How do I calculate a percentage?

Three Types of Percentage Problems

Almost every percentage question falls into one of three categories. Once you identify the type, the math becomes straightforward.

Type 1: Finding a Percentage of a Number

This is the most common type. "What is 15% of 200?" means you want to find a portion of a total. The formula is simple: multiply the number by the percentage and divide by 100. So 200 × 15 ÷ 100 = 30. You use this type when calculating tips, sales tax, discounts, and investment returns.

Type 2: Finding What Percent One Number Is of Another

Questions like "45 is what percent of 180?" ask you to express a relationship as a percentage. Divide the part by the whole, then multiply by 100: (45 ÷ 180) × 100 = 25%. This type appears in grades (you got 42 out of 50 questions right — what's your score?), market share calculations, and nutritional labels.

Type 3: Percentage Change (Increase or Decrease)

When a value goes from one number to another, you often want to know the percentage change. The formula is ((New Value - Old Value) ÷ Old Value) × 100. If your rent went from $1,200 to $1,350, the increase is (($1,350 - $1,200) ÷ $1,200) × 100 = 12.5%. A positive result is an increase; a negative result is a decrease.

Mental Math Shortcuts for Percentages

You don't always need a calculator. These mental math tricks let you estimate percentages quickly and accurately in everyday situations.

The 10% Anchor Method

Start by finding 10%, which is the easiest percentage to calculate — just move the decimal point one place to the left. From there, you can build almost any common percentage:

• 10% — move the decimal one place left. 10% of $85 = $8.50.
• 5% — take half of 10%. 5% of $85 = $4.25.
• 15% — add 10% and 5% together. 15% of $85 = $8.50 + $4.25 = $12.75.
• 20% — double 10%. 20% of $85 = $17.00.
• 25% — divide by 4. 25% of $85 = $21.25.
• 1% — move the decimal two places left. 1% of $85 = $0.85. Useful for building up to oddball percentages.

For example, to tip 18% on an $85 dinner: 10% is $8.50, 5% is $4.25, and 3% is 3 × $0.85 = $2.55. Add them together: $8.50 + $4.25 + $2.55 = $15.30.

Real-World Percentage Applications

Tips and Gratuities

Restaurant tips in the US typically range from 15% to 20%. For a $65 meal, a 15% tip is $65 × 0.15 = $9.75, while a 20% tip is $65 × 0.20 = $13.00. Many people round to the nearest dollar for convenience.

Sales Tax

Sales tax is added at the point of sale. If your state charges 7.5% sales tax and you're buying a $250 item, the tax is $250 × 0.075 = $18.75, making the total $268.75. Tax rates vary by state and sometimes by city, ranging from 0% (Oregon, Montana) to over 10% in parts of California and Tennessee.

Discounts and Sale Prices

A "30% off" sale means you pay 70% of the original price. A $120 jacket at 30% off costs $120 × 0.70 = $84. Stacking discounts is multiplicative, not additive — a 20% off coupon on top of a 30% off sale is not 50% off. It's 0.70 × 0.80 = 0.56, or 44% off the original price.

Grades and Test Scores

Your grade is the number of points earned divided by total points, times 100. If you scored 87 out of 100, your grade is 87%. If you scored 42 out of 50, it's (42 ÷ 50) × 100 = 84%.

Investment Returns

If your investment portfolio was worth $10,000 last year and is now worth $10,850, your return is (($10,850 - $10,000) ÷ $10,000) × 100 = 8.5%. Note that annual returns compound — a 10% gain followed by a 10% loss does not bring you back to even. $10,000 × 1.10 = $11,000, then $11,000 × 0.90 = $9,900, a net loss of 1%.

Common Percentage Mistakes to Avoid

The Increase/Decrease Asymmetry Trap

A 50% increase followed by a 50% decrease does NOT return to the original value. If a $100 item increases 50% to $150, then decreases 50%, it drops to $75 — not $100. This is because the decrease is taken from the higher number. This asymmetry catches people off guard with investments and pricing.

Percentage vs. Percentage Points

These are not the same thing. If an interest rate goes from 4% to 5%, it increased by 1 percentage point but by 25 percent (because 1 is 25% of 4). News headlines often conflate these, which can be misleading. "Unemployment rose 2 percentage points (from 3% to 5%)" is very different from "unemployment rose 2% (from 3% to 3.06%)."

Base Rate Confusion

Always ask: "percent of what?" A store that marks up prices 100% and then offers 50% off is selling at the original price, not at a loss. The markup is calculated on cost; the discount is calculated on the marked-up price. Different bases lead to different results even with seemingly offsetting percentages.

Reverse Percentage Calculations

Sometimes you know the result and need to work backward. If a discounted price is $68 after a 15% discount, the original price was $68 ÷ 0.85 = $80. If a price including 8% tax is $54, the pre-tax price was $54 ÷ 1.08 = $50. The key is to divide by the decimal multiplier instead of multiplying.