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. Versatile, accurate, and requires no signup.

Basic Percentage Calculation

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X is what % of Y?

Percentage Change

How to Use This Calculator

Using the Percentage Calculator is straightforward. Select the type of calculation you need using the tabs at the top:

  • What is X% of Y? Use this to find a specific percentage of a given number. Enter the percentage (X) and the total value (Y).
  • X is what % of Y? Use this to find what percentage one number (X) represents out of another number (Y).
  • Percentage Change: Use this to calculate the percentage increase or decrease from an original value to a new value.

Once you've selected the appropriate tab, enter the required numbers into the input fields. Click 'Calculate' to see the result instantly displayed below. Use the 'Reset' button to clear the fields for 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:

  • 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%.

Basic Percentage Calculations

The most common percentage calculations 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

  • 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.

Common Percentage Formulas

  • Percentage Formula: Part = (Percentage / 100) * Whole
  • Percentage of Formula: Percentage = (Part / Whole) * 100
  • Percentage Change Formula: % Change = [(New Value - Original Value) / |Original Value|] * 100

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 (FAQs)

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. The word "percentage" comes from the Latin "per centum," meaning "by the hundred."

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 (Increase): ((New Value - Original Value) ÷ Original Value) × 100. Formula (Decrease): ((Original Value - New 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.

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%.

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).

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 and allow comparison to guidelines.