Achievable CCMA

34. Essential calculations and measurement systems

Math basics for medications

6 min read

Medical math and dosage calculations

All medical assistants should be able to convert between units of measure. It is also important to be able to accurately calculate medication dosages. This section discusses different types of math problems that a medical assistant should be able to solve. Please note that in some states, calculating medical dosages may be outside the legal scope of practice for medical assistants. State laws vary.

The following sections present guidelines for writing and calculating dosages. The medical assistant should always verify answers for dose calculations with a co-worker or the provider.

Healthcare rules when writing numbers

With medications, it is important to be accurate in calculating and documenting amounts. There are three rules to follow when writing medication dosages in healthcare:

Rule 1: Use the correct unit abbreviation

Follow the number with the correct abbreviation for the unit of measure. Leave a space between the number and the abbreviation. Do not use a period with the abbreviations.

Correct examples

2 mg

10 mL

Incorrect examples

2 mg.

10mL

Rule 2: Write fractions as decimals

Write a fraction of a dose as a decimal.

Correct examples

0.2 mg

0.5 mg

Rule 3: Use a leading zero, never a trailing zero

If the dose is less than 1, place a zero to the left of the decimal point so the dose isn’t misread as a whole number. Never place a decimal point and a zero after a whole number - it can be misread as a much larger dose and cause an overdose.

Correct examples

0.75 mcg

0.2 mL

2 mL

5 mL

Incorrect examples

.75 mcg

.2 mL

2.0 mL

5.0 mL

Rounding numbers

When you calculate answers, sometimes the number needs to be rounded.

Steps for rounding

Find the place value where you want to end up.
Look at the number to the right of the place value.
- 4 or below → drop the remaining digits.
- 5 or above → add 1 to the rounded digit and drop the remaining digits.

Examples

Example 1

$569.365$

The 3 is in the tenths place. The next digit is 6, so round up.

Answer: 569.4

Example 2

$339.926$

The 9 is in the tenths place. The next digit is 2, so drop the remaining digits.

Answer: 339.9

Measurement systems and conversions

Three systems of measurement turn up in medication orders, and a medical assistant has to move between them. The metric system is the standard for healthcare - it is what drug labels, syringes, and dosage calculations use. The household system is what patients use at home: teaspoons, tablespoons, cups, ounces, and pounds. It is the system a medical assistant coaches a patient in, which is why an order written in metric so often has to be translated at the end of a visit. The apothecary system is an older system that has largely been retired, but grains (gr) still appear on a few labels.

Metric equivalents

Unit	Equivalent
1 kilogram (kg)	1000 grams (g)
1 gram (g)	1000 milligrams (mg)
1 milligram (mg)	1000 micrograms (mcg)
1 liter (L)	1000 milliliters (mL)
1 milliliter (mL)	1 cubic centimeter (cc)
1 meter (m)	100 centimeters (cm)
1 centimeter (cm)	10 millimeters (mm)

Household and metric equivalents

Household	Metric
1 teaspoon (tsp)	5 mL
1 tablespoon (tbsp), or 3 teaspoons	15 mL
1 fluid ounce (fl oz), or 2 tablespoons	30 mL
1 cup, or 8 fluid ounces	240 mL
1 pint, or 2 cups	480 mL
1 quart, or 2 pints	960 mL
2.2 pounds (lb)	1 kilogram (kg)
1 inch	2.54 cm

Apothecary equivalents

Apothecary	Metric or household
1 grain (gr)	60 mg in most medical assisting references, 65 mg in some (which is why aspirin gr V is labelled 325 mg). Use one or the other throughout a calculation, never both
1 dram	4 mL, or about 1 teaspoon
1 ounce	30 mL
1 minim	About 0.06 mL, or roughly 1 drop (gtt)

To convert pounds to kilograms, divide by 2.2; to convert kilograms to pounds, multiply by 2.2. Weight-based doses are always calculated from the weight in kilograms, so this is the conversion done most often.

Example: Weight-based dose

A pediatric patient weighs 44 lb, and the provider orders 10 mg/kg. What is the correct dose in milligrams?

