Key Takeaways
- The metric system uses base units: gram (mass), liter (volume), meter (length) with prefixes kilo-, centi-, milli-, micro-
- Key nursing conversions: 1 kg = 2.2 lbs, 1 inch = 2.54 cm, 1 oz = 30 mL, 1 tsp = 5 mL, 1 tbsp = 15 mL
- Dimensional analysis (factor-label method) is the safest way to convert between units — multiply by conversion factors until unwanted units cancel
- Temperature conversion: F = (C x 9/5) + 32 and C = (F - 32) x 5/9
- The dosage formula: Desired dose / Available dose x Quantity = Amount to administer
- Weight-based dosing requires converting patient weight from pounds to kilograms first (divide by 2.2)
- Military (24-hour) time is used in healthcare: add 12 to PM hours (e.g., 3:00 PM = 15:00)
- Roman numerals are still used in some prescriptions: I=1, V=5, X=10, L=50, C=100, D=500, M=1000
Dosage Calculations & Unit Conversions
Accurate dosage calculations and unit conversions are among the most important skills for nursing students. Errors in medication dosing can have life-threatening consequences, which is why the HESI A2 tests these skills thoroughly.
The Metric System
The metric system is the standard measurement system in healthcare. Understanding metric prefixes is essential:
| Prefix | Symbol | Meaning | Example |
|---|---|---|---|
| kilo- | k | 1,000 | 1 kg = 1,000 g |
| hecto- | h | 100 | 1 hg = 100 g |
| deka- | da | 10 | 1 dag = 10 g |
| (base) | — | 1 | gram, liter, meter |
| deci- | d | 0.1 | 1 dg = 0.1 g |
| centi- | c | 0.01 | 1 cm = 0.01 m |
| milli- | m | 0.001 | 1 mg = 0.001 g |
| micro- | mc (mcg) | 0.000001 | 1 mcg = 0.000001 g |
Essential Nursing Conversions
| Conversion | Value |
|---|---|
| 1 kilogram (kg) | 2.2 pounds (lbs) |
| 1 inch (in) | 2.54 centimeters (cm) |
| 1 ounce (oz) | 30 milliliters (mL) |
| 1 teaspoon (tsp) | 5 mL |
| 1 tablespoon (tbsp) | 15 mL (3 tsp) |
| 1 cup | 240 mL (8 oz) |
| 1 pint | 480 mL (16 oz) |
| 1 quart | 960 mL (32 oz) |
| 1 liter (L) | 1,000 mL |
| 1 gram (g) | 1,000 milligrams (mg) |
| 1 milligram (mg) | 1,000 micrograms (mcg) |
Dimensional Analysis (Factor-Label Method)
Dimensional analysis uses conversion factors to systematically convert between units. Units you want to eliminate are placed so they cancel out.
Example: Convert 165 lbs to kg
165 lbs x (1 kg / 2.2 lbs) = 165 / 2.2 = 75 kg
Example: Convert 3 cups to mL
3 cups x (240 mL / 1 cup) = 720 mL
Multi-step Example: A patient drinks 2.5 pints of water. How many liters is this?
2.5 pints x (480 mL / 1 pint) x (1 L / 1000 mL) = 1200 / 1000 = 1.2 L
Dosage Formula
The basic dosage formula helps calculate how much medication to administer:
Desired / Have x Quantity = Amount to Give
- Desired (D): The dose ordered by the provider
- Have (H): The dose available (on the medication label)
- Quantity (Q): The form it comes in (1 tablet, 5 mL, etc.)
Example: The provider orders 500 mg of amoxicillin. The pharmacy supplies 250 mg capsules. How many capsules should you give?
D/H x Q = 500 mg / 250 mg x 1 capsule = 2 capsules
Example: The provider orders 150 mg of a liquid medication. The available concentration is 100 mg per 5 mL. How many mL should you administer?
D/H x Q = 150 / 100 x 5 mL = 7.5 mL
Temperature Conversions
| Direction | Formula | Example |
|---|---|---|
| Celsius to Fahrenheit | F = (C x 9/5) + 32 | 37C = (37 x 1.8) + 32 = 98.6F |
| Fahrenheit to Celsius | C = (F - 32) x 5/9 | 101.3F = (101.3 - 32) x 0.556 = 38.5C |
Key reference temperatures:
- Normal body temperature: 98.6F / 37C
- Water freezing: 32F / 0C
- Water boiling: 212F / 100C
- Fever threshold: 100.4F / 38C
Military (24-Hour) Time
Healthcare facilities use 24-hour time to prevent AM/PM confusion:
| Standard Time | Military Time | Rule |
|---|---|---|
| 12:00 AM (midnight) | 0000 | |
| 1:00 AM | 0100 | |
| 12:00 PM (noon) | 1200 | |
| 1:00 PM | 1300 | Add 12 to PM hours |
| 6:30 PM | 1830 | |
| 11:45 PM | 2345 |
Roman Numerals
| Roman | Value | Roman | Value |
|---|---|---|---|
| I | 1 | L | 50 |
| V | 5 | C | 100 |
| X | 10 | D | 500 |
| M | 1,000 |
Rule: A smaller numeral before a larger one means subtraction. Example: IX = 9 (10 - 1), XL = 40 (50 - 10).
