Percentage Calculator
Calculate percentages, find values based on percentages, or determine percentage changes between values. Perfect for discounts, tips, taxes, or analyzing statistical changes.
How could this calculator be better?
We're always looking to improve our tools. Here are some ideas we're considering:
- Add more percentage calculation types
- Include visual representations of percentages
- Add percentage distribution calculations
- Include common percentage shortcuts (10%, 25%, etc.)
- Add percentage comparison between multiple values
Email us at yoursmartcalculator@gmail.com with your suggestions!
Related Calculators
Quick Facts
- •The word "percent" comes from the Latin "per centum," meaning "by the hundred"
- •The percentage symbol % evolved from the Italian abbreviation "per cento"
- •A 100% increase means the value has doubled
- •A 50% decrease means the value has been halved
Understanding Percentage Calculations
What is a Percentage?
A percentage is a way to express a number as a fraction of 100. It is often denoted using the percent sign, %. For example, 45% represents 45 out of 100, or 45/100, or 0.45 as a decimal.
Percentages are used in everyday life for various purposes, including calculating discounts, tips, taxes, interest rates, and statistical data.
Basic Percentage Formulas
This calculator supports three common percentage calculations:
Finding what percentage X is of Y:
Formula: (X ÷ Y) × 100 = Percentage
Example: What percentage is 50 of 200? (50 ÷ 200) × 100 = 25%
Finding the value of X% of Y:
Formula: (X ÷ 100) × Y = Value
Example: What is 25% of 200? (25 ÷ 100) × 200 = 50
Finding the percentage change from X to Y:
Formula: ((Y - X) ÷ X) × 100 = Percentage Change
Example: What is the percentage change from 100 to 125? ((125 - 100) ÷ 100) × 100 = 25% increase
Common Percentage Applications
Percentages are used in many real-world scenarios:
- Discounts: A 20% discount on a $100 item means you save $20 and pay $80
- Tips: A 15% tip on a $50 meal means you leave $7.50 extra
- Taxes: A 7% sales tax on a $200 purchase means you pay an additional $14
- Interest: A 5% annual interest rate on a $1,000 loan means you pay $50 in interest per year
- Growth: A company that grows from 100 to 150 employees has experienced a 50% increase
Percentage Increase vs. Decrease
When calculating percentage change, the result can be positive (indicating an increase) or negative (indicating a decrease).
For example, if a value changes from 100 to 80, the percentage change is ((80 - 100) ÷ 100) × 100 = -20%, indicating a 20% decrease. Conversely, if a value changes from 100 to 120, the percentage change is ((120 - 100) ÷ 100) × 100 = 20%, indicating a 20% increase.
Frequently Asked Questions
How do I calculate a discount?
To calculate a discount, use the "X% of Y is what?" calculation type. Enter the discount percentage as X and the original price as Y. The result will be the discount amount. To find the final price, subtract this amount from the original price.
How do I calculate a percentage increase?
Use the "% change from X to Y" calculation type. Enter the original value as X and the new value as Y. If the result is positive, it's a percentage increase. If it's negative, it's a percentage decrease.
What's the difference between percentage points and percentages?
Percentage points refer to the arithmetic difference between two percentages, while percentage change refers to the relative change. For example, if a value increases from 40% to 50%, that's a 10 percentage point increase, but a 25% relative increase (because 10 is 25% of 40).
How do I calculate a tip?
To calculate a tip, use the "X% of Y is what?" calculation type. Enter the tip percentage (e.g., 15%) as X and the bill amount as Y. The result will be the tip amount. To find the total bill with tip, add this amount to the original bill.
Can percentages be greater than 100%?
Yes, percentages can exceed 100%. A percentage greater than 100% indicates that a value is more than the reference value. For example, 150% of 100 is 150, and a change from 100 to 250 represents a 150% increase.