Percentage Calculator

Our free percentage calculator simplifies finding percentages, calculating increases/decreases, discounts, and more. Understand percentages in finance, academics, and daily life with step-by-step solutions. Whether you're calculating tips, discounts, grade percentages, or financial returns, this versatile tool provides accurate results instantly with no signup required.

Calculate Your Percentage

Basic Percentage Calculation

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X is what % of Y?

Percentage Change

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Percentage Increase Calculator Percentage Decrease Calculator Percentage Change Calculator Fraction Calculator

How to Use This Calculator

  1. Select the Calculation Type: Choose from the three tabs at the top based on what you need to calculate - finding a percentage of a number, determining what percentage one number is of another, or calculating percentage change.
  2. Enter Your Values: Input the required numbers into the appropriate fields. All fields accept both whole numbers and decimals for precise calculations.
  3. Click Calculate: Press the 'Calculate' button to see your result instantly displayed below with a clear explanation of the calculation.
  4. Reset if Needed: Use the 'Reset' button to clear all fields and start a new calculation.

Understanding Percentages

A percentage is essentially a fraction where the denominator is 100. The word "percent" comes from the Latin "per centum," meaning "per hundred." It's a way to express a part of a whole in a standardized manner, making comparisons and understanding proportions easier. For example, 25% means 25 out of every 100 parts.

Converting Between Percentages, Decimals, and Fractions

Understanding how to convert between these forms is crucial for mathematical calculations:

  • Percentage to Decimal: Divide the percentage by 100 (or move the decimal point two places to the left). Example: 50% = 50 / 100 = 0.50.
  • Decimal to Percentage: Multiply the decimal by 100 (or move the decimal point two places to the right) and add the '%' sign. Example: 0.75 = 0.75 × 100 = 75%.
  • Percentage to Fraction: Write the percentage as a fraction with a denominator of 100, then simplify. Example: 40% = 40/100 = 2/5.
  • Fraction to Percentage: Convert the fraction to a decimal (divide the numerator by the denominator), then convert the decimal to a percentage. Example: 3/4 = 0.75 = 75%.

Common Percentage Calculations

Basic Percentage Formulas

The most common percentage calculations you'll encounter include:

  1. Finding a percentage of a number: (Percentage / 100) × Total Number. Example: What is 20% of 150? (20 / 100) × 150 = 0.20 × 150 = 30.
  2. Finding what percentage one number is of another: (Part / Whole) × 100. Example: What percentage is 45 of 180? (45 / 180) × 100 = 0.25 × 100 = 25%.

Calculating Percentage Increase and Decrease

Percentage change measures the relative difference between two values. It's widely used in finance, statistics, and everyday comparisons.

  • Formula: Percentage Change = [(New Value - Original Value) / Original Value] × 100
  • Increase Example: Price increased from $50 to $60. Percentage Increase = [($60 - $50) / $50] × 100 = ($10 / $50) × 100 = 0.20 × 100 = 20% increase.
  • Decrease Example: Score decreased from 80 to 68. Percentage Decrease = [(68 - 80) / 80] × 100 = (-12 / 80) × 100 = -0.15 × 100 = -15% (or a 15% decrease).

Real-World Applications of Percentages

Percentages are used extensively in everyday life and professional settings:

  • Discounts and Sales: Calculating how much you save (e.g., 30% off a $200 item means a $60 discount).
  • Taxes: Calculating sales tax or income tax based on percentage rates.
  • Tips: Calculating gratuity at restaurants (e.g., 15-20% of the bill).
  • Interest Rates: Understanding loan interest (APR) or investment returns (APY).
  • Statistics: Representing data proportions (e.g., 65% of respondents agreed).
  • Nutrition: Reading food labels (% Daily Value).
  • Academic Grades: Calculating scores as percentages.
  • Business Metrics: Profit margins, growth rates, and market share.

Tips for Accurate Calculations

  • Double-check inputs: Ensure you're entering the correct numbers in the right fields.
  • Understand the question: Are you finding a percentage of a number, or what percentage one number is of another?
  • Use the correct base for percentage change: Always divide by the original value.
  • Convert percentages to decimals correctly: Remember 5% is 0.05, not 0.5.
  • Be mindful of rounding: Round only at the final step if necessary.

Frequently Asked Questions (FAQ)

FAQ Index

A percentage is a number expressed as a fraction of 100, used to express a proportion or rate. The symbol % is used to indicate a percentage. For example, 50% means 50 out of 100, or half of the total. Percentages provide a standardized way to compare proportions and make calculations easier to understand and communicate.

To calculate what percent one number is of another, divide the first number (the part) by the second number (the whole), then multiply by 100. The formula is: Percentage = (Part ÷ Whole) × 100. For example, to find what percent 15 is of 60: (15 ÷ 60) × 100 = 0.25 × 100 = 25%.

To calculate a percentage increase or decrease: 1. Find the difference between the new value and the original value. 2. Divide this difference by the original value. 3. Multiply by 100. Formula: ((New Value - Original Value) ÷ Original Value) × 100. Example (Increase $80 to $100): ((100 - 80) ÷ 80) × 100 = 25%.

A percentage point is the arithmetic difference between two percentages (e.g., 7% - 5% = 2 percentage points). A percentage change is the relative change (e.g., increasing from 5% to 7% is a 40% increase). Percentage points are used for rates/proportions, percentage changes for relative differences.

Divide the percentage by 100 or move the decimal point two places to the left. Example: 75% = 75 ÷ 100 = 0.75. This conversion is essential for many mathematical calculations involving percentages.

Multiply the decimal by 100 or move the decimal point two places to the right and add the % symbol. Example: 0.35 = 0.35 × 100 = 35%. This is useful when converting probability or proportion values to percentages.

Calculate the discount amount (Original Price × Discount Percentage ÷ 100) and subtract it from the original price. Alternatively: Sale Price = Original Price × (1 - Discount Percentage ÷ 100). Example (25% off $80): $80 × (1 - 25 ÷ 100) = $60.

Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100. This works for both increases (positive result) and decreases (negative result). Always use the original value as the denominator for accurate results.

Multiply the bill amount by the tip percentage (as a decimal). Tip Amount = Bill Amount × (Tip Percentage ÷ 100). Total Bill = Bill Amount + Tip Amount. Example ($60 bill, 20% tip): Tip = $60 × 0.20 = $12. Total = $72.

Percentages help structure budgets like the 50/30/20 rule (50% needs, 30% wants, 20% savings/debt) or zero-based budgeting (allocating 100% of income). They scale with income changes and allow comparison to financial guidelines and benchmarks.