How to Calculate Percentages: Formulas, Shortcuts & Examples

Whether you are calculating a restaurant tip, figuring out a holiday retail discount, or analyzing quarterly corporate sales growth, understanding percentage math is one of the most useful life skills. Here are the three primary formulas broken down simply.

1. What Does "Percent" Really Mean?

The word percentage stems from the Latin per centum, meaning "by the hundred." A percentage is simply a fraction with a denominator of 100. For instance, 25% is mathematically identical to 25/100 or 0.25.

2. Formula 1: Finding X% of a Number

To find a percentage of any number, convert the percentage into a decimal (divide by 100) and multiply by the total amount:

Result = (Percentage ÷ 100) × Total Amount

Example: What is 18% tip on a \$75 dinner bill?
(18 ÷ 100) × 75 = 0.18 × 75 = \$13.50 tip.

3. Formula 2: Finding What Percent X is of Y

To determine what proportion a smaller number represents out of a whole:

Percentage = (Part ÷ Whole) × 100

Example: If you scored 42 points out of 50 on an exam:
(42 ÷ 50) × 100 = 0.84 × 100 = 84%.

4. Formula 3: Calculating Percentage Increase or Decrease

To measure how much a value changed relative to its starting baseline:

Percentage Change = [ (New Value - Old Value) ÷ Old Value ] × 100

• If the result is positive, it represents a percentage increase.
• If the result is negative, it represents a percentage decrease.

Example: A company's website traffic grew from 20,000 to 28,000 visitors:
[ (28,000 - 20,000) ÷ 20,000 ] × 100 = (8,000 ÷ 20,000) × 100 = +40% Increase.

5. Quick Mental Math Shortcuts

• To find 10%: Move the decimal point one place to the left (10% of \$84 is \$8.40).
• To find 5%: Find 10% and divide by 2 (5% of \$84 is \$4.20).
• To find 15%: Add your 10% and 5% calculations together (\$8.40 + \$4.20 = \$12.60).
• To find 20%: Find 10% and double it (\$8.40 × 2 = \$16.80).

6. Frequently Asked Questions