Percentage Calculator – 3 Ways to Calculate %

What is a percentage calculator?

Use this free percent calculator to compute percentage values using standard formulas. Our percentage calculator answers 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.

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.

Working it out by hand

One fixed pair per mode, each matching what the calculator returns for the same inputs:

1. What is 35% of 80? Convert the percent to a decimal and multiply: 35 ÷ 100 = 0.35, then 80 × 0.35 = 28.
2. 45 is what percent of 60? Divide the part by the whole and scale: 45 ÷ 60 = 0.75, then 0.75 × 100 = 75%.
3. 18 is 30% of what? Divide the part by the percent as a decimal: 30 ÷ 100 = 0.30, then 18 ÷ 0.30 = 60.

All three are the same relationship, part = whole × rate, solved for a different unknown. Picking the mode is just picking which of the three quantities you do not know yet.

Edge cases

• Percent vs percentage points. A rate moving from 10% to 12% rose by 2 percentage points but by 20 percent in relative terms. The two are different numbers answering different questions, and mixing them up is the single most common percentage mistake in news and reports.
• Results over 100%. Nothing special happens: 150% of 80 is 120, and 90 is 150% of 60. A percent above 100 just means the part exceeds the reference value.
• Negative numbers. The calculator accepts them and returns signed results, which is occasionally useful, but signed change questions belong to the percentage increase and percent decrease calculators, which handle the direction explicitly.
• Reverse percentage. To recover an original price, convert the discount to what remains before using the third mode: $45 after 25% off is 75% of the original, and 45 ÷ 0.75 = 60. Entering the discount percent itself is the classic wrong turn.
• Display rounding. Steps and results show up to six decimal places, so 1 ÷ 3 appears as 33.333333%. The arithmetic underneath is full floating-point precision; only the display rounds.

Your numbers stay in the page

Every value you type is processed by this page in your browser. Your numbers are not sent to a server, not stored after you close the tab, and not visible to anyone else. There is no account and nothing to sign up for.

Related tools

• Scientific calculator for a full button-driven calculator that handles general math beyond percentages.
• Ratio calculator to simplify a ratio and check equivalence.
• Proportion calculator to solve A : B = C : D for one missing value.
• 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.