Math

Percent Calculator

Four percentage modes: find X% of Y, determine what percent X is of Y, solve reverse percentages, and calculate percentage increase or decrease.

Quick Answer

To find X% of Y, multiply Y by X/100. To find what % X is of Y, divide X by Y and multiply by 100. Percentage change = ((new - old) / |old|) × 100. To find the original number when X is Y% of it, divide X by Y/100.

What is X% of Y?

Enter a percentage and a number to find the result.

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About This Tool

The Percent Calculator handles the four most common percentage problems people encounter. Whether you are calculating a discount at the store, figuring out a test score, working out a salary increase, or reverse-engineering a tax-inclusive price, this tool gives you the answer instantly with the formula shown. It covers every percentage scenario you are likely to face in school, business, or daily life.

Four Calculation Modes

"What is X% of Y?" is the most basic percentage operation. It answers questions like "What is 20% of 150?" (answer: 30). Multiply the number by the percentage divided by 100. This mode handles discounts, tips, commissions, tax amounts, and interest calculations.

"X is what % of Y?" reverses the direction. Given two numbers, it tells you what fraction the first represents of the second, expressed as a percentage. Score 42 out of 50 on a test? That is 84%. This is the mode for understanding proportions, market shares, completion rates, and relative comparisons.

"X is Y% of what?" solves the reverse percentage problem. You know the result and the percentage, and need to find the original number. If a discounted price is $85 after a 15% discount, the original price was $85 / 0.85 = $100. This comes up frequently in tax calculations, discount recovery, and financial analysis.

Percentage Change measures the increase or decrease from one value to another. The formula uses the absolute value of the old number as the denominator: ((new - old) / |old|) × 100. A positive result means growth; a negative result means decline. This mode is essential for comparing prices over time, tracking business metrics, and analyzing data trends.

The Asymmetry of Percentage Change

One of the most common misconceptions about percentages is that a 25% increase followed by a 25% decrease returns you to the starting value. It does not. If you start at 100 and increase by 25%, you reach 125. A 25% decrease from 125 takes you to 93.75, not 100. This happens because the base changes. The increase is 25% of 100, but the decrease is 25% of 125. Understanding this asymmetry is critical for financial analysis, inflation calculations, and investment returns.

Percentages in Everyday Life

Percentages are everywhere. Sales tax, income tax brackets, mortgage rates, credit card APR, nutrition labels, battery charge levels, humidity readings, election poll results, grade curves, stock returns, and sports statistics all use percentages. Being able to quickly convert between a percentage and its underlying numbers is a fundamental life skill. This calculator eliminates the mental arithmetic and shows you the formula so you can verify the logic yourself.

Tips for Working with Percentages

A few practical shortcuts: to find 10% of any number, move the decimal point one place left. To find 1%, move it two places. To find 15% (a common tip), find 10% and add half of that. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. To convert a percentage to a decimal, divide by 100. These mental math tricks pair well with the calculator for quick verification.

Frequently Asked Questions

How do I calculate X% of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 200: (15 / 100) × 200 = 30. This works for any percentage, including values over 100% (e.g., 150% of 80 = 120) and decimal percentages (e.g., 2.5% of 400 = 10).
What is the formula for percentage change?
Percentage change = ((New Value - Old Value) / |Old Value|) × 100. A positive result indicates an increase; a negative result indicates a decrease. For example, going from 80 to 100 is a 25% increase: ((100 - 80) / 80) × 100 = 25%. Going from 100 to 80 is a 20% decrease: ((80 - 100) / 100) × 100 = -20%.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 42 out of 50, that is (42 / 50) × 100 = 84%. This formula works for any comparison — sales figures, test scores, budget allocations, or population proportions.
What does 'X is Y% of what number' mean?
This is a reverse percentage problem. You know the result (X) and the percentage (Y%), and you need to find the original number. The formula is: Original = X / (Y / 100). For example, if 30 is 15% of some number: 30 / (15/100) = 30 / 0.15 = 200. This is useful for reverse-engineering discounts, tax-inclusive prices, or partial measurements.
Why is percentage increase from 80 to 100 different from decrease from 100 to 80?
Because the base (denominator) changes. Going from 80 to 100 is a 25% increase (20/80 = 0.25). Going from 100 to 80 is a 20% decrease (20/100 = 0.20). The same absolute change of 20 produces different percentages because the reference value differs. This asymmetry is fundamental to percentages and catches many people off guard.

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