Percentage Calculator

What is a percentage calculator?

A percentage calculator finds the answer to the three main percent questions: what is a given percent of a number, what percent one number is of another, and what whole gives a specific percent. It runs the right formula for the question you pick and shows the steps so the math is easy to check.

How the percentage calculator works

Pick a question type, enter the two numbers, and the calculator:

• Converts the percent to a decimal when applicable.
• Applies the formula for the chosen question.
• Shows the answer with the formula written out.
• Prints a short step by step trace of the calculation.
• Writes a one-line interpretation of the result.

What is X percent of Y?

Multiply Y by X and divide by 100. Equivalently, convert the percent to a decimal (X ÷ 100) and multiply by Y. For example, 20 percent of 150: 150 × 20 ÷ 100 = 30, or 150 × 0.20 = 30. This is the question that shows up in tips, discounts, sales tax, and most everyday percent-of-a-number problems.

X is what percent of Y?

Divide X by Y and multiply by 100. For example, 30 is what percent of 150: 30 ÷ 150 = 0.2, then 0.2 × 100 = 20 percent. This is the question for things like a test score, a completion rate, or any part-to-whole ratio framed as a percent.

X is Y percent of what?

Divide X by the decimal form of Y. For example, 30 is 20 percent of what: 30 ÷ (20 ÷ 100) = 30 ÷ 0.20 = 150. This question comes up when you know the part and the percent and need to find the whole, such as working backward from a discount to the original price.

Percentage formulas

• answer = Y × X / 100 for X percent of Y
• percent = X / Y × 100 for X is what percent of Y
• whole = X / (Y / 100) for X is Y percent of what

All three are rearrangements of the same basic relationship between a part, a whole, and a percent. The trick is picking the right rearrangement for what you know.

How percentages are used

Percentages show up everywhere: tips on restaurant bills, tax on a purchase, a discount at the store, a markup at a business, a test score, a probability, a battery level, an interest rate, a price change in a stock chart. The math is the same in every case; only the framing changes.

For some of these specific uses, we have dedicated calculators: the tip calculator splits bills with custom rates, the discount calculator applies a percentage off, the markup calculator works from cost to selling price, and the sales tax calculator adds or removes tax from a total.

Worked examples

• 20% of 150 = 150 × 20 / 100 = 30
• 30 is what percent of 150 = 30 / 150 × 100 = 20%
• 30 is 20% of what = 30 / 0.20 = 150
• 15% of 40 (a 15% tip on a $40 bill) = 40 × 0.15 = $6

Common mistakes

• Forgetting to divide by 100 when converting a percent to a decimal. 20 percent is 0.20, not 20.
• Swapping the part and the whole when finding X is what percent of Y. The part goes on top.
• Confusing X percent of Y with X is Y percent of what. The first multiplies; the second divides.
• Treating a percentage change as a plain percentage. Percentage change involves two values; a plain percentage involves one part and one whole. The percentage increase calculator handles the change case.
• Forgetting that a percent over 100 just means the part is larger than the whole, which is perfectly valid in growth and markup contexts.

Related tools

• Percentage increase calculator for percent change between two values.
• Percent error calculator for experimental vs accepted value comparisons.
• Discount calculator for applying a percentage off a price.
• Markup calculator for cost-to-selling-price math.
• Tip calculator for splitting bills with custom tips.
• Sales tax calculator for adding or removing tax.
• Fraction calculator for fraction arithmetic, decimals, and mixed numbers.
• All education calculators and all money calculators.