Percentage Calculator

What a percentage means

“Percent” means “per hundred”. 36% is 36 out of every 100, which you can also write as the fraction 36/100 or the decimal 0.36. Because every percentage is a fraction of 100, percentages let you compare proportions of totals that are very different sizes. For example, 9 out of 25 and 360 out of 1,000 are both 36%.

The three percentage questions

Almost every everyday percentage problem is one of three questions. Each one rearranges the same relationship, so you only need to remember one formula.

Choose the matching tab in the percentage calculator above. The labels say which number goes where, so you don’t need to rearrange anything yourself.

How to use the percentage calculator

1. Pick the question you’re answering: X% of Y, X is what % of Y, or X is P% of what.
2. Type the two numbers you know. You can use commas as thousands separators, such as 12,500.
3. The answer updates as you type. The working line underneath shows the exact sum, so you can check it or copy it into your notes.
4. Use Copy result to copy the answer as a sentence, or Share to send a link that opens the calculator with the same numbers.

In the X% of Y mode you also see the whole increased and decreased by the percentage. This is handy for adding sales tax or applying a discount in one step.

How to calculate a percentage by hand

Each of the three questions takes one or two steps on paper. The trick is to turn the percentage into a decimal first by dividing it by 100, which moves the decimal point two places to the left: 35% becomes 0.35, 4.5% becomes 0.045.

Finding a percentage of a number

To find 35% of 260, convert 35% to 0.35 and multiply: 0.35 × 260 = 91. If you’d rather avoid decimals, divide by 100 first and then multiply: 260 ÷ 100 = 2.6, and 2.6 × 35 = 91.

Finding what percent one number is of another

To find what percent 18 is of 72, divide the part by the whole, then multiply by 100: 18 ÷ 72 = 0.25, and 0.25 × 100 = 25%. The number after “of” is almost always the whole, so it goes on the bottom.

Finding the whole from a part

If 54 is 45% of some number, divide the part by the percentage as a decimal: 54 ÷ 0.45 = 120. To check, take 45% of 120, which gives 54 again.

Common percentages of common numbers

This table covers the percentages that come up most often in shopping, tipping and grading. Read across from the percentage and down from the number.

Because percentages scale in a straight line, you can combine rows. 35% of 80 is 30% of 80 plus 5% of 80: 24 + 4 = 28.

Mental math shortcuts

• 10% and 1%. Move the decimal point one place left for 10% and two places left for 1%. 10% of 64 is 6.4, and 1% is 0.64.
• 5% is half of 10%. For 15%, add 10% and 5%. For 20%, double 10%.
• Fractions you already know. 50% is a half, 25% is a quarter, 20% is a fifth and 75% is three quarters. A quarter of 360 is 90, so 25% of 360 is 90.
• Swap the numbers. 4% of 75 is the same as 75% of 4, which is 3. Pick whichever order is easier.
• Add or remove in one multiplication. To add 7%, multiply by 1.07. To take 30% off, multiply by 0.70. This skips the separate subtraction.

Real-life uses

Percent off: discounts and sales tax

A store sign says 30% off a $120 coat. Ten percent of 120 is 12, so 30% is 36, and you’d pay $84. Sales tax works the other way: at a 7% rate, a $45 purchase costs 45 × 1.07 = $48.15. When a price tag already includes tax and you want the pre-tax amount, divide. An item costing $54 including 8% tax was $54 ÷ 1.08 = $50 before tax.

Tip percentages

For a 20% tip on a $38 bill, take 10% ($3.80) and double it to get $7.60. For 15%, add half of the 10% figure to itself: $3.80 + $1.90 = $5.70. Many people tip on the pre-tax total, so if your receipt separates tax, use the subtotal.

Percentages for grades and test scores

If you scored 46 out of 50, divide 46 by 50 and multiply by 100 to get 92%. The same method works with any number of questions, which is why percentages are used to compare tests of different lengths. To combine several tests into one grade, average the scores with the average calculator, or weight them by points if the tests count differently.

Commission, fees and interest

A real estate agent earning 3% commission on a $320,000 sale receives $9,600. A 2.9% card processing fee on a $250 order is $7.25. Percentages of money that grow over time, such as interest, are handled by the simple interest calculator and the compound interest calculator.

Nutrition labels

The % Daily Value on a U.S. food label is a percentage of a reference amount. The Daily Value for sodium is 2,300 mg, so a serving with 460 mg of sodium shows 20%. Put 460 and 2,300 into the “X is what % of Y” mode to check.

Common mistakes

• Taking the percentage of the wrong number. In “what percent of the class passed?”, the whole is the number of students in the class, not the number who passed.
• Mixing up percentages and percentage points. If an interest rate moves from 4% to 5%, it rose by 1 percentage point. That’s a 25% increase in the rate itself. For that kind of comparison, use the percentage change calculator.
• Undoing a percentage with the same percentage. A 20% discount followed by a 20% markup doesn’t return the original price: 100 → 80 → 96. To undo a percentage, use the “X is P% of what” mode.
• Adding stacked discounts. “20% off, then an extra 10% off” is not 30% off. The second discount applies to the already reduced price, so you pay 0.80 × 0.90 = 0.72 of the original, a 28% discount in total.
• Subtracting tax to remove it. Taking 8% off a $54 tax-inclusive price gives $49.68, not the correct $50, because the tax was 8% of the pre-tax price, not of the total.

Related concepts

• Percentage point: the plain difference between two percentages. From 12% to 15% is 3 percentage points.
• Basis point: one hundredth of a percentage point, used for interest rates. 25 basis points is 0.25 percentage points.
• Percentage change: how much a value moved relative to where it started. See the percentage change calculator and the guide on how to calculate percentage change.
• Fraction and decimal forms: 3/8 = 0.375 = 37.5%. The guide to converting fractions, decimals and percentages has a full conversion table, and the fraction calculator does exact fraction arithmetic.
• Ratio: a comparison of two parts, such as 3 : 2, rather than a part of a whole. The ratio calculator simplifies and scales them.