How to Use This Percentage Calculator
Our percentage calculator has four sections to help you solve different percentage problems:
1. What is p% of x?
Calculate a given percentage of a number:
- Enter the percentage
- Enter the number of which you need to find the percentage
- The result appears instantly
Example: You scored 80% on a test with 30 total points. Result: 24 points.
2. x is what percent of y?
Determine the percentage of two given numbers:
- Enter the number whose percentage you want to determine
- Enter the number against which this percentage must be evaluated
- Get the percentage instantly
Example: Gavin's rent is $1,245 per month, while his budget is $4,000. Result: 31.125%
3. x is p% of what?
Find the value for which a given number is a known percentage:
- Enter the number for which you know the percentage
- Provide the percentage
- See the whole value right away
Example: 10 is 5% of what? Result: 200
4. What is x increased/decreased by p%?
Determine the effects of an increase or decrease by a given percent:
- Enter the initial value
- Select increase or decrease
- Enter the percent change
- See the changed value instantly
Example: A candy bar price of $5 increased by 30%. Result: $6.50
What is the Percentage?
Percentage is one of many ways to express a dimensionless relation between two numbers (the other methods being ratios and fractions).
One percent is a hundredth. As a percent sign, we usually use %, but sometimes it is denoted by pct. It means that:
- 5% = 5 pct = 0.05 = 5/100 = five-hundredths
Percentages are very popular since they can describe situations that involve:
- Large numbers (e.g., lottery chances)
- Averages (e.g., final course grade)
- Very small numbers (e.g., air pollution levels)
How to Calculate the Percentage - Formulas
Depending on what you want to estimate, you can use these percentage formulas:
1. Find percentage:
percentage = 100 × (part / whole)
Answers: "What percentage of 20 is 8?"
2. Find part:
part = whole × (percentage / 100)
Answers: "What is 40% of 20?"
3. Find whole:
whole = 100 × (part / percentage)
Answers: "What is 100% if 8 is 40%?"
4. Increase/Decrease:
result = number × (1 ± percentage/100)
Answers: "What is 100 increased/decreased by 20%?"
Percentage Examples
Example 1: Test Score
You scored 123 out of 150 points on an exam. What's your percentage?
Solution: (123 / 150) × 100 = 82%
Example 2: Shopping Discount
A $50 item has a 20% discount. What's the new price?
Solution: $50 × (1 - 20/100) = $50 × 0.8 = $40
Example 3: Finding the Whole
You spent $12 on bubble gum, which is 30% of your budget. How much money did you have?
Solution: ($12 × 100) / 30 = $40
History of Percentage - The Percent Sign
Although Ancient Romans used Roman numerals, calculations were often performed in fractions divided by 100. It was equivalent to the computing of percentages that we know today.
The term percent is often attributed to Latin per centum, which means "by a hundred." Actually, it came from Italian per cento — "for a hundred."
The percent sign % evolved by the gradual contraction of those words over centuries. Eventually, cento took the shape of two circles separated by a horizontal line, from which the modern % symbol is derived.
Related Symbols
- ‰ (per mille) - per thousand (1/1000 or 0.1%)
- ‱ (basis point) - per ten thousand (1/10000 or 0.01%)
Percentage Points vs Percent
Percentage points are different from percent! This is a common mistake:
Wrong example: "Unemployment rose from 10% to 12%, an increase of 2%"
Correct: "Unemployment rose from 10% to 12%, an increase of 2 percentage points (or 20% relative increase)"
Understanding the difference:
- Percentage points (pp): The absolute difference between two percentages (12% - 10% = 2 pp)
- Percent change: The relative change ((12-10)/10 × 100 = 20%)
Frequently Asked Questions
What is the percentage?
The percentage is a dimensionless ratio of two numbers. It can be used to compare two numbers and find out how much one is more than the other, or compare the two numbers against a common scale.
How do I calculate x percent of y?
- Divide x by 100
- Multiply the result by y
- The result is x% of y
Example: 60% of 1260 = (60/100) × 1260 = 0.6 × 1260 = 756
How much percent of y is x?
- Divide x by y
- Multiply the result by 100
- The result is the percentage
How much is 60% of 1260?
60% of 1260 is equal to 756.
Calculation: 60/100 = 0.6, then 0.6 × 1260 = 756
How do I convert percentage to decimal?
Divide the percentage by 100. For example: 15% = 15/100 = 0.15
How do I calculate percentage increase?
- Subtract the original value from the new value
- Divide the result by the original value
- Multiply by 100
Example: Price increased from $50 to $60: ((60-50)/50) × 100 = 20%
What is the difference between percent and percentage points?
Percent is used for relative changes, while percentage points measure absolute differences between two percentages. If a value changes from 10% to 12%, that's a 2 percentage point increase, but a 20% relative increase.