Convert the patient’s weight to kilograms: $44 \div 2.2 = 20$ kg

Multiply by the ordered dose per kilogram: $20 \times 10 = 200$ mg

Answer: 200 mg

Example: Household-to-metric conversion

A provider orders 2 teaspoons of a liquid medication for a patient to take at home. How many milliliters is that?

Each teaspoon equals 5 mL: $2 \times 5 = 10$ mL

Answer: 10 mL

Temperature conversion

Medical assistants also convert between Fahrenheit (°F) and Celsius (°C) when documenting patient temperatures.

$C = (F - 32) \times \frac{5}{9}$

$F = (C \times \frac{9}{5}) + 32$

Here, $F$ is the temperature in degrees Fahrenheit and $C$ is the temperature in degrees Celsius.

Example: Converting Fahrenheit to Celsius

A patient’s temperature reads 102°F. What is this in Celsius?

$C = (102 - 32) \times \frac{5}{9} = 70 \times \frac{5}{9} = 38.9$

Answer: 38.9°C (rounded to the nearest tenth)

Decimal-to-percentage conversion

To convert a decimal to a percentage, multiply by 100 and add a percent sign: $0.75 \times 100 = 75%$ .

Healthcare rules when writing numbers

Use correct unit abbreviations with space, no period (e.g., 2 mg, 10 mL)
Write fractions as decimals; use leading zero if <1 (e.g., 0.5 mg, 0.2 mL)
Do not add trailing zero after whole numbers (e.g., 2 mL, not 2.0 mL)

Rounding numbers

Round to nearest tenth (one decimal place)
If next digit is 5 or more, round up; if 4 or less, round down

Roman numerals

Know basic Roman numerals (i, v, x, l, c, d, m)
Used occasionally in medication orders, often in lowercase

Measurement systems

Three systems: apothecary, household, metric
Metric system is most accurate and preferred in healthcare

Apothecary system

Oldest system; uses grains (gr) for weight, minims for volume
Abbreviations before Roman numerals (e.g., gr v)
Largely replaced by metric system

Household system

Common abbreviations: gtt (drop), tsp (teaspoon), tbsp (tablespoon), fl oz (fluid ounce), oz (ounce), qt (quart), pt (pint), lb (pound)
Used for patient instructions, less precise than metric

Converting between household and metric equivalents

Use proportion method: set up equivalent fractions, cross-multiply, then divide
Keep units and labels consistent on both sides of equation

Metric system

Weight: grams (g); Volume: liters (L); Length: meters (m)
Convert within the same base unit (e.g., g to mg, cm to mm)
Use proportion method for conversions (e.g., 1 g = 1000 mg)

Temperature conversion

Fahrenheit to Celsius: (°F − 32) ÷ 1.8 = °C
Celsius to Fahrenheit: (°C × 1.8) + 32 = °F
Round answers to nearest tenth

Next | 34.2 Drug labels and core mathematical principles

Math basics for medications

Medical math and dosage calculations

The following sections present guidelines for writing and calculating dosages. The medical assistant should always verify answers for dose calculations with a co-worker or the provider.

Healthcare rules when writing numbers

With medications, it is important to be accurate in calculating and documenting amounts. There are three rules to follow when writing medication dosages in healthcare:

Rule 1: Use the correct unit abbreviation

Follow the number with the correct abbreviation for the unit of measure. Leave a space between the number and the abbreviation. Do not use a period with the abbreviations.

Correct examples

2 mg

10 mL

Incorrect examples

2 mg.

10mL

Rule 2: Write fractions as decimals

Write a fraction of a dose as a decimal.

Correct examples

0.2 mg

0.5 mg

Rule 3: Use a leading zero, never a trailing zero

Correct examples

0.75 mcg

0.2 mL

2 mL

5 mL

Incorrect examples

.75 mcg

.2 mL

2.0 mL

5.0 mL

Rounding numbers

When you calculate answers, sometimes the number needs to be rounded.

Steps for rounding

Find the place value where you want to end up.
Look at the number to the right of the place value.
- 4 or below → drop the remaining digits.
- 5 or above → add 1 to the rounded digit and drop the remaining digits.

Examples

Example 1

$569.365$

The 3 is in the tenths place. The next digit is 6, so round up.

Answer: 569.4

Example 2

$339.926$

The 9 is in the tenths place. The next digit is 2, so drop the remaining digits.

