How do I calculate a percentage of a number?

To find X% of Y, multiply Y by X and divide by 100. The formula is: Result = (X × Y) &div; 100. For example, 15% of 200 is (15 × 200) &div; 100 = 30. This works for any combination of values, including decimals. A common shortcut for mental math is to find 10% first (move the decimal one place left) and then adjust. For 15% of 200, 10% is 20 and 5% is 10, so the answer is 30. This formula is used daily for calculating tips, sales tax, discounts, commissions, and more. Our calculator above handles this instantly as you type.

What is the difference between percentage change and percentage difference?

Percentage change measures how much a single value has increased or decreased over time, calculated as ((New − Old) &div; Old) × 100. It requires a clear "before" and "after." Percentage difference compares two independent values relative to their average: |A − B| &div; ((A + B) &div; 2) × 100. Use percentage change when tracking something over time (a stock went from $50 to $65 = 30% increase). Use percentage difference when comparing two separate things at the same point in time (City A's rent is $1,200 and City B's is $1,500 = 22.2% difference). Mixing these up is a common error in reports and presentations, so choosing the right formula matters for accurate communication.

What is the difference between markup and margin?

Markup and margin both describe profit as a percentage, but they use different denominators. Markup is the percentage added to cost: ((Selling Price − Cost) &div; Cost) × 100. Margin is the percentage of selling price that is profit: ((Selling Price − Cost) &div; Selling Price) × 100. If you buy a product for $60 and sell it for $100, the $40 profit represents a 66.7% markup (relative to cost) but a 40% margin (relative to selling price). Markup is always higher than margin for the same transaction. This distinction is critical for pricing strategy: many businesses accidentally set prices using margin when they intended markup (or vice versa), leading to lower-than-expected profits. A 50% markup produces a 33.3% margin, not a 50% margin.

How do I convert between fractions, decimals, and percentages?

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%. To convert a percentage to a decimal, divide by 100 (or move the decimal two places left): 37.5% = 0.375. To convert a decimal to a percentage, multiply by 100 (move the decimal two places right): 0.375 = 37.5%. To convert a percentage to a fraction, put the percentage over 100 and simplify: 37.5% = 37.5/100 = 375/1000 = 3/8. These conversions come up frequently in cooking (recipe scaling), finance (interest rates), science (concentration solutions), and everyday math. Our percentage calculator handles decimal inputs, so you can use it to quickly verify your conversions.

Why does a 50% increase followed by a 50% decrease not return to the original value?

This is one of the most counterintuitive aspects of percentage math. Starting at $100, a 50% increase brings you to $150. But a 50% decrease from $150 takes away $75 (half of 150), leaving you at $75, not $100. The reason is that each percentage is calculated on a different base number. The increase was 50% of 100, but the decrease was 50% of 150. This asymmetry means equal percentage gains and losses never cancel out. To return from $150 to $100, you would need a 33.3% decrease, not 50%. This principle is crucial in investing: if your portfolio drops 20%, you need a 25% gain to break even; a 50% loss requires a 100% gain to recover. Understanding this helps set realistic expectations for investment recovery timeframes.

What is the difference between percentage and percentile?

A percentage expresses a proportion out of 100. If you score 85% on a test, you answered 85 out of every 100 questions correctly (or the equivalent ratio). A percentile, on the other hand, indicates your ranking within a dataset. If your test score is in the 90th percentile, it means you scored higher than 90% of all test-takers, regardless of your actual percentage score. You could score 72% on a very difficult exam and still be in the 95th percentile if almost everyone else scored below 72%. Percentiles are used extensively in standardized testing (SAT, GRE), growth charts for children (height and weight), income distribution statistics, and performance benchmarking. The two concepts answer fundamentally different questions: "how much?" versus "how do I rank?"

Percentage Calculator

Quick Answer

To find X percent of a number Y, multiply (X / 100) x Y. For percentage change between two values, use ((new - old) / old) x 100. For example, 20% of 150 equals (20/100) x 150 = 30, and a change from 80 to 100 is a 25% increase.

Also searched as: percentage calculator, percentage, percent calculator

What is X% of Y?

Percentage (%)

Number

Result

X is what % of Y?

Number (X)

is what % of

Number (Y)

Result

15%

Percentage Change from X to Y

From (Old Value)

To (New Value)

Change

25% increase

How to Calculate Percentages

A percentage represents a fraction of 100 and is denoted by the symbol %. The word itself comes from the Latin "per centum," meaning "by the hundred." Percentages are one of the most frequently used mathematical concepts in daily life, appearing in everything from restaurant tips and shopping discounts to investment returns and school grades. This calculator handles the three core percentage formulas you will encounter most often.

Formula 1: What is X% of Y? This finds a specific percentage of a number. The formula is:

Result = (X × Y) ÷ 100

Example: What is 15% of 200? Result = (15 × 200) ÷ 100 = 3,000 ÷ 100 = 30. This formula is used whenever you need to find a portion of a total, such as calculating a 20% tip on a $85 dinner bill (answer: $17) or determining how much a 30% discount saves on a $150 item (answer: $45).

Formula 2: X is what % of Y? This determines what percentage one number represents of another. The formula is:

Percentage = (X ÷ Y) × 100

Example: 45 is what percent of 180? Percentage = (45 ÷ 180) × 100 = 0.25 × 100 = 25%. This is commonly used for calculating test scores (you got 42 out of 50 questions right = 84%), conversion rates in marketing (150 conversions from 3,000 visitors = 5%), or determining what share of your budget goes to rent.

