Calculate percentages, increases, decreases, and more
Example: What is 20% of 150?
Solution: 20% × 150 = 30
Percentage
20%
Value
30
20% of 150 = 30
100 to 150 = 50% increase
200 to 150 = 25% decrease
30 is 20% of 150
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
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Calculate percentages, increases, decreases, ratios, and percentage points with comprehensive formulas.
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Percentage = (Value ÷ Total) × 100
Find what percentage one number is of another
Value = (Percentage ÷ 100) × Total
Find the value given percentage and total
Total = Value ÷ (Percentage ÷ 100)
Find total given value and percentage
Increase = Original × (1 + %/100)
Calculate percentage increase
Decrease = Original × (1 - %/100)
Calculate percentage decrease
% Change = ((New - Old) ÷ Old) × 100
Calculate percentage change
Calculate sale prices, discounts, and savings
Analyze survey results and data trends
Calculate taxes, tips, interest, and investments
Percentage points measure absolute difference (e.g., from 10% to 15% is a 5 percentage point increase), while percent change measures relative difference (from 10% to 15% is a 50% increase). Understanding this distinction is crucial for accurate data interpretation.
To find the original number after a percentage increase or decrease, use the formula: Original = Final ÷ (1 ± Percentage/100). For example, if you have $115 after a 15% increase, the original amount is $115 ÷ 1.15 = $100.
When adding multiple percentages, don't simply sum them. Instead, apply them sequentially: Final = Original × (1 + %1/100) × (1 + %2/100). For example, a 10% increase followed by a 20% increase results in 1.10 × 1.20 = 1.32, or a 32% total increase, not 30%.
10% = move decimal left one place, 5% = half of 10%
Verify results by working backwards or using different methods
Consider whether you need percentage of, percentage change, or percentage points
Round numbers for quick estimates before precise calculations