Answer: 339.9

Measurement systems and conversions

Metric equivalents

Unit	Equivalent
1 kilogram (kg)	1000 grams (g)
1 gram (g)	1000 milligrams (mg)
1 milligram (mg)	1000 micrograms (mcg)
1 liter (L)	1000 milliliters (mL)
1 milliliter (mL)	1 cubic centimeter (cc)
1 meter (m)	100 centimeters (cm)
1 centimeter (cm)	10 millimeters (mm)

Household and metric equivalents

Household	Metric
1 teaspoon (tsp)	5 mL
1 tablespoon (tbsp), or 3 teaspoons	15 mL
1 fluid ounce (fl oz), or 2 tablespoons	30 mL
1 cup, or 8 fluid ounces	240 mL
1 pint, or 2 cups	480 mL
1 quart, or 2 pints	960 mL
2.2 pounds (lb)	1 kilogram (kg)
1 inch	2.54 cm

Apothecary equivalents

Apothecary	Metric or household
1 grain (gr)	60 mg in most medical assisting references, 65 mg in some (which is why aspirin gr V is labelled 325 mg). Use one or the other throughout a calculation, never both
1 dram	4 mL, or about 1 teaspoon
1 ounce	30 mL
1 minim	About 0.06 mL, or roughly 1 drop (gtt)

Example: Weight-based dose

A pediatric patient weighs 44 lb, and the provider orders 10 mg/kg. What is the correct dose in milligrams?

Convert the patient’s weight to kilograms: $44 \div 2.2 = 20$ kg

Multiply by the ordered dose per kilogram: $20 \times 10 = 200$ mg

Answer: 200 mg

Example: Household-to-metric conversion

A provider orders 2 teaspoons of a liquid medication for a patient to take at home. How many milliliters is that?

Each teaspoon equals 5 mL: $2 \times 5 = 10$ mL

Answer: 10 mL

Temperature conversion

Medical assistants also convert between Fahrenheit (°F) and Celsius (°C) when documenting patient temperatures.

$C = (F - 32) \times \frac{5}{9}$

$F = (C \times \frac{9}{5}) + 32$

Here, $F$ is the temperature in degrees Fahrenheit and $C$ is the temperature in degrees Celsius.

Example: Converting Fahrenheit to Celsius

A patient’s temperature reads 102°F. What is this in Celsius?

$C = (102 - 32) \times \frac{5}{9} = 70 \times \frac{5}{9} = 38.9$

Answer: 38.9°C (rounded to the nearest tenth)

Decimal-to-percentage conversion

To convert a decimal to a percentage, multiply by 100 and add a percent sign: $0.75 \times 100 = 75%$ .

Key points

Healthcare rules when writing numbers

Use correct unit abbreviations with space, no period (e.g., 2 mg, 10 mL)
Write fractions as decimals; use leading zero if <1 (e.g., 0.5 mg, 0.2 mL)
Do not add trailing zero after whole numbers (e.g., 2 mL, not 2.0 mL)

Rounding numbers

Round to nearest tenth (one decimal place)
If next digit is 5 or more, round up; if 4 or less, round down

Roman numerals

Know basic Roman numerals (i, v, x, l, c, d, m)
Used occasionally in medication orders, often in lowercase

Measurement systems

Three systems: apothecary, household, metric
Metric system is most accurate and preferred in healthcare

Apothecary system

Oldest system; uses grains (gr) for weight, minims for volume
Abbreviations before Roman numerals (e.g., gr v)
Largely replaced by metric system

Household system

Common abbreviations: gtt (drop), tsp (teaspoon), tbsp (tablespoon), fl oz (fluid ounce), oz (ounce), qt (quart), pt (pint), lb (pound)
Used for patient instructions, less precise than metric

Converting between household and metric equivalents

Use proportion method: set up equivalent fractions, cross-multiply, then divide
Keep units and labels consistent on both sides of equation

Metric system

Weight: grams (g); Volume: liters (L); Length: meters (m)
Convert within the same base unit (e.g., g to mg, cm to mm)
Use proportion method for conversions (e.g., 1 g = 1000 mg)

Temperature conversion

Fahrenheit to Celsius: (°F − 32) ÷ 1.8 = °C
Celsius to Fahrenheit: (°C × 1.8) + 32 = °F
Round answers to nearest tenth

Medical math and dosage calculations

The following sections present guidelines for writing and calculating dosages. The medical assistant should always verify answers for dose calculations with a co-worker or the provider.

