Percentage Calculator
Three percentage calculators in one: find a percentage of a number, calculate what percent one number is of another, or find the percentage change between two values.
The Three Types of Percentage Problems
Most percentage questions fall into exactly three patterns. Knowing which type you are dealing with prevents the most common calculation mistakes.
- Type 1. Percentage of a number: "What is 20% of 85?" Multiply the number by the percentage expressed as a decimal: 85 × 0.20 = 17. This covers discounts, tax amounts, and tip calculations.
- Type 2. What percent is X of Y? "45 is what percent of 180?" Divide the part by the whole and multiply by 100: (45 ÷ 180) × 100 = 25%. This covers test scores, survey results, and market share.
- Type 3. Percentage change: "A price went from $80 to $92. What is the percentage increase?" Subtract the old value from the new, divide by the old, and multiply by 100: (92 − 80) ÷ 80 × 100 = 15%. A negative result means a decrease.
Worked Examples
Sales tax: A $340 item with 8.5% sales tax. Type 1: 340 × 0.085 = $28.90 tax, total = $368.90.
Grade calculation: You scored 73 out of 90. Type 2: (73 ÷ 90) × 100 = 81.1%.
Stock gain: A share bought at $42 is now worth $56.70. Type 3: (56.70 − 42) ÷ 42 × 100 = 35% gain.
Common Percentage Shortcuts
A few mental math tricks speed up everyday percentage work. To find 10% of any number, move the decimal one place left: 10% of 470 = 47. Then halve it for 5%, or double it for 20%. To find 1%, move the decimal two places left. Combining these lets you approximate most percentages in seconds without a calculator. 15% of 80 is 10% (8) + 5% (4) = 12.
Percentage points and percentages are not the same thing. If an interest rate rises from 4% to 6%, it increased by 2 percentage points, but by 50% relative to its original value. The distinction matters in finance and statistics, where "percent" without qualification is ambiguous.