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Every dosage calculation, from a single tablet to an ICU drip, is built from a handful of basic math skills: fractions, decimals, percents, and ratios. Nursing programs review these first, because a small slip here, like a misplaced decimal point, becomes a big error in a dose.
Each topic below explains the idea, shows the steps, works an example, and points out the mistake students make most often. Use the jump links to skip anything you already know, then try the practice problems at the end. Each topic also links to a full lesson if you want more.
Already know some of this? Skip straight to what you need.
Some prescriptions, older references, and exams still use Roman numerals, often in lowercase (ii tablets).
There are only a few symbols you need: I = 1, V = 5, X = 10, L = 50, C = 100. Write the symbols from largest to smallest and add them. When a smaller symbol comes right before a larger one, subtract it instead.
Only I, X, and C are subtracted, and only from the next two larger symbols: IV = 4, IX = 9, XL = 40, XC = 90. A symbol is never repeated more than three times in a row.
Watch out: Reading IV as 6. When the smaller symbol is first, subtract: IV = 5 − 1 = 4. VI = 5 + 1 = 6.
Every dosage formula is a fraction, so this is the most important skill on the page.
A fraction is a division. The top number (numerator) is divided by the bottom number (denominator): 34 means 3 ÷ 4 = 0.75. In a dose, 500 mg250 mg means “how many 250s fit in 500,” which is 2.
Learn more: Introduction to fractions
Divide the top and bottom by the same number. The value doesn't change, only how it's written. Keep going until no number (other than 1) divides both.
Watch out: Dividing only the top or only the bottom. Whatever you do to one, do to the other.
Multiplying the top and bottom by the same number gives an equivalent fraction: 12 = 24 = 50100.
To compare two fractions, give them the same denominator, or change both to decimals. With the same top number, the bigger bottom number means a smaller fraction, because the whole is cut into more pieces.
Learn more: Comparing fractions
A mixed number has a whole part and a fraction part, like 2¾. To multiply or divide, first change it to an improper fraction (top bigger than bottom).
Learn more: Multiplying mixed numbers
You can only add or subtract fractions that have the same denominator. If they don't, rewrite them with a common denominator first, then add or subtract the tops and keep the bottom.
Watch out: Adding the bottoms: 12 + 13 is not 25.
Learn more: Adding fractions · Subtracting fractions
Multiply the tops together and the bottoms together. Canceling first (dividing a top and a bottom by the same number) keeps the numbers small. This is exactly what you do in the dosage formula and in dimensional analysis.
Learn more: Multiplying fractions
Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). Then multiply.
Watch out: Flipping the first fraction instead of the second.
Learn more: Dividing fractions
Most medication strengths and volumes are decimals: 0.125 mg, 2.5 mL, 0.9% saline.
Each place after the decimal point is 10 times smaller than the one before: tenths, hundredths, thousandths. Read the number as a whole number, then name the last place.
Always write a zero before the decimal point when there is no whole number (0.5, never .5). This is a safety rule, not just a style.
Learn more: Understanding decimals
Line up the decimal points. Add zeros at the end so both numbers have the same number of decimal places. Then compare digit by digit from the left.
Watch out: Thinking more digits means a bigger number. 0.25 has more digits than 0.5, but it is smaller.
Learn more: Comparing decimals
Write the numbers in a column with the decimal points lined up. Fill empty places with zeros. Add or subtract as with whole numbers, and bring the decimal point straight down.
Watch out: Lining up the last digits instead of the decimal points.
Learn more: Adding decimals · Subtracting decimals
Ignore the decimal points and multiply the whole numbers. Then count the total number of decimal places in both factors, and place the decimal point so the answer has that many places.
You can't divide easily by a decimal, so make the divisor (the number you divide by) a whole number first. Move its decimal point to the right, and move the decimal point in the other number the same number of places. Then divide.
Watch out: Moving the decimal point in only one of the numbers.
This is the shortcut behind every metric conversion. Multiplying by 10, 100, or 1,000 moves the decimal point right 1, 2, or 3 places. Dividing moves it left. Add zeros if you run out of digits.
Watch out: Moving the wrong direction. Multiplying makes the number bigger, so the point moves right.
Learn more: Decimal place value
Fraction to decimal: divide the top by the bottom. Decimal to fraction: write the digits over 10, 100, or 1,000 (one zero for each decimal place), then simplify.
Learn more: Fractions to decimals
Find the place you are rounding to. Look at the digit just to its right. If that digit is 5 or more, add 1 to your place. If it is 4 or less, leave your place alone. Then drop all the digits to the right.
In nursing, round only the final answer, never the steps in between, and follow your program's rounding rules.
Watch out: Rounding in several steps (2.449 → 2.45 → 2.5). Round once from the original: 2.449 → 2.4.
Learn more: Rounding decimals
IV fluids, creams, and solutions are labeled in percents, and nurses also use percents for intake and for checking rate changes.
Percent means “out of 100.” To change a percent to a decimal, divide by 100: move the decimal point 2 places left and drop the % sign. To change a decimal to a percent, multiply by 100: move the point 2 places right and add %.
Watch out: Writing 0.9% as 0.9 or 0.09. It is 0.009, less than one percent.
Learn more: Percent to decimal · Decimal to percent
To change a percent to a fraction, write it over 100 and simplify. To change a fraction to a percent, change it to a decimal first, then multiply by 100.
Learn more: Introduction to percents
“Of” means multiply. Change the percent to a decimal and multiply it by the number.
Learn more: Finding a percentage
Divide the part by the whole, then multiply by 100. Nurses use this to record how much of a meal or drink a patient finished, and to see how much a rate changed.
Watch out: Dividing the whole by the part. Always put the part on top.
A medication label is a ratio, and the ratio-and-proportion method is one of the three ways to calculate a dose.
A ratio compares two amounts. It can be written three ways that mean the same thing: with a colon, as a fraction, or with “per.” Dividing a ratio down to “per 1” gives a unit rate.
Learn more: Ratios
Some solutions are labeled as a ratio, like epinephrine 1:1,000. For solids dissolved in liquid, it means 1 g of drug in that many mL of solution.
Watch out: Thinking 1:10,000 is stronger than 1:1,000. It is 10 times weaker.
A proportion says two ratios are equal. When one number is missing, call it x and cross-multiply: multiply each top by the other bottom and set them equal. Then divide to get x by itself.
Watch out: Mixing up the layout, like mg on top in one fraction and mL on top in the other. Keep matching units in matching places.
Learn more: Solving proportions
Two habits that keep multi-step calculations correct.
When a calculation has several steps, do them in this order: parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right.
Watch out: Working left to right without paying attention to parentheses.
Treat units like numbers. When the same unit is on the top and the bottom, it cancels. This is the idea behind dimensional analysis: set up the fractions so every unit cancels except the one you want.
Watch out: Ending with a unit you didn't want (like mg²/mL). That means a fraction was flipped.
Work each problem on paper first, then open the answers. The answers show the key step.
Next, put these skills to work converting units.
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