How to Calculate a Percentage
The three core percentage formulas, mental math shortcuts, and worked examples for the most common real-world scenarios.
The three percentage problems
Every percentage calculation is one of three types. Recognizing the type tells you exactly which formula to use.
Result = (X ÷ 100) × Y
Example: What is 15% of $80? → (15 ÷ 100) × 80 = $12
Result = (X ÷ Y) × 100
Example: 30 is what percent of 200? → (30 ÷ 200) × 100 = 15%
Result = ((Y − X) ÷ X) × 100
Example: Price went from $50 to $65. What's the percent increase? → ((65 − 50) ÷ 50) × 100 = 30%
Mental math shortcuts
These shortcuts let you calculate common percentages in your head without a calculator.
10% → Move the decimal one place left
10% of $84 = $8.40
5% → Half of 10%
5% of $84 = $4.20
20% → Double the 10% value
20% of $84 = $16.80
25% → Divide by 4
25% of $84 = $21.00
15% → 10% + 5%
15% of $84 = $8.40 + $4.20 = $12.60
1% → Move the decimal two places left
1% of $84 = $0.84Common real-world scenarios
- Sales tax
- Multiply the price by the tax rate. A $45 item with 8.5% sales tax: 45 × 0.085 = $3.83 tax → total $48.83. Or: find 10% ($4.50), subtract 1.5% ($0.68) → $3.82 (close enough for estimation).
- Tip calculation
- 20% tip: find 10% and double it. On a $67 bill: 10% = $6.70 → 20% tip = $13.40. For 15%: find 10% ($6.70) + half of that ($3.35) = $10.05.
- Discount / sale price
- For a 30% off discount: multiply by 0.70 (what you keep). A $120 item at 30% off: 120 × 0.70 = $84. Or: find 30% (120 × 0.30 = $36) and subtract: 120 − 36 = $84.
- Grade / test score
- Divide your score by the total and multiply by 100. Got 43 out of 55: (43 ÷ 55) × 100 = 78.2%.
- Interest rate on a loan
- Monthly interest on a $10,000 balance at 18% APR: 18% ÷ 12 = 1.5% per month → 10,000 × 0.015 = $150 in interest that month. If you only pay $200/month, only $50 goes to principal.
- Salary increase
- A 4% raise on a $65,000 salary: 65,000 × 0.04 = $2,600 → new salary $67,600. Or directly: 65,000 × 1.04 = $67,600.
Percent vs. percentage points
These two terms are not interchangeable and the difference matters.
If an interest rate rises from 4% to 6%:
- It increased by 2 percentage points (the arithmetic difference: 6 − 4 = 2)
- It increased by 50% (the relative change: (6 − 4) ÷ 4 × 100 = 50%)
Saying a rate "increased 50%" and "increased 2 percentage points" are both technically correct but describe very different magnitudes. News coverage of rate changes often mixes these up.
Frequently asked questions
- What is the difference between percent and percentage?
- "Percent" (%) is used with a specific number: "the price dropped 12 percent." "Percentage" is used when no specific number is given: "a large percentage of users." In practice, the distinction is minor in casual usage.
- How do I calculate the original price before a discount?
- Divide the sale price by (1 minus the discount rate). If something costs $63 after a 30% discount: 63 ÷ 0.70 = $90 original price. This is the reverse of the standard discount formula and a common mistake in retail math.
- How do compound percentages work?
- Percentages don't add directly when applied in sequence. A 20% increase followed by a 20% decrease does not return to the original: 100 → 120 → 96 (a net loss of 4%). For compound effects, multiply the factors: 1.20 × 0.80 = 0.96 = a 4% net decrease.
- What does basis point mean?
- One basis point (bps) equals 0.01 percentage points. Used in finance to avoid ambiguity: a rate rising from 3.50% to 3.75% increased by 25 basis points. "25 bps" is clearer than "0.25%" (which could be confused with a 0.25% relative change).