Percentage Calculator
Calculate percentages, percentage change, and what percent a number is of another.
Percentages are the universal language of comparison, used in everything from shopping discounts to tax rates. Our Percentage Calculator is a versatile tool that handles three common scenarios: finding a percentage of a number, determining what percentage one number is of another, and calculating the percentage change (increase or decrease) between two values. Master the math behind the sales and statistics with ease.
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Frequently Asked Questions
Mastering Percentages: A Complete Guide
What is a Percentage?
The word "percentage" comes from the Latin per centum, meaning "by the hundred." It is a dimensionless number used to express a fraction with a denominator of 100. For example, 50% is simply another way of saying 50/100, or 0.5. Providing a standardized way to compare quantities, percentages are essential for everything from shopping discounts to scientific research.
Common Percentage Formulas
Our calculator handles the three most common tasks:
Formula: (Percentage / 100) × Value
Ex: 20% of 50 = 0.2 × 50 = 10
Formula: (Part / Total) × 100
Ex: 5 is what % of 20? = (5/20) × 100 = 25%
Formula: [(New - Old) / Old] × 100
Ex: Price went from $40 to $50 = (10/40) × 100 = 25% Increase
Real-World Examples
- Tipping: Standard tips range from 15% to 20%. For a $60 bill, a 20% tip is $12.
- Discounts: A "30% off" sale means you pay 70% of the original price. If a jacket is $100, you pay $70.
- Test Scores: If you got 45 questions right out of 50, your percentage score is (45/50) × 100 = 90%.
Common Mistakes
- Percent vs. Percentage Points: If a tax rate increases from 10% to 15%, it rose by 5 percentage points, but the relative increase is actually 50%.
- Reversing the Base: "X is 50% larger than Y" does not mean "Y is 50% smaller than X." If X=150 and Y=100, X is 50% larger. But Y is only 33.3% smaller than X.
Frequently Asked Questions (FAQs)
How do I calculate a percentage increase?
Subtract the old number from the new number, divide by the old number, and multiply by 100. If the result is positive, it's an increase; if negative, it's a decrease.
Can percentages be over 100%?
Yes. If something doubles in size, it has increased by 100%. If it triples, it increased by 200%. However, you typically cannot have more than 100% of a finite resource (like eating 110% of a pizza).
What is per mille?
Per mille (‰) means "per thousand." It is similar to percent (per hundred) but deals with smaller fractions, often used in chemistry or legal limits.