Nursing Math & Dosage Foundations · Master Study Guide
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Move the decimal three places per metric step among g–mg–mcg and L–mL.
The college version
1. Conversion Chart
| Conversion | Value | Type |
|---|---|---|
| 1 kg | ≈ 2.2 lb | rounded (nursing convention) |
| 1 tsp | 5 mL | exact |
| 1 tbsp | 15 mL | exact |
| 1 fl oz | ≈ 30 mL | rounded (nursing convention) |
| 1 L | 1000 mL | exact |
| 1 g | 1000 mg | exact |
| 1 mg | 1000 mcg | exact |
| 1 lb | ≈ 0.45 kg (16 oz) | rounded |
Move the decimal three places per metric step among g–mg–mcg and L–mL.
2. Major Formulas
| Purpose | Formula |
|---|---|
| Basic dose | Desired / Have × Quantity = Amount (D/H × Q = X) |
| Pump rate | mL/hr = Total Volume (mL) ÷ Total Time (hr) |
| Gravity drip | gtt/min = [Volume (mL) × Drop Factor (gtt/mL)] ÷ Time (min) |
| Weight | kg = lb ÷ 2.2 |
| Concentration | mg/mL = total mg ÷ total mL |
3. Dimensional-Analysis Checklist
- Identify the wanted unit (e.g., mL, gtt/min, mL/hr).
- Start with the given quantity or an appropriate conversion factor.
- Arrange factors so unwanted units cancel (numerator ↔ denominator).
- Keep going until only the wanted unit remains.
- Multiply numerators, multiply denominators, divide.
- Round only at the final step per the stated rule.
- Attach the correct unit.
- Reasonableness check — is the number clinically plausible?
4. Rounding Reminders
- Tablets/capsules → whole or half tablet (only if safe/splittable).
- Oral liquids → nearest tenth or hundredth (device-dependent; state which).
- mL/hr (pump) → whole or tenth (state which).
- gtt/min → whole drop.
- Weight (lb→kg) → nearest tenth only when the question says so.
- No intermediate rounding unless explicitly required.
5. IV Flow-Rate Formulas
- mL/hr = mL ÷ hr (convert minutes to hours first: min ÷ 60).
- gtt/min = (mL × drop factor) ÷ min.
- Completion time = start time + duration.
- Remaining volume = total − infused; time remaining = remaining mL ÷ mL/hr.
6. Pediatric Safe-Range Workflow (7 steps)
- Convert weight: kg = lb ÷ 2.2 (round to nearest tenth if instructed).
- Identify whether the range is per dose or per day.
- Calculate minimum safe dose.
- Calculate maximum safe dose.
- Multiply by doses/day if the range is daily.
- Compare the ordered dose (per dose and per day) to the range.
- Conclude SAFE or UNSAFE; only then calculate administration volume if asked.
7. Critical-Care Drip Workflow
Order → pump rate (mL/hr):
- Convert to a common time base (per min or per hr).
- Multiply by weight (kg) for kg-based orders (mcg/kg/min, mg/kg/hr).
- Convert drug mass to volume using concentration (mg/mL or mcg/mL).
- Ensure only mL/hr remains.
Pump rate → actual dose (reverse):
- mL/hr → drug/hr using concentration.
- ÷ weight (kg).
- Convert time base back to the requested unit (mcg/kg/min).
8. Medication-Order Safety Checklist
- Verify the order is complete (drug, dose, route, frequency, duration).
- Verify the medication label against the order (drug, strength, concentration).
- Compare against appropriate dosing references / safe ranges.
- Consider maximum doses and high-alert status.
- Confirm patient weight (reweigh if uncertain, especially pediatrics).
- Clarify any ambiguous, incomplete, or unsafe order before giving.
- Use the correct measuring device (oral syringe, calibrated cup, insulin syringe).
- Independent double-check high-alert drugs per facility policy.
9. High-Risk Abbreviation Reminders
The Joint Commission "Do Not Use" (must not be used):
| Avoid | Use |
|---|---|
| U | "unit" |
| IU | "international units" |
| Q.D., QD, q.d., qd | "daily" |
| Q.O.D., QOD, q.o.d., qod | "every other day" |
| trailing zero (X.0 mg) | X mg |
| missing leading zero (.X mg) | 0.X mg |
| MS / MSO4 / MgSO4 | spell out "morphine sulfate" / "magnesium sulfate" |
Broader ISMP error-prone items (avoid where possible): µg (use "mcg"), cc (use "mL"), HS (use "half-strength" or "at bedtime" spelled out), @, >, <.
The Joint Commission list is the required minimum; ISMP's list is broader recommended practice. Always follow facility policy.
Study tools & related lessonsRelated
Sources & references
- The Joint Commission — "Do Not Use" List of Abbreviations.
- ISMP (Institute for Safe Medication Practices) — List of Error-Prone Abbreviations, Symbols, and Dose Designations.
- ISMP — High-Alert Medications in Acute Care Settings.
- FDA — Medication Guides / drug labeling.
- USP — General Chapter <7> Labeling and pharmaceutical compounding references (as applicable).
- CDC — Vaccine administration / injection-safety references (as applicable).
- Official manufacturer labeling — drug-specific concentrations, reconstitution, stability, and beyond-use information (accessed per drug via DailyMed).
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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