Percentage Calculator
Use this free percentage calculator to solve various percentage problems. Calculate percentages, find what percent one number is of another, or find a number when a percentage of it is known.
How to Calculate Percentages
Finding a Percentage of a Number
To find a percentage of a number, you multiply the percentage (converted to a decimal) by the number.
This calculation is useful for finding discounts, tips, taxes, or any situation where you need to find a portion of a value based on a percentage.
Finding What Percentage One Number is of Another
To find what percentage one number is of another, divide the first number (part) by the second number (whole), then multiply by 100.
This calculation is useful for determining proportions, such as what percentage of a task is complete, what percentage of your budget you've spent, or what percentage of students passed a test.
Finding a Number When a Percentage of It is Known
To find the original number when you know a percentage of it, divide the known value by the percentage (converted to a decimal).
This calculation is useful for finding original prices before discounts, total populations from samples, or complete quantities when only a percentage is known.
Understanding Percentages
What is a Percentage?
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 express how large or small one quantity is relative to another quantity.
For example, if 25 out of 100 students passed a test, then 25% of the students passed. If the price of an item increases from $80 to $100, the percentage increase is 25%.
Real-World Applications of Percentages
Percentages are used in many real-world situations:
- Shopping: Discounts, sales tax, and tips are all calculated using percentages.
- Finance: Interest rates, investment returns, and inflation are expressed as percentages.
- Education: Test scores and grades are often given as percentages.
- Business: Profit margins, growth rates, and market share are measured in percentages.
- Statistics: Survey results, probabilities, and demographic data are frequently presented as percentages.
Common Percentage Mistakes to Avoid
When working with percentages, be careful to avoid these common mistakes:
- Adding percentages directly: If something increases by 10% and then by another 10%, the total increase is not 20%, but 21% (1.1 × 1.1 = 1.21).
- Confusing percentage points with percentages: If an interest rate increases from 5% to 7%, that's a 2 percentage point increase, but a 40% increase in the rate itself.
- Calculating percentage change incorrectly: Always use the original value as the denominator when calculating percentage change.
- Forgetting to convert percentages to decimals: When using percentages in calculations, remember to divide by 100 (or move the decimal point two places to the left).
Frequently Asked Questions
How do I calculate a 15% tip on a restaurant bill?
To calculate a 15% tip on a restaurant bill, multiply the bill amount by 0.15. For example, if your bill is $50, the tip would be $50 × 0.15 = $7.50. Alternatively, you can use our percentage calculator: enter 15 as the percentage and 50 as the number, and the result will be $7.50.
How do I calculate a discount from an original price?
To calculate a discounted price, multiply the original price by (1 - discount percentage/100). For example, if an item costs $80 and is discounted by 25%, the sale price would be $80 × (1 - 25/100) = $80 × 0.75 = $60. You can also use our percentage calculator: enter 25 as the percentage and 80 as the number, and subtract the result ($20) from the original price.
How do I calculate my test score as a percentage?
To calculate a test score as a percentage, divide the number of points you earned by the total possible points, then multiply by 100. For example, if you got 42 points out of 50 possible points, your percentage score would be (42/50) × 100 = 84%. You can use our "What % is Number of Number" calculator: enter 42 as the part value and 50 as the whole value.
How do I find the original price before a percentage increase?
To find the original price before a percentage increase, divide the new price by (1 + percentage increase/100). For example, if the current price is $100 after a 25% increase, the original price would be $100 ÷ (1 + 25/100) = $100 ÷ 1.25 = $80. You can use our "Number is % of What" calculator: enter 100 as the result value and 125 as the percentage (100% + 25%).
Can percentages be greater than 100%?
Yes, percentages can be greater than 100%. A percentage greater than 100% means that the value being described is greater than the reference value. For example, if a company's profits increase from $100,000 to $250,000, that's a 150% increase. Similarly, if you scored 120 points on a test with a maximum possible score of 100 points (due to bonus questions), your percentage score would be 120%.