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① What is X% of a number?
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How to calculate percentages
A percentage is simply a number expressed as a fraction of 100. "Per cent" literally means "per hundred." The three most common percentage calculations each answer a slightly different question — and all three are handled above.
Type 1 (What is X% of Y?): Multiply Y by X divided by 100. Example: 20% of 150 = 150 × 0.20 = 30.
Type 2 (X is what % of Y?): Divide X by Y and multiply by 100. Example: 30 is what % of 150? → 30 ÷ 150 × 100 = 20%.
Type 3 (% change): Subtract the old value from the new, divide by the old value, multiply by 100. A positive result is an increase; negative is a decrease. Example: from 80 to 100 → (100−80) ÷ 80 × 100 = 25% increase.
Common percentage examples
Shopping discount
30% off a $85 item
Discount: $25.50 · You pay: $59.50
Salary raise
From $52,000 to $56,000
Increase: 7.69%
Test score
42 correct out of 50 questions
Score: 84%
Sales tax
8.25% tax on a $200 purchase
Tax: $16.50 · Total: $216.50
Tip
18% tip on a $64 restaurant bill
Tip: $11.52 · Total: $75.52
Price drop
Item went from $120 to $90
Decrease: 25%
Frequently asked questions
How do I calculate a percentage on a calculator?
For "X% of Y": type Y × X ÷ 100. For example, 20% of 150: press 150 × 20 ÷ 100 = 30. Many calculators also have a % button — pressing 150 × 20% directly gives you 30.
How do I calculate a percentage increase or decrease?
Subtract the original from the new value, divide by the original, then multiply by 100. Formula: ((New − Old) ÷ Old) × 100. If the result is positive it's an increase; if negative, it's a decrease.
How do I find the original price after a percentage discount?
If you know the sale price and the discount percentage, divide the sale price by (1 − discount/100). Example: an item is $68 after a 20% discount. Original price = 68 ÷ 0.80 = $85.
What is the difference between percentage and percentage points?
A percentage point is an absolute difference between two percentages. If interest rates go from 3% to 5%, that's an increase of 2 percentage points — but it's a 66.7% increase in the rate itself. The distinction matters in finance, statistics, and polling.
How do I calculate a grade percentage?
Divide the points you earned by the total points possible, then multiply by 100. Example: 42 points out of 50 → 42 ÷ 50 × 100 = 84%. Use calculator ② above — enter 42 as X and 50 as Y.
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