Formula 3: Percentage change from X to Y. This calculates how much a value has increased or decreased in relative terms. The formula is:

Change = ((New Value − Old Value) ÷ |Old Value|) × 100

Example: A stock price went from $80 to $100. Change = ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase. A positive result indicates an increase; a negative result indicates a decrease. This formula is essential for tracking investment returns, comparing year-over-year revenue, measuring population growth, and analyzing price inflation.

Key Concepts

Percentage change vs. percentage difference. These are related but distinct concepts. Percentage change measures how much a single value has increased or decreased over time (old value to new value). Percentage difference measures how two values compare to each other relative to their average, and is calculated as: |Value1 − Value2| ÷ ((Value1 + Value2) ÷ 2) × 100. Use percentage change when tracking how something evolves over time (stock prices, population). Use percentage difference when comparing two independent values at the same point in time (salaries in two cities, prices at two stores).

Markup vs. margin. These terms confuse many business owners. Markup is the percentage added to cost to determine selling price: Markup% = ((Selling Price − Cost) ÷ Cost) × 100. Margin (also called profit margin) is the percentage of selling price that is profit: Margin% = ((Selling Price − Cost) ÷ Selling Price) × 100. If you buy a product for $60 and sell it for $100, the markup is 66.7% but the margin is 40%. They describe the same profit from different perspectives. Many pricing errors come from confusing the two. Use our Markup Calculator for business pricing math.

Percentage points vs. percentages. A percentage point is the arithmetic difference between two percentages. If an interest rate rises from 3% to 5%, it increased by 2 percentage points but by 66.7% in percentage terms ((5-3)/3 × 100). This distinction matters in financial reporting, polling data, and academic research. Mixing up the two can dramatically misrepresent the magnitude of a change.

Compound percentages. When percentages are applied repeatedly (as with compound interest or cumulative discounts), the results are not simply additive. A 10% gain followed by a 10% loss does not return you to the original value. Starting at $100: +10% = $110, then −10% = $99. You end up $1 short because the 10% loss applies to the larger number. Similarly, two successive 50% discounts do not equal a 100% discount; they equal a 75% discount. For compound interest calculations, try our Compound Interest Calculator.

Formula Reference Table

Question	Formula	Example	Answer
What is X% of Y?	(X × Y) ÷ 100	20% of 150	30
X is what % of Y?	(X ÷ Y) × 100	36 is what % of 144?	25%
% change from X to Y	((Y − X) ÷ \|X\|) × 100	From 50 to 65	30% increase
% difference between X and Y	\|X−Y\| ÷ ((X+Y)/2) × 100	Between 40 and 60	40%
Markup %	((Price − Cost) ÷ Cost) × 100	Cost $60, Price $100	66.7%
Profit margin %	((Price − Cost) ÷ Price) × 100	Cost $60, Price $100	40%

Practical Examples

Shopping discounts. A jacket originally priced at $120 is on sale for 35% off. The discount amount is (35 × 120) ÷ 100 = $42, so the sale price is $120 − $42 = $78. If sales tax is 8.25%, the tax on $78 is (8.25 × 78) ÷ 100 = $6.44, making the total $84.44. To calculate combined or successive discounts, remember they do not simply add up: a 20% discount followed by an additional 15% discount is not 35% off. The first discount brings $100 to $80, and the second brings $80 to $68, for a total effective discount of 32%.

Tax calculations. Sales tax is a straightforward percentage-of-a-number problem. If your state charges 7% sales tax on a $250 purchase, the tax is (7 × 250) ÷ 100 = $17.50, making the total $267.50. For income tax brackets, each bracket's rate applies only to income within that range. If the 22% tax bracket starts at $44,725, you pay 22% only on the portion of income above that threshold, not on your entire income. For detailed US tax math, try our US Income Tax Calculator.

Grade calculations. If a student scores 42 out of 50 on a test, the percentage score is (42 ÷ 50) × 100 = 84%. For weighted grades, multiply each assignment's percentage score by its weight and sum the results. If homework (worth 20% of the grade) averages 90% and exams (worth 80%) average 75%, the overall grade is (0.20 × 90) + (0.80 × 75) = 18 + 60 = 78%. Our GPA Calculator can help with grade point average conversions.

Tip calculations. Restaurant tips are a percentage-of-a-number calculation. For a $65 dinner bill with a 20% tip: (20 × 65) ÷ 100 = $13. Quick mental math shortcut: find 10% by moving the decimal point one place left ($6.50), then double it for 20% ($13.00). For 15%, add half of 10% to 10%: $6.50 + $3.25 = $9.75.

Investment returns. If you invest $10,000 and your portfolio grows to $12,500, the percentage return is ((12,500 − 10,000) ÷ 10,000) × 100 = 25%. However, this is the total return. If it took 3 years, the annualized return is different due to compounding. Use our Investment Return Calculator for time-adjusted calculations.

Common Percentage Conversions Table

Converting between fractions, decimals, and percentages is a fundamental math skill. The table below provides quick reference for the most commonly used conversions.

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333...	33.33%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%
1/10	0.1	10%
2/3	0.666...	66.67%
3/4	0.75	75%
1/6	0.1667	16.67%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%

To convert any fraction to a percentage, divide the numerator by the denominator and multiply by 100. To convert a percentage to a decimal, divide by 100 (move the decimal point two places left). To convert a decimal to a percentage, multiply by 100 (move the decimal point two places right). Use our Fraction Calculator for more complex fraction arithmetic.