Weight-Based Dosing
Many medications are dosed based on patient weight in kilograms. This is especially common in pediatrics and critical care.
Steps for weight-based dosing:
- Convert the patient's weight from pounds to kilograms (divide by 2.2)
- Calculate the dose: Patient weight (kg) x Dose per kg = Total dose
- Determine how much to administer using the available concentration
Example: A child weighs 44 lbs. The provider orders amoxicillin 25 mg/kg/day in 2 divided doses. Available: 250 mg/5 mL suspension.
- Weight: 44 lbs / 2.2 = 20 kg
- Total daily dose: 20 kg x 25 mg/kg = 500 mg/day
- Per dose: 500 / 2 = 250 mg per dose
- Volume: 250 mg / (250 mg/5 mL) = 5 mL per dose
IV Flow Rate Calculations
Nurses frequently calculate IV drip rates:
Drip Rate (drops/min) = (Volume in mL x Drop Factor) / Time in minutes
Common Drop Factors:
| IV Tubing Type | Drop Factor |
|---|---|
| Macrodrip | 10, 15, or 20 drops/mL |
| Microdrip | 60 drops/mL |
Example: Infuse 1,000 mL of NS over 8 hours using tubing with a drop factor of 15 drops/mL.
- Time in minutes: 8 hours x 60 = 480 minutes
- Drip rate = (1,000 mL x 15 drops/mL) / 480 min = 15,000 / 480 = 31.25 ≈ 31 drops/min
Intake and Output (I&O) Calculations
Nurses track patient fluid intake and output:
Intake includes: IV fluids, oral fluids, tube feedings, blood products Output includes: Urine, drainage, emesis, blood loss
Example: During one shift, a patient received:
- IV: 500 mL
- Oral intake: 240 mL (1 cup) + 180 mL + 120 mL
- Total intake: 500 + 240 + 180 + 120 = 1,040 mL
Output: 450 mL urine + 100 mL drainage = 550 mL
Net fluid balance: 1,040 - 550 = +490 mL (positive balance)
Temperature Conversions
Healthcare uses both Fahrenheit (°F) and Celsius (°C). You must know how to convert between them:
| Formula | Direction |
|---|---|
| °F = (°C x 9/5) + 32 | Celsius to Fahrenheit |
| °C = (°F - 32) x 5/9 | Fahrenheit to Celsius |
Key reference temperatures:
| Temperature | °F | °C |
|---|---|---|
| Water freezes | 32°F | 0°C |
| Normal body temperature | 98.6°F | 37°C |
| Water boils | 212°F | 100°C |
| Fever threshold | 100.4°F | 38°C |
| Hypothermia threshold | 95°F | 35°C |
Conversion examples:
- Patient temp 102.2°F → °C = (102.2 - 32) x 5/9 = 70.2 x 5/9 = 39°C (fever)
- Lab temp 25°C → °F = (25 x 9/5) + 32 = 45 + 32 = 77°F (room temperature)
Order of Operations (PEMDAS)
When solving math expressions with multiple operations, follow PEMDAS:
| Letter | Operation | Example |
|---|---|---|
| P | Parentheses | Solve (3 + 2) first |
| E | Exponents | Then 4^2 |
| M/D | Multiplication/Division (left to right) | Then 6 x 3 or 12 / 4 |
| A/S | Addition/Subtraction (left to right) | Then 5 + 3 or 10 - 2 |
Example: Solve 3 + 4 x (2 + 1)^2 / 6
- Parentheses: (2 + 1) = 3
- Exponents: 3^2 = 9
- Multiplication: 4 x 9 = 36
- Division: 36 / 6 = 6
- Addition: 3 + 6 = 9
Common mistake: Adding before multiplying. In 3 + 4 x 2, the answer is 11 (not 14).
A patient weighs 176 pounds. What is their weight in kilograms?
Convert 101.3°F to Celsius.
A provider orders 750 mg of a medication. The available tablets are 250 mg each. How many tablets should be administered?
There are _____ milliliters in one teaspoon.
Type your answer below
What is 3:45 PM in military (24-hour) time?
Match each measurement conversion to its correct value.
Match each item on the left with the correct item on the right
How many milliliters are in 2.5 liters?