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How to Calculate a Percentage

Percentage problems come in three main types:

  1. What is X% of Y? (e.g., what's 25% of 80?)
  2. X is what percent of Y? (e.g., 20 is what percent of 80?)
  3. What's the percentage change from X to Y? (e.g., 80 → 100, what percent increase?)

This guide walks through all three with worked examples, mental math shortcuts, and the formulas behind them. To skip the math, use our percentage calculator or percentage increase calculator.

7 min read

What does 'percent' mean?

The word 'percent' comes from Latin 'per centum' meaning 'per hundred.' A percentage is a fraction with 100 as the denominator.

25% means 25 out of 100 — or 25/100 — or 0.25 as a decimal.

To convert between forms:

  • Decimal to percentage: multiply by 100 (0.25 → 25%)
  • Percentage to decimal: divide by 100 (25% → 0.25)
  • Fraction to percentage: divide numerator by denominator, multiply by 100 (3/4 → 0.75 → 75%)

Most percentage formulas require converting the percent to a decimal first. Forgetting this conversion is one of the most common percentage calculation mistakes.

Type 1: What is X% of Y?

FORMULA: (X / 100) × Y

Or equivalently: X% as decimal × Y

WORKED EXAMPLE: What is 25% of 80?

  • Step 1: Convert percent to decimal: 25 / 100 = 0.25
  • Step 2: Multiply by Y: 0.25 × 80 = 20

Answer: 25% of 80 is 20.

This is the type of percentage used for:

  • Tips at restaurants (15% of the bill)
  • Sales discounts (30% off original price)
  • Sales tax (8% of purchase)
  • Commission (5% of sale)
  • Most everyday percentage problems

Type 2: X is what percent of Y?

FORMULA: (X / Y) × 100

WORKED EXAMPLE: 20 is what percent of 80?

  • Step 1: Divide X by Y: 20 / 80 = 0.25
  • Step 2: Multiply by 100: 0.25 × 100 = 25

Answer: 20 is 25% of 80.

This is the type of percentage used for:

  • Test scores (got 18 out of 20 = what percent?)
  • Survey results (32 out of 50 people = what percent?)
  • Probability calculations
  • Statistical analysis
  • Comparing parts to wholes

Type 3: Percentage change

FORMULA: ((New value − Old value) / Old value) × 100

WORKED EXAMPLE 1: Stock went from $50 to $75. What's the percentage increase?

  • Step 1: Subtract old from new: 75 − 50 = 25
  • Step 2: Divide by OLD value: 25 / 50 = 0.50
  • Step 3: Multiply by 100: 0.50 × 100 = 50%

Answer: 50% increase.

WORKED EXAMPLE 2: Price dropped from $80 to $60. What's the percentage decrease?

  • Step 1: Subtract: 60 − 80 = −20 (negative means decrease)
  • Step 2: Divide by OLD value: −20 / 80 = −0.25
  • Step 3: Multiply by 100: −25%

Answer: 25% decrease.

CRITICAL: Always divide by the ORIGINAL value, not the new one. A 50% increase from 50 to 75 is NOT the same as a 50% decrease from 75 to 50.

  • 50 → 75: 50% increase (25/50)
  • 75 → 50: 33.3% decrease (25/75)

The two percentages aren't inverses because the base changes.

Mental math shortcuts

You can do most everyday percentage calculations in your head with these tricks:

10% TRICK: Move the decimal one place left.
  • 10% of 80 = 8
  • 10% of 240 = 24
  • 10% of $35.50 = $3.55
5% TRICK: Half of 10%.
  • 5% of 80 = 4
  • 5% of 240 = 12
1% TRICK: Move the decimal two places left.
  • 1% of 80 = 0.80
  • 1% of 240 = 2.40
20% TRICK (common tip): Double 10%.
  • 20% of $45 = $9
  • 20% of $87 = $17.40
15% TRICK (also common tip): 10% + 5% (half of 10%).
  • 15% of $40 = $4 + $2 = $6
  • 15% of $60 = $6 + $3 = $9
25% TRICK: Divide by 4.
  • 25% of 80 = 20
  • 25% of 240 = 60
50% TRICK: Divide by 2.
  • 50% of anything is half

Common percentage mistakes

Six errors that throw off percentage calculations:

  1. FORGETTING TO DIVIDE BY 100. The percent symbol is shorthand for division by 100. 25% means 0.25, not 25. If your answer is 100× too large, you forgot this step.
  2. DIVIDING BY THE NEW VALUE INSTEAD OF THE OLD VALUE in percentage change calculations. Always use the ORIGINAL value as the base.
  3. ADDING PERCENTAGES THAT SHOULDN'T BE ADDED. A 10% increase followed by a 10% decrease does NOT return to the original. $100 + 10% = $110, then $110 − 10% = $99. Multiplicative changes don't add linearly.
  4. CONFUSING 'X% OF Y' WITH 'X IS Y% OF WHAT'. These are different questions with different formulas.
  5. CONFUSING PERCENTAGE POINTS WITH PERCENTAGES. If interest rates rise from 5% to 7%, that's a 2 percentage POINT increase but a 40% PERCENTAGE increase (2/5 × 100). Financial news often confuses these.
  6. ROUNDING TOO EARLY. When chaining percentage calculations, keep extra decimal places until the final answer. Rounding intermediate steps to whole numbers introduces compounding errors.

Real-world examples

  • TIP CALCULATION: Restaurant bill is $42. You want to leave a 20% tip.
    20% of 42 = 0.20 × 42 = $8.40 tip. Total: $50.40.
  • DISCOUNT CALCULATION: $80 shirt on sale for 30% off.
    30% off 80 = 80 × 0.30 = $24 off. Sale price: $80 − $24 = $56.
    Or equivalently: 80 × (1 − 0.30) = 80 × 0.70 = $56.
  • SALES TAX: $50 purchase with 8% sales tax.
    Tax: 50 × 0.08 = $4. Total: $54.
    Or: 50 × 1.08 = $54.
  • GRADE CALCULATION: Scored 38 out of 50 on a quiz.
    Percentage: (38 / 50) × 100 = 76%.
  • PAY RAISE: Salary going from $52,000 to $58,000.
    Increase: (58,000 − 52,000) / 52,000 × 100 = 11.5% raise.
  • STOCK RETURN: Bought stock at $100, now worth $145.
    Return: (145 − 100) / 100 × 100 = 45% return.
  • POPULATION GROWTH: City was 100,000, now 125,000.
    Growth: (125,000 − 100,000) / 100,000 × 100 = 25% growth.

Use our calculators

For automatic percentage calculations:

For specific everyday uses: Tip Calculator (restaurant tips), Discount Calculator (sales discounts), Sales Tax Calculator (tax math), Markup Calculator (business pricing).