How Percentage Calculators Work
Percentages sound simple until you try to explain them. This guide walks through the small handful of formulas that cover almost every real-world use.
Last updated July 16, 20265 min read
The basics
A percentage is just a fraction of 100. 20% means 20 per 100, or 0.20 as a decimal.
Almost every percentage question reduces to one of three operations: taking a percentage of a number, expressing one number as a percentage of another, or computing a change from one number to another.
Percent of a number
To find X% of Y, multiply Y by X/100.
Example: 15% of 80 = 80 × 0.15 = 12.
Expressing one number as a percentage of another
To ask what percentage A is of B, divide A by B and multiply by 100.
Example: 18 out of 25 questions correct = 18 ÷ 25 × 100 = 72%.
Percentage change
The percentage change from an old value to a new value is (new − old) ÷ old × 100. A positive result is an increase, negative is a decrease.
Example: Price rises from $40 to $50 → (50 − 40) ÷ 40 × 100 = 25% increase.
Everyday uses
- Sales and discounts: 30% off $60 saves $18, so you pay $42.
- Tips: 18% on a $54 meal is 54 × 0.18 = $9.72.
- Taxes and interest: 8% sales tax on $120 adds $9.60.
- Grades: 42 correct out of 50 is 84%.