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Medication Dosage
Calculations

Master the formula method and dimensional analysis to deliver safe, accurate medication doses every time.

NCLEX-RN

Why Dosage Math Matters

Medication errors are a leading cause of patient harm. A misplaced decimal or wrong conversion can mean a 10-fold overdose. As a nurse, you are the last safety check before a drug reaches the patient.

Three Key Terms

Desired (D)
The dose the provider ordered for the patient.
On Hand (H)
The strength of the drug available in stock.
Quantity (Q)
The volume or form that holds the on-hand dose.

Know Your Conversions

Before calculating, the desired dose and on-hand dose must be in the same unit. Memorize these high-yield conversions:

FromToFactor
1 gram (g)milligrams (mg)1000 mg
1 milligram (mg)micrograms (mcg)1000 mcg
1 kilogram (kg)pounds (lb)2.2 lb
1 liter (L)milliliters (mL)1000 mL
1 teaspoon (tsp)milliliters (mL)5 mL

The Core Formula

$$ \frac{D}{H} \times Q = \text{Amount to Give} $$
 "Desired over Have, times Quantity" D = Desired   H = On Hand   Q = Quantity

Method Two: Dimensional Analysis

Dimensional analysis multiplies the order by conversion factors so that unwanted units cancel, leaving only the unit you want to administer.

$$ \text{Order} \times \frac{\text{Quantity}}{\text{On Hand}} = \text{Amount} $$
 Set up so the unwanted unit appears in both numerator and denominator

Formula vs. Dimensional Analysis

Formula MethodDimensional Analysis
Setup\( \frac{D}{H} \times Q \)Chain of fractions
Unit handlingConvert firstCancels along the way
SpeedFast for simple problemsBest for multi-step
Error catchingManual unit checkWrong units flag setup error

Step-by-Step Approach

1
Read the order. Identify what is desired (\(D\)).
2
Read the label. Identify the dose on hand (\(H\)) and its quantity (\(Q\)).
3
Match the units. Convert \(D\) and \(H\) to the same unit.
4
Plug into \( \frac{D}{H} \times Q \) and solve.
5
Sanity check. Is the answer a reasonable amount to give?

Worked Example 1

Order: Give 750 mg of amoxicillin. On hand: 250 mg capsules. How many capsules?

$$ \frac{750\ \text{mg}}{250\ \text{mg}} \times 1\ \text{cap} = 3\ \text{caps} $$

Worked Example 2

Order: Give 0.5 g of a drug. On hand: 250 mg per 5 mL. How many mL?

$$ 0.5\ \text{g} = 500\ \text{mg} \quad(\text{convert first}) $$
$$ \frac{500\ \text{mg}}{250\ \text{mg}} \times 5\ \text{mL} = 10\ \text{mL} $$

Worked Example 3

Order: \(5 \text{ mg/kg/day}\) for a 44 lb child, given once daily. On hand: 100 mg per 5 mL. How many mL per dose?

$$ 44\ \text{lb} \div 2.2 = 20\ \text{kg} $$
$$ 20\ \text{kg} \times 5\ \frac{\text{mg}}{\text{kg}} = 100\ \text{mg} $$
$$ \frac{100\ \text{mg}}{100\ \text{mg}} \times 5\ \text{mL} = 5\ \text{mL} $$

IV Flow Rate Formula

For IV infusions, calculate drops per minute (gtt/min) using the volume, the drop factor, and the time:

$$ \text{gtt/min} = \frac{\text{Volume (mL)} \times \text{Drop factor}}{\text{Time (min)}} $$

Common Mistakes

✕ Mismatched Units
Plugging in mg over g without converting. Always match first.
✕ Decimal Errors
Misplacing the decimal causes 10× or 100× dose errors.
✕ Skipping the Check
Failing to ask if the answer is reasonable to administer.
✕ Rounding Too Early
Round only at the final step to keep accuracy.

Quick Reference

GoalFormula
Tablets / mL to give\( \frac{D}{H} \times Q \)
Weight-based dose\( \text{kg} \times \text{mg/kg} \)
lb to kg\( \text{lb} \div 2.2 \)
IV drip rate\( \frac{V \times \text{gtt/mL}}{t} \)
g to mg\( \times 1000 \)

Before You Test

Question 1 of 5

Order: 500 mg. On hand: 250 mg tablets. How many tablets?

Question 2 of 5

Order: 1 g. On hand: 500 mg per 5 mL. How many mL?

Question 3 of 5

A patient weighs 66 lb. What is the weight in kilograms?

Question 4 of 5

Order: 0.125 mg. On hand: 0.25 mg tablets. How many tablets?

Question 5 of 5

Infuse 500 mL over 4 hours with a 20 gtt/mL drop factor. What is the rate in gtt/min?