What is a Percentage?
A percentage is a ratio expressed as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." When we say 25%, we mean 25 per 100, or equivalently 0.25 as a decimal or 1/4 as a fraction.
Percentages are used to express proportions, rates, and changes in a standardized way that makes comparisons easy regardless of the original quantities involved. Whether you are comparing test scores of 42/56 and 68/80, or comparing a 3% sales tax in one state with a 7% tax in another, percentages normalize the values for direct comparison.
The three fundamental percentage calculations that our calculator handles are: finding what percentage of a number equals (e.g., "What is 15% of 200?"), finding what percentage one number is of another (e.g., "30 is what percent of 150?"), and finding percentage change between two values (e.g., "What is the percentage increase from 80 to 100?").
Percentage Formulas
The three percentage calculations each use a simple formula:
Type 1: Result = (X ÷ 100) × Y
Type 2: Percentage = (X ÷ Y) × 100
Type 3: Change = [(New − Old) ÷ Old] × 100
Real-World Percentage Applications
Understanding percentages is a foundational financial literacy skill. Here are the most common everyday applications:
Shopping and Discounts: A jacket priced at $120 with a 30% discount costs $120 × (1 - 0.30) = $84. Knowing how to quickly calculate discounts helps you evaluate whether a "sale" represents genuine savings.
Restaurant Tips: A 20% tip on a $65 bill is $65 × 0.20 = $13. A quick mental shortcut: 10% of any number is just the number divided by 10. 20% is double that. 15% is 10% plus half of 10%.
Interest Rates: Credit cards often charge 22-28% APR. Understanding that a $5,000 balance at 22% costs you $1,100 per year just in interest helps motivate paying it off.
Exam Scores: Convert raw scores to percentages for easy comparison: 42 correct out of 56 = (42÷56)×100 = 75%. This immediately tells you where you stand relative to a passing threshold.
Tax Calculations: Adding 8.5% sales tax to a $250 purchase: $250 × 1.085 = $271.25. Our GST/tax calculator handles this automatically.
Percentage Increase vs Percentage Points
This distinction causes significant confusion in finance, politics and everyday life:
If your salary increases from $50,000 to $55,000, that is a 10% increase ($5,000 is 10% of $50,000).
If a tax rate increases from 20% to 25%, that is a 5 percentage point increase. As a percentage increase, the tax rate went up by 25% (5 is 25% of 20). These are very different — always clarify which is meant when reading about rate changes.
When someone says "our market share grew from 20% to 25%," they might mean it grew by 5 percentage points. But the percentage growth in market share was actually 25% (from 20 to 25 is a 25% increase). Context is everything.