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Introduction
Every percentage formula boils down to a simple relationship: a part compared to a whole, multiplied by 100. Yet the way that relationship gets applied can vary dramatically depending on what you already know and what you need to find. Understanding the three core formulas—and the percent change equation—turns percentage problems from guesswork into straightforward arithmetic.
This guide breaks down each formula with clear examples. You will learn not just the equations themselves, but also when to use which one and how to avoid the most common mistakes. For a broader overview of percentage calculators and how they work, see our percentage calculator guide . For step-by-step practice applying these formulas, read our how to calculate percentages guide .
The Three Core Percentage Formulas
Every percentage formula you encounter falls into one of three categories. Once you recognize which type of problem you are facing, the math becomes routine.
Formula 1: Finding a Percentage of a Number
This solves the question: what is X% of Y? The formula is (X / 100) multiplied by Y. For example, to find 20% of 150, you divide 20 by 100 to get 0.2, then multiply by 150. The result is 30.
This formula applies when you know the percentage and the whole, and need the part. Typical uses include calculating a tip on a restaurant bill, finding the discount amount on a sale item, or determining how much tax to pay on a purchase.
Formula 2: Finding What Percentage One Number Is of Another
This solves the question: X is what percent of Y? The formula is (X / Y) multiplied by 100. For example, if you answered 42 questions correctly out of 50, you divide 42 by 50 to get 0.84, then multiply by 100. The result is 84%.
This formula applies when you know the part and the whole, and need the percentage. Typical uses include calculating test scores, determining what portion of your income goes to rent, or figuring out your body fat percentage.
Formula 3: Finding the Whole from a Percentage
This solves the question: X is Y% of what number? The formula is (X / Y) multiplied by 100. For example, if 15 is 30% of a number, you divide 15 by 30 and multiply by 100 to get 50.
This formula applies when you know the part and the percentage, and need the whole. Typical uses include reverse-engineering a pre-discount price or calculating a total population from a known sample.
The Percent Change Formula
Beyond the three core equations, the percentage formulas family includes percent change. This formula answers the question: by what percentage did something increase or decrease?
The formula is: ((New Value – Old Value) / Old Value) multiplied by 100. If you spent $200 on groceries last month and $250 this month, the change is $50. Divide $50 by the original $200 to get 0.25. Multiply by 100 to get a 25% increase.
When the result is negative, it simply means a decrease. A move from $300 to $240 produces a change of -$60. Dividing by $300 gives -0.2, or a 20% decrease.
For a dedicated deep dive into this specific calculation, see our percentage change calculator guide .
Common Mistakes to Avoid
Even simple percentage formulas can trip people up.
The most common error is using the wrong base. If a price increases from $100 to $120, the increase is $20. Dividing by the new price ($120) gives 16.7%, which is wrong. The correct base is the original price ($100), giving a 20% increase. Always ask: compared to what original amount?
Another frequent mistake involves confusing percentage points with percent. If an interest rate rises from 4% to 6%, that is a 2 percentage point increase. But as a percent change, it is a 50% increase. The context determines which framing is appropriate.
A third pitfall involves adding and subtracting percentages incorrectly. A 20% discount followed by a 20% markup does not return you to the original price. If a $100 item gets a 20% discount, it costs $80. A 20% markup on $80 adds $16, bringing the price to $96—not $100. Percentages always operate on the current base, not the original one.
When to Use Each Formula
To decide which percentage formula to apply, identify what you already know. If you know the percentage and the whole, use Formula 1 to find the part. If you know the part and the whole, use Formula 2 to find the percentage. If you know the part and the percentage, use Formula 3 to find the whole. If you have two values and want to know how much they differ in percentage terms, use the percent change formula.
For worked examples of all these formulas applied to real-world situations, see our percentage calculation examples guide .
Conclusion
Percentage formulas are not complicated once you recognize the pattern. Three core equations cover nearly every situation: finding a percentage of a number, finding what percent one number is of another, and finding the whole from a percentage. The percent change formula handles increases and decreases. The key is identifying which pieces of the puzzle you already have and which one you need. With practice, these formulas become second nature.
