Percentage Calculator Guide
Percentages appear in everyday life constantly: discounts, tax rates, tips, grade scores, interest rates, statistics, and measurements. Despite this ubiquity, percentage questions trip people up because there are three fundamentally different types of calculation that all involve percentages.
Mastering all three types — finding a percentage of a number, finding what percentage one number is of another, and finding the original number when a percentage of it is known — covers virtually every percentage question you will encounter.
The Three Types of Percentage Calculations
Type 1: What is X% of Y? Answer = Y × (X/100) Example: What is 15% of $80? → 80 × 0.15 = $12 Type 2: X is what % of Y? Answer = (X/Y) × 100 Example: 12 is what % of 80? → (12/80) × 100 = 15% Type 3: X is Y% of what number? Answer = X ÷ (Y/100) = X × (100/Y) Example: 12 is 15% of what? → 12 ÷ 0.15 = 80
Common Applications
Discounts: Type 1. A 25% off sale on a $120 item: $120 × 0.25 = $30 discount. Sale price = $90. Or: $120 × 0.75 = $90 directly.
Grade percentages: Type 2. You scored 43 out of 50 on a test: (43/50) × 100 = 86%. You got an 86.
Tax: Type 1. 8.5% sales tax on $65: $65 × 0.085 = $5.525. Total = $70.52.
Finding the original price: Type 3. A sale item is $75 after a 25% discount. What was the original price? $75 ÷ 0.75 = $100.
Percentage Change (Increase/Decrease)
Percentage change measures how much a value has changed relative to its starting value. Formula: ((new − old) / old) × 100. Positive = increase; negative = decrease.
Example: price goes from $50 to $65. Change: (65 − 50)/50 × 100 = 30% increase. Price goes from $65 to $50. Change: (50 − 65)/65 × 100 = −23.1% decrease. Note that a 30% increase followed by a 23.1% decrease returns to the original.
Quick Tips
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For 10%: move the decimal left one place. 10% of $347 = $34.70.
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For 1%: move decimal left two places. 1% of $347 = $3.47.
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Build any percentage from 10% and 1%. 15% = 10% + 5% (half of 10%). 22% = 20% + 2%.
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Sale price shortcut: subtract the discount from 100% and multiply. 30% off = 70% of original price. Multiply by 0.70.
Frequently Asked Questions
What is 20% of 150?
150 × 0.20 = 30.
45 is what percent of 180?
(45/180) × 100 = 25%.
30 is 15% of what number?
30 ÷ 0.15 = 200.
How do I calculate tax on a purchase?
Multiply the pre-tax price by the tax rate (as a decimal). $85 at 7% tax: 85 × 0.07 = $5.95 tax. Total = $90.95. Or: 85 × 1.07 = $90.95 directly.
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Sources
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