How to Calculate Percentages Three Different Ways
Percentages show up in sales tax, test scores, tips, and discount pricing every day. This guide teaches the three core percentage calculations so you can solve any problem quickly and confidently.
The Three Most Common Percentage Problems
Nearly every percentage question falls into one of three categories. The first is finding a percentage of a number, such as calculating 20% of $85 for a restaurant tip. The second is finding what percent one number is of another, such as determining what percent 34 is of 50 when you got 34 correct on a 50-question test. The third is finding a percentage change, such as calculating how much a stock price rose or fell compared to yesterday.
Once you recognize which type of problem you are solving, the math becomes straightforward. Each type has its own formula, and all three formulas use simple multiplication and division. You do not need a calculator for most everyday percentage problems once the logic clicks.
This guide walks through each type with a clear formula, a worked example, and tips for avoiding the mistakes that trip most people up.
Method 1: What Is X% of Y?
The formula for finding a percentage of a number is: result equals (percentage divided by 100) multiplied by the total. For example, to find 15% of $200, you divide 15 by 100 to get 0.15, then multiply 0.15 by 200, giving you $30.
A quick mental shortcut is to find 10% first by moving the decimal one place to the left, then adjust. Ten percent of $200 is $20. Half of that is $10, which represents 5%. Adding $20 and $10 gives you $30, the same answer. This shortcut works especially well for common percentages like 5%, 10%, 15%, 20%, and 25%.
This calculation type is the most common in everyday life. You use it for calculating sales tax on a purchase, figuring out how much to tip at a restaurant, and finding the discount amount during a sale.
Method 2: X Is What Percent of Y?
To find what percent one number is of another, divide the part by the whole and multiply by 100. The formula is: percentage equals (part divided by whole) multiplied by 100. If you scored 42 out of 60 on a test, divide 42 by 60 to get 0.70, then multiply by 100 to get 70%.
The key to this method is correctly identifying which number is the part and which is the whole. The whole is the total or the reference value, and the part is the amount you are comparing to it. In the test example, 60 is the total possible score (the whole), and 42 is what you actually scored (the part).
You use this method when you know both numbers but need to express their relationship as a percentage. Comparing survey results, tracking how much of a budget has been spent, and evaluating completion rates all require this approach.
Method 3: Percentage Change From X to Y
Percentage change measures how much a value has grown or shrunk relative to its starting point. The formula is: percentage change equals ((new value minus old value) divided by old value) multiplied by 100. If a product cost $80 last year and now costs $92, the change is $12. Divide $12 by $80 to get 0.15, then multiply by 100, giving a 15% increase.
A positive result means an increase and a negative result means a decrease. If the same product dropped from $80 to $68, the change is negative $12. Dividing negative $12 by $80 gives negative 0.15, or a 15% decrease. The sign tells you the direction of the change automatically.
Percentage change is essential for understanding investment returns, year-over-year revenue growth, weight loss progress, and any situation where you want to understand how much things have shifted over time relative to the original value.
Putting It All Together
When you encounter a percentage problem, pause for a moment to identify which of the three types it is. Are you finding a percent of a known total? Are you converting a part-to-whole relationship into a percent? Or are you measuring how much something changed over time? Matching the problem to the correct formula eliminates most errors before they happen.
Practice helps make these calculations feel instinctive. Try estimating percentage tips before looking at suggested amounts on a receipt, or calculate the percentage discount before purchasing a sale item. These small exercises build the mental flexibility to switch between formula types without effort.
Online percentage calculators can verify your work and handle complex calculations quickly. But understanding the underlying formulas means you will never be caught off guard when you do not have a device handy, and you will catch errors that tools sometimes make when inputs are entered incorrectly.