $60. What's the percent increase?
- New − Old: $60 − $50 = $10
- Divide by Old: $10 ÷ $50 = 0.2
- Multiply by 100: 20% increase
Worked example (decrease): Price dropped from $80 to $60.
- New − Old: $60 − $80 = −$20
- Divide by Old: −$20 ÷ $80 = −0.25
- Multiply by 100: −25%, or a 25% decrease
Common mistake: percent vs percentage points
If interest rates rise from 5% to 6%, the rate went up by:
- 1 percentage point (the absolute difference)
- 20 percent (the relative change: 1 ÷ 5 × 100)
News articles often confuse these. "Rates rose 20%" sounds bigger than "rates rose 1 percentage point" but they describe the same thing.
Reverse percentage: finding the original price
You bought something on 25% off and paid $60. What was the original price?
You paid 75% of the original (because 100% − 25% = 75%).
Original = paid ÷ (1 − discount/100)
Original = $60 ÷ 0.75 = $80.
Adding a percentage (like sales tax)
You see an item priced at $50 and need to add 8% sales tax. What's the total?
Two ways:
- Long: 50 × 0.08 = 4, total = 50 + 4 = $54
- Short: 50 × 1.08 = $54 (multiply by 1.[tax rate])
The "× 1.08" shortcut works for any markup. For 18% tip on $50: 50 × 1.18 = $59 total.
Subtracting a percentage (like a discount)
20% off $80? Multiply by 0.80 (or 1 − 0.20):
$80 × 0.80 = $64.
Stacked percentages don't add
20% off, then another 10% off, is NOT 30% off.
$100 × 0.80 = $80, then $80 × 0.90 = $72. That's 28% off the original — not 30%.
This is why retailers love "Save additional 10% at checkout" promotions. They sound bigger than they are.
Quick reference table
| Question | Formula |
|---|---|
| X% of Y | Y × (X/100) |
| X is what % of Y | (X/Y) × 100 |
| % change from old to new | ((new − old)/old) × 100 |
| Original price (after X% off, paid Y) | Y / (1 − X/100) |
| Add X% to Y | Y × (1 + X/100) |
| Subtract X% from Y | Y × (1 − X/100) |
Skip the math
Our percentage calculator handles all six patterns. Pick a mode (% of a number / X is what % of Y / percent change), enter your numbers, and get the answer instantly. Useful for sanity-checking deals, tips, and any percentage math.