What is X% of Y?
Three Types of Percentage Calculations
- Percent of a number — "What is 20% of 150?" → 30. Formula: (Percentage ÷ 100) × Number
- What percent is X of Y — "30 is what % of 150?" → 20%. Formula: (X ÷ Y) × 100
- Percentage change — "What is the % change from 80 to 100?" → +25%. Formula: ((New − Old) ÷ Old) × 100
Percentage Formulas Explained
Percentages express a number as a fraction of 100. Here's how each calculation works:
- Finding X% of Y: Multiply Y by the decimal equivalent of X%. Example: 15% of 200 = 200 × 0.15 = 30. Or equivalently, (200 × 15) ÷ 100 = 30.
- Finding what percentage X is of Y: Divide X by Y and multiply by 100. Example: 45 out of 180 = (45 ÷ 180) × 100 = 25%.
- Percentage increase: When the new value is greater than the original, ((New − Original) ÷ Original) × 100 gives a positive percentage.
- Percentage decrease: When the new value is less, the result is negative. Example: 100 to 80 = ((80 − 100) ÷ 100) × 100 = −20%.
Everyday Uses for Percentage Calculations
- Discounts: Calculate the sale price after a 30% discount.
- Tax: Find 8.5% sales tax on a purchase total.
- Tips: Calculate a 20% gratuity on a restaurant bill.
- Finance: Find the percentage return on an investment.
- Grades: Convert raw scores to percentage grades.
- Statistics: Express a proportion as a percentage of the total.
- Business: Calculate profit margin or revenue growth rate.
Frequently Asked Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. Example: 15% of 200 = 200 × 15 ÷ 100 = 30. Alternatively, convert the percentage to a decimal first: 15% = 0.15, then 200 × 0.15 = 30.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original, then multiply by 100. Example: from 80 to 100 = (100 − 80) ÷ 80 × 100 = 25% increase.
What is percentage decrease?
When the new value is less than the original, the percentage change is negative (a decrease). Example: from 100 to 75 = (75 − 100) ÷ 100 × 100 = −25%.
How do I work backwards from a percentage?
If you know the result and the percentage, divide the result by the decimal equivalent. Example: if 30 is 15% of some number, then: 30 ÷ 0.15 = 200. Or use the "what percent is X of Y" calculator with X and the result.
What's the difference between percentage points and percent?
Percentage points measure an absolute difference between two percentages. If a rate goes from 5% to 8%, it increased by 3 percentage points but by 60% relative to its original value. These are different and often confused in news reporting.