Percentage Calculator

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum" which means "out of one hundred." The symbol % is used to denote percentage.

Percentages are a universal language in mathematics, finance, statistics, and everyday life. They allow us to easily compare proportions and understand relationships between numbers in an intuitive way.

Why are percentages useful?

Percentages are essential for:

• Discounts and sales - "50% off" is easier to understand than "save $25 on $50"
• Academic grades - Standardized scoring across different tests
• Finance - Interest rates, investment returns, tax calculations
• Statistics - Survey results, demographic data, growth rates
• Comparisons - Easier to compare "20% growth" than absolute numbers

Our calculator handles the three main percentage scenarios:

Type 1: What is X% of Y?

Question: "What is 15% of 200?"

Formula: (Percentage ÷ 100) × Total

Calculation:

• 15% of 200 = (15 ÷ 100) × 200
• = 0.15 × 200
• = 30

Real example: A sweater costs $200 and has a 15% discount. How much do you save?

• Savings = 15% of $200 = $30
• Final price = $200 - $30 = $170

Type 2: X is what percent of Y?

Question: "25 is what percent of 200?"

Formula: (Part ÷ Total) × 100

Calculation:

• 25 is what % of 200 = (25 ÷ 200) × 100
• = 0.125 × 100
• = 12.5%

Real example: You scored 85 out of 100 on an exam. What's your percentage?

• Score = (85 ÷ 100) × 100 = 85%

Type 3: X is Y% of what number?

Question: "30 is 15% of what number?"

Formula: (Part ÷ Percentage) × 100

Calculation:

• 30 is 15% of X
• X = (30 ÷ 15) × 100
• X = 2 × 100
• X = 200

Real example: You saved $30, which is 15% of the original price. What was the original price?

• Original price = (30 ÷ 15) × 100 = $200

Situation: It's Black Friday and you're shopping for a laptop. The original price is $800, and there's a 35% discount. After the discount, you have a coupon for an additional 10% off. How much will you pay in total?

Solution step by step:

1. First discount (35% off $800):

   • Discount amount = 35% of $800
   • = (35 ÷ 100) × 800
   • = 0.35 × 800 = $280
   • Price after first discount = $800 - $280 = $520

2. Second discount (10% off $520):

   • Additional discount = 10% of $520
   • = (10 ÷ 100) × 520
   • = 0.10 × 520 = $52
   • Final price = $520 - $52 = $468

Result: You'll pay $468, saving $332 (41.5% total savings)

Important note: Notice that 35% + 10% ≠ 45% total discount! Sequential discounts multiply, they don't add. The total savings is 41.5%, not 45%.

✅ Understand the context: Is it % OF something or % increase/decrease? They're different calculations.

✅ Check if discounts stack: In retail, not all discounts can be combined. Read the fine print.

✅ Percentage change formula: For increases/decreases, use: ((New - Old) ÷ Old) × 100

✅ Mental math trick: For 10%, move decimal one place left. For 5%, halve the 10% result.

• Example: 10% of 230 = 23, so 5% = 11.5

✅ Verify your answer: Does it make sense? 50% of 100 should be 50, not 200.

✅ Use parentheses: In complex calculations, use parentheses to avoid order-of-operation errors.

What's the difference between percentage and percentile?

Percentage expresses a proportion out of 100. Percentile indicates where a value ranks in a dataset. For example, scoring in the 90th percentile means you scored higher than 90% of test-takers, not that you scored 90%.

How do I calculate percentage increase or decrease?

Formula: ((New Value - Old Value) ÷ Old Value) × 100

• Positive result = increase
• Negative result = decrease Example: Price goes from $50 to $65: ((65-50)÷50)×100 = 30% increase

Why can't I just add sequential percentages?

Percentages are relative to their base. A 20% decrease followed by a 20% increase doesn't return you to the original. Example: $100 → 20% decrease = $80 → 20% increase = $96 (not $100!).

How do I convert a fraction to a percentage?

Divide the numerator by the denominator, then multiply by 100. Example: 3/4 = 0.75 → 0.75 × 100 = 75%.

What does "per capita" mean in percentage context?

"Per capita" means "per person." It's often used with percentages to show proportions relative to population. Example: "GDP per capita grew by 3%" means the economic output per person increased by 3%.

How do I calculate compound percentages?

Multiply the factors. Example: Two consecutive 10% increases: 1.10 × 1.10 = 1.21, which is a 21% total increase (not 20%).