Percentage Calculator

Understanding Percentage Calculations

Percentages are a fundamental mathematical concept used in almost every aspect of daily life, from calculating tips at a restaurant to analyzing corporate financial growth. The term "percent" simply means "per hundred." A percentage is a number or ratio expressed as a fraction of 100. Our calculator suite simplifies the three most common ways people interact with percentages.

1. Finding the Percentage of a Number

This is the most straightforward calculation. It answers the question: "What is X% of Y?"

Formula: (X / 100) × Y = Result

Example: What is 20% of 150?

• Convert the percentage to a decimal: 20 / 100 = 0.20
• Multiply the decimal by the whole number: 0.20 × 150 = 30
• So, 20% of 150 is 30.

This formula is what you use when calculating sales tax, a tip, or a discount on an item.

2. Finding What Percentage One Number is of Another

This calculation determines the proportional relationship between two numbers. It answers the question: "X is what percent of Y?"

Formula: (X / Y) × 100 = Percentage Result

Example: 30 is what percent of 150?

• Divide the part by the whole: 30 / 150 = 0.20
• Convert the decimal to a percentage: 0.20 × 100 = 20%
• So, 30 is 20% of 150.

This formula is frequently used in academia to calculate unweighted grades on a test. If you're looking for more complex academic grading tools involving weights and target finals, check out our Grade Calculator.

3. Calculating Percentage Change (Growth or Decrease)

Percentage change is used to track how a value shifts over time. This is critical in business (revenue growth), finance (stock returns), and statistics (population shifts). It answers the question: "What is the percentage increase or decrease from an old value to a new value?"

Formula: ((New Value - Old Value) / |Old Value|) × 100 = Percentage Change

Example of Growth: Your website traffic went from 1,000 visitors last month to 1,250 visitors this month. What is the growth rate?

• Find the difference: 1,250 - 1,000 = +250
• Divide by the old value: 250 / 1,000 = 0.25
• Convert to a percentage: 0.25 × 100 = 25% Increase

Example of Decrease: The price of a laptop dropped from $1,000 to $800. What is the percentage decrease?

• Find the difference: 800 - 1,000 = -200
• Divide by the old value: -200 / 1,000 = -0.20
• Convert to a percentage: -0.20 × 100 = -20% (A 20% Decrease)

Percentage Change vs. Percentage Difference

It's important to distinguish between percentage change and percentage difference. Percentage change always involves an old value and a new value—there is chronological directionality. You are comparing how a specific metric moved from Point A in time to Point B.

Percentage difference is used when comparing two values that are not necessarily linked by time, and you want to know how different they are relative to their average. For example, comparing the heights of two different buildings. The formula for percentage difference is (|Value A - Value B| / ((Value A + Value B) / 2)) × 100. Our calculator above specifically handles Percentage Change.

Common Pitfalls to Avoid

• Adding percentages incorrectly: A 10% increase followed by a 10% decrease does not bring you back to the original number. If you start with $100, add 10% ($110), and then take 10% off $110, you are left with $99.
• Using the wrong base for percentage change: Always divide the difference by the original (old) value, never the new value.
• Confusing percentage points with percentage increase: If an interest rate goes from 5% to 6%, it increased by 1 percentage point. However, the percentage increase is actually 20% (because 1 is 20% of 5).