How to Calculate a Percentage: 3 Formulas With Examples

To calculate a percentage, divide the part by the whole and multiply by 100: percent = part ÷ whole × 100. If you scored 42 out of 50 on a test, 42 ÷ 50 = 0.84, and 0.84 × 100 = 84%. Every percentage problem is a version of that one relationship, rearranged to find whichever of the three numbers you are missing.

The word comes from the Latin per centum, “by the hundred.” A percent is simply a fraction with 100 in the denominator, so 84% means 84/100, or 0.84. Keeping that in mind makes every formula below feel obvious rather than memorized.

The three percentage formulas

Every percentage question involves three quantities:

• the whole (also called the base), the total you are comparing against;
• the part, the piece of the whole you care about;
• the percent, the rate that links them.

If you know any two, you can find the third.

A useful habit is to find the word “of” in the question. The number right after “of” is almost always the whole.

Worked examples

Finding a percentage of a number

What is 18% of 250? Convert 18% to a decimal by moving the decimal point two places left: 0.18. Then multiply: 0.18 × 250 = 45.

Finding what percent one number is of another

36 is what percent of 48? Divide the part by the whole: 36 ÷ 48 = 0.75. Multiply by 100 to get 75%.

Finding the whole from a part and a percent

27 is 15% of what number? Divide the part by the decimal rate: 27 ÷ 0.15 = 180. Check it by running the first formula forward: 15% of 180 is 0.15 × 180 = 27.

If you would rather not do the arithmetic, the percentage calculator handles all three question types and shows each step.

Converting between percents, decimals and fractions

Most mistakes in percentage problems come from converting the rate incorrectly. The rules are short:

• Percent to decimal: divide by 100 (move the decimal point two places left). 7.5% = 0.075.
• Decimal to percent: multiply by 100. 0.6 = 60%.
• Fraction to percent: divide the top by the bottom, then multiply by 100. 3/8 = 0.375 = 37.5%.

Thirds and sixths repeat forever, so their percents are rounded. For other values, the percent to decimal calculator and the fraction to percent calculator do the conversion exactly. If you need to go from a decimal back to a fraction, see how to convert a decimal to a fraction.

Mental math shortcuts

You can find most everyday percentages without a calculator by building them from a few easy pieces.

• 10%: move the decimal point one place left. 10% of $64 is $6.40.
• 1%: move it two places left. 1% of $64 is $0.64.
• 5%: take half of 10%. 5% of $64 is $3.20.
• 15%: add 10% and 5%. $6.40 + $3.20 = $9.60, a typical restaurant tip on a $64 bill.
• 20%: double 10%. 20% of $64 is $12.80.
• 25%: divide by 4. 25% of 64 is 16.
• 50%: divide by 2.

Swap the numbers when it helps. Because multiplication works in either order, x% of y equals y% of x. Finding 8% of 50 looks awkward, but 50% of 8 is obviously 4, and the two are the same.

For restaurant bills split among several people, the tip calculator does the 15%, 18% or 20% math and the per-person split at once.

Adding or subtracting a percentage

To increase a number by a percentage, multiply by (1 + rate). To decrease it, multiply by (1 − rate).

Sales tax: a $64 item with 7.25% sales tax costs 64 × 1.0725 = $68.64.

Discount: an $80 jacket at 20% off costs 80 × 0.80 = $64. The discount calculator also shows how much you save and handles stacked coupons.

Working backward: if you paid $68.64 including 7.25% tax, the pre-tax price was 68.64 ÷ 1.0725 = $64. Dividing by the multiplier undoes it. Subtracting 7.25% of $68.64 would not, because that percentage is taken from a different base.

Common mistakes

Undoing a percent with the same percent. If a price drops 20% from $80 to $64 and then rises 20%, it lands at 64 × 1.20 = $76.80, not $80. The second 20% is calculated on the smaller number. To get back to $80 from $64 you would need a 25% increase. This asymmetry is covered in detail in how to calculate percentage change.

Adding percentages from different groups. If 80% of one class and 60% of another pass a test, the overall pass rate is not 70% unless the classes are the same size. You need a weighted average, explained in how to calculate a weighted average.

Confusing percent with percentage points. An interest rate that moves from 4% to 5% rose by 1 percentage point, but by 25% in relative terms. News reports mix these up constantly.

Forgetting to convert. Multiplying 250 by 18 instead of 0.18 gives 4,500, a hundred times too large. If an answer looks wildly off, check the decimal point first.

Percentages in spreadsheets

In Excel or Google Sheets, a percentage is just a division formatted as a percent. With the part in A2 and the whole in B2, enter =A2/B2 and apply the percent format; 36 and 48 display as 75%. To find a percentage of a number, type the rate with its percent sign, as in =B2*18%, and the spreadsheet handles the conversion to 0.18 for you.