Percentage Calculator
Calculate percentages, percentage increase/decrease, and percentage of a number with our free percentage calculator.
What is X% of Y?
X is what percent of Y?
Percentage Change
Add/Subtract Percentage
Understanding Percentages: Theory, Usage, and History
What Are Percentages?
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used to compare proportions and express ratios in a standardized way.
Basic Formula: Percentage = (Part / Whole) × 100
Common Percentage Calculations
Finding X% of Y
Formula: (X/100) × Y
Example: 25% of 200 = (25/100) × 200 = 50
Finding What % X is of Y
Formula: (X/Y) × 100
Example: 50 is what % of 200? = (50/200) × 100 = 25%
Percentage Change
Formula: ((New - Old)/Old) × 100
Example: 100 to 120 = ((120-100)/100) × 100 = 20%
Adding/Subtracting %
Formula: X ± (X × P/100)
Example: 100 + 15% = 100 + (100 × 15/100) = 115
How to Use This Calculator
- What is X% of Y: Enter the percentage and the number to find the result
- X is what % of Y: Enter a number and total to find what percentage it represents
- Percentage Change: Enter original and new values to calculate the change
- Add/Subtract %: Enter a base number and percentage to add or subtract
Tip: All calculations update automatically as you type. No need to click a calculate button!
History of Percentages
The concept of percentages has ancient roots. Roman emperors used a form of percentage to calculate taxes, often expressed as a fraction of 100. The modern percentage symbol (%) evolved from a shorthand notation used by Italian merchants in the 15th century.
The symbol "%" is believed to have originated from the Italian "per cento" (per hundred), which was abbreviated as "pc" and eventually stylized into the symbol we use today. The first recorded use of the % symbol appeared in an anonymous Italian manuscript from 1425.
Percentages became widely adopted in commerce, science, and statistics during the Renaissance period as trade and banking expanded across Europe. Today, percentages are fundamental to fields ranging from finance and economics to science and everyday calculations.
Real-World Applications
Finance
- • Interest rates
- • Investment returns
- • Loan calculations
- • Tax calculations
Business
- • Sales discounts
- • Profit margins
- • Market share
- • Growth rates
Science
- • Concentration levels
- • Error margins
- • Statistical analysis
- • Probability
Common Percentage Mistakes
- Confusing percentage points with percentages (e.g., 5% to 10% is a 5 percentage point increase, but a 100% relative increase)
- Not considering the base when calculating percentage changes
- Mixing up "percent of" vs "percent more than"
- Forgetting to convert decimals to percentages (0.25 = 25%)
- Adding percentages incorrectly (50% + 50% ≠ 100% in many contexts)
Related Calculators
Quick Tips
- • Remember: 100% = 1.0 as a decimal
- • Use percentage change for comparing growth
- • Be careful with percentage points vs percentages
- • Double-check your base value in calculations