How to Calculate Percentages: Every Formula You Need (With Examples)

Basic Percentage Formula

A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum" meaning "per hundred." Every percentage calculation is a variation of one core relationship:

These three forms solve three different question types. Know which variable you're looking for and use the appropriate form. Everything else in percentage math builds on this triangle relationship.

Finding a Percentage of a Number

This is the most common calculation: "What is X% of Y?"

Formula: Result = (X ÷ 100) × Y

Example 1 — Discount: A $120 jacket is 25% off. Discount = (25 ÷ 100) × $120 = 0.25 × $120 = $30. Sale price = $120 − $30 = $90.

Example 2 — Sales tax: Your restaurant bill is $84 and tax is 8.5%. Tax = 0.085 × $84 = $7.14. Total = $84 + $7.14 = $91.14.

Example 3 — Investment return: You invest $5,000 and earn a 7% annual return. Return = 0.07 × $5,000 = $350 in year 1.

Mental shortcut: To find 10% of any number, just move the decimal point one place to the left. 10% of 360 = 36. Then scale: 5% = half of 10% = 18; 20% = double 10% = 72; 15% = 10% + 5% = 36 + 18 = 54.

What Percent Is X of Y?

This question type asks you to express one number as a percentage of another: "X is what percent of Y?"

Formula: Percentage = (X ÷ Y) × 100

Example 1 — Exam score: You scored 47 out of 60 on a test. Grade = (47 ÷ 60) × 100 = 78.3%.

Example 2 — Budget utilization: You've spent $1,840 of a $2,500 budget. Utilization = (1,840 ÷ 2,500) × 100 = 73.6%.

Example 3 — Market share: Company A sold 3.2 million units out of an industry total of 14.8 million. Market share = (3.2 ÷ 14.8) × 100 = 21.6%.

Percentage Increase and Decrease

These formulas measure change relative to the original value — they're essential for understanding price changes, salary raises, and financial performance.

Percentage Increase: ((New − Old) ÷ Old) × 100

Percentage Decrease: ((Old − New) ÷ Old) × 100

A combined formula that handles both (positive result = increase, negative = decrease): ((New − Old) ÷ Old) × 100

Example 1 — Salary raise: Your salary goes from $55,000 to $60,500. Change = ((60,500 − 55,000) ÷ 55,000) × 100 = (5,500 ÷ 55,000) × 100 = 10% increase.

Example 2 — Price drop: A phone falls from $999 to $799. Change = ((799 − 999) ÷ 999) × 100 = (−200 ÷ 999) × 100 = −20.02% (a 20% decrease).

Example 3 — Inflation: The price of a basket of goods rises from $350 to $385 in one year. Inflation rate = ((385 − 350) ÷ 350) × 100 = 10%.

Note: a 50% increase followed by a 50% decrease does NOT return to the original value. $100 × 1.5 = $150, then × 0.5 = $75. This asymmetry is why sequential percentage changes require multiplication, not addition.

Reverse Percentage (Finding the Original)

Reverse percentage answers "what was the original value before the change?" This comes up when you see a final price after a discount or tax and need to find the original.

After a percentage increase: Original = Final ÷ (1 + percentage/100)

After a percentage decrease: Original = Final ÷ (1 − percentage/100)

Example 1 — Finding pre-discount price: A pair of shoes costs $68 after a 15% discount. Original = $68 ÷ (1 − 0.15) = $68 ÷ 0.85 = $80.

Example 2 — Finding pre-tax price: A hotel bill totals $162.50 including 8.33% tax. Original = $162.50 ÷ 1.0833 = $150.

Example 3 — Finding original salary: After a 12% raise, your salary is $67,200. Original = $67,200 ÷ 1.12 = $60,000.

The most common mistake here is to subtract the percentage directly. For the shoe example, you might think "add 15% to $68" — but 15% of $68 is $10.20, giving $78.20, not $80. This is wrong because 15% was taken off the original price, not off the discounted price. Always divide by the percentage factor.

Cumulative Percentage Changes

When percentages change over multiple periods, you must multiply the factors, not add the percentages.

A product's price increases 10% in year 1, then 8% in year 2, then decreases 5% in year 3. Starting price $200:

• Year 1: $200 × 1.10 = $220
• Year 2: $220 × 1.08 = $237.60
• Year 3: $237.60 × 0.95 = $225.72

Total cumulative change: ($225.72 − $200) ÷ $200 × 100 = 12.86%. Note: this is NOT 10% + 8% − 5% = 13%. The multiplicative compounding creates a slight difference.

For investment returns, this compounding matters enormously over long periods. A 7% annual return over 30 years doesn't give 210% total — it gives 700%+ because each year's return compounds on all previous gains. This is the power of compound interest explored in our guide to loan amortization.

Real-World Applications

Shopping discounts: Use the "percentage of" formula. A $250 coat at 30% off: 0.30 × $250 = $75 discount, sale price $175. Stacked discounts? Multiply: 20% off, then an extra 10% off = $250 × 0.80 × 0.90 = $180 (not $175, which would be a flat 28% off).

Restaurant tips: 20% tip on $94 bill: $94 × 0.20 = $18.80. Mental trick: move decimal for 10% ($9.40), double for 20% ($18.80).

Exam grades: 53/65 questions correct = (53 ÷ 65) × 100 = 81.5%. What score do you need to get 90%? Part = (90/100) × 65 = 58.5 — round to 59 correct.

Pay raises: To understand whether a 5% raise keeps up with 4% inflation, compare them: real raise = ((1.05 ÷ 1.04) − 1) × 100 = 0.96% real increase in purchasing power.

Loan interest: A $15,000 car loan at 5.9% interest: annual interest ≈ $15,000 × 0.059 = $885 in year 1 (before principal reduction). Over the life of the loan, use the EMI formula for precise calculation.

Nutrition labels: A food item has 650 calories and 26g of fat. At 9 calories per gram of fat: fat calories = 26 × 9 = 234. Fat as % of total calories = (234 ÷ 650) × 100 = 36%.

Common Mistakes to Avoid

1. Adding percentages instead of multiplying: A 20% increase followed by a 20% decrease is NOT zero. $100 × 1.20 × 0.80 = $96 — a 4% net loss.

2. Confusing percentage and percentage points: If interest rates go from 2% to 3%, that's a 1 percentage point increase but a 50% percentage change. These are completely different and are often conflated in media.

3. Calculating reverse percentage wrong: "An item is 20% off and costs $80. Original price was $80 + 20% of $80 = $96." Wrong. The original is $80 ÷ 0.80 = $100.

4. Percentage of vs percentage from: "30% more than 50" = 50 × 1.30 = 65. "30% of 50" = 15. These mean different things.

5. Base confusion in year-over-year comparisons: If something grew 100% last year and shrinks 50% this year, it's back to the original — not a 50% net gain. Always track absolute values alongside percentages.