Healthcare rules when writing numbers

With medications, it is important to be accurate in calculating and documenting amounts. There are three rules to follow when writing medication dosages in healthcare:

Rule 1: Use the correct unit abbreviation

Follow the number with the correct abbreviation for the unit of measure. Leave a space between the number and the abbreviation. Do not use a period with the abbreviations.

Correct examples

2 mg

10 mL

Incorrect examples

2 mg.

10mL

Rule 2: Write fractions as decimals

Write a fraction of a dose as a decimal.

Correct examples

0.2 mg

0.5 mg

Rule 3: Use a leading zero, never a trailing zero

Correct examples

0.75 mcg

0.2 mL

2 mL

5 mL

Incorrect examples

.75 mcg

.2 mL

2.0 mL

5.0 mL

Rounding numbers

When you calculate answers, sometimes the number needs to be rounded.

Steps for rounding

Find the place value where you want to end up.
Look at the number to the right of the place value.
- 4 or below → drop the remaining digits.
- 5 or above → add 1 to the rounded digit and drop the remaining digits.

Examples

Example 1

$569.365$

The 3 is in the tenths place. The next digit is 6, so round up.

Answer: 569.4

Example 2

$339.926$

The 9 is in the tenths place. The next digit is 2, so drop the remaining digits.

Answer: 339.9

Measurement systems and conversions

Metric equivalents

Unit	Equivalent
1 kilogram (kg)	1000 grams (g)
1 gram (g)	1000 milligrams (mg)
1 milligram (mg)	1000 micrograms (mcg)
1 liter (L)	1000 milliliters (mL)
1 milliliter (mL)	1 cubic centimeter (cc)
1 meter (m)	100 centimeters (cm)
1 centimeter (cm)	10 millimeters (mm)

Household and metric equivalents

Household	Metric
1 teaspoon (tsp)	5 mL
1 tablespoon (tbsp), or 3 teaspoons	15 mL
1 fluid ounce (fl oz), or 2 tablespoons	30 mL
1 cup, or 8 fluid ounces	240 mL
1 pint, or 2 cups	480 mL
1 quart, or 2 pints	960 mL
2.2 pounds (lb)	1 kilogram (kg)
1 inch	2.54 cm

Apothecary equivalents

Apothecary	Metric or household
1 grain (gr)	60 mg in most medical assisting references, 65 mg in some (which is why aspirin gr V is labelled 325 mg). Use one or the other throughout a calculation, never both
1 dram	4 mL, or about 1 teaspoon
1 ounce	30 mL
1 minim	About 0.06 mL, or roughly 1 drop (gtt)

Example: Weight-based dose

A pediatric patient weighs 44 lb, and the provider orders 10 mg/kg. What is the correct dose in milligrams?

Convert the patient’s weight to kilograms: $44 \div 2.2 = 20$ kg

Multiply by the ordered dose per kilogram: $20 \times 10 = 200$ mg

Answer: 200 mg

Example: Household-to-metric conversion

A provider orders 2 teaspoons of a liquid medication for a patient to take at home. How many milliliters is that?

Each teaspoon equals 5 mL: $2 \times 5 = 10$ mL

Answer: 10 mL

Temperature conversion

Medical assistants also convert between Fahrenheit (°F) and Celsius (°C) when documenting patient temperatures.

$C = (F - 32) \times \frac{5}{9}$

$F = (C \times \frac{9}{5}) + 32$

Here, $F$ is the temperature in degrees Fahrenheit and $C$ is the temperature in degrees Celsius.

Example: Converting Fahrenheit to Celsius

A patient’s temperature reads 102°F. What is this in Celsius?

$C = (102 - 32) \times \frac{5}{9} = 70 \times \frac{5}{9} = 38.9$

Answer: 38.9°C (rounded to the nearest tenth)

Decimal-to-percentage conversion

To convert a decimal to a percentage, multiply by 100 and add a percent sign: $0.75 \times 100 = 75%$ .