Percentage Calculator Formula

Understand the math behind the percentage calculator. Each variable explained with a worked example.

Use the Percentage Calculator

Formulas Used

Result

result = value * percentage / 100

Remaining

remaining = value - value * percentage / 100

Variables

VariableDescriptionDefault
valueNumber200
percentagePercentage(%)15

How It Works

How Percentage Calculations Work

A percentage is a number out of 100. When someone says "20% of 500," they mean 20 out of every 100 units, applied to 500. Multiply 500 by 20, divide by 100, and you get 100. That's the core of every percentage calculation.

The Three Types of Percentage Problems

Finding a percentage of a number: X% of Y = (X * Y) / 100. Example: 15% of 80 = 12.

Finding what percentage one number is of another: (Part / Whole) * 100. Example: 25 is what percent of 200? Answer: (25/200) * 100 = 12.5%.

Finding the whole when you know a part and percentage: Whole = Part / (Percentage / 100). Example: 30 is 20% of what? Answer: 30 / 0.20 = 150.

When You'd Use This

Tipping at a restaurant, calculating a sale discount, figuring out tax on a purchase, checking what share of your income goes to rent, grading tests, or splitting a bill. Percentages show up constantly in finance, shopping, cooking, and school.

Where People Go Wrong

  • Confusing percentage increase with percentage of. A 20% increase on 100 gives you 120 (not 20). The increase is 20, but the result is 120.
  • Percentage decrease traps. If something goes up 50% and then down 50%, you don't end up where you started. $100 up 50% is $150. $150 down 50% is $75. You lost $25.
  • Stacking percentages incorrectly. A 10% discount plus a 20% discount is not a 30% discount. It's 10% off, then 20% off the reduced price, which equals a 28% total discount.

    • Worked Example

    What is 15% of 200?

    value = 200percentage = 15
    1. 0115% of 200 = 200 × 15/100
    2. 02= 200 × 0.15
    3. 03= 30

    When to Use This Formula

    • Calculating a tip at a restaurant by finding what 15%, 18%, or 20% of the bill comes to.
    • Determining the sale price of an item after a percentage discount, or figuring out what percentage off a marked-down price represents.
    • Converting test scores or survey results into percentages for easy comparison across different total-point scales.
    • Calculating tax amounts on purchases, income, or invoices where the tax rate is given as a percentage.
    • Finding what fraction of a budget a specific expense represents, to identify where most of the money is going.
    • Splitting costs proportionally among people who owe different shares of a total bill.

    Common Mistakes to Avoid

    • Dividing the whole by the part instead of the part by the whole — "what percent is 25 of 200" is 25/200 = 12.5%, not 200/25 = 800%.
    • Confusing "percent of" with "percent off" — 20% of $50 is $10, but 20% off $50 means you pay $40, not $10.
    • Applying successive percentages by adding them — a 20% discount followed by an additional 10% discount is not 30% off; it is 20% off first, then 10% off the reduced price, yielding 28% total.
    • Forgetting to move the decimal point when converting between percentages and decimals — 5% is 0.05, not 0.5, and this factor-of-ten error cascades through every calculation.

    Frequently Asked Questions

    How do I calculate a percentage?

    Multiply the number by the percentage divided by 100. For example, 25% of 80 = 80 × 0.25 = 20.

    How do I find what percent one number is of another?

    Divide the part by the whole, then multiply by 100. For example, 30 is what percent of 200? Answer: (30/200) × 100 = 15%.

    How do I calculate percentage change?

    Percentage change = ((New Value - Old Value) / Old Value) × 100. A positive result means an increase; a negative result means a decrease. For example, a price that goes from $40 to $50 is a 25% increase: ((50-40)/40) × 100 = 25%.

    What is the difference between percentage and percentage points?

    A percentage is a ratio expressed out of 100. Percentage points measure the arithmetic difference between two percentages. If an interest rate goes from 3% to 5%, it increased by 2 percentage points, but the percentage increase is (5-3)/3 × 100 = 66.7%.

    Learn More

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