Nursing Math & Dosage Foundations · Master Study Guide

Rapid-Review Reference Sheets

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On this page 4 sections
  1. In 30 seconds
  2. The college version
  3. Study tools
  4. Sources & references

In 30 seconds

Move the decimal three places per metric step among g–mg–mcg and L–mL.

The college version

1. Conversion Chart

ConversionValueType
1 kg≈ 2.2 lbrounded (nursing convention)
1 tsp5 mLexact
1 tbsp15 mLexact
1 fl oz≈ 30 mLrounded (nursing convention)
1 L1000 mLexact
1 g1000 mgexact
1 mg1000 mcgexact
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

PurposeFormula
Basic doseDesired / Have × Quantity = Amount (D/H × Q = X)
Pump ratemL/hr = Total Volume (mL) ÷ Total Time (hr)
Gravity dripgtt/min = [Volume (mL) × Drop Factor (gtt/mL)] ÷ Time (min)
Weightkg = lb ÷ 2.2
Concentrationmg/mL = total mg ÷ total mL

3. Dimensional-Analysis Checklist

  1. Identify the wanted unit (e.g., mL, gtt/min, mL/hr).
  2. Start with the given quantity or an appropriate conversion factor.
  3. Arrange factors so unwanted units cancel (numerator ↔ denominator).
  4. Keep going until only the wanted unit remains.
  5. Multiply numerators, multiply denominators, divide.
  6. Round only at the final step per the stated rule.
  7. Attach the correct unit.
  8. 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)

  1. Convert weight: kg = lb ÷ 2.2 (round to nearest tenth if instructed).
  2. Identify whether the range is per dose or per day.
  3. Calculate minimum safe dose.
  4. Calculate maximum safe dose.
  5. Multiply by doses/day if the range is daily.
  6. Compare the ordered dose (per dose and per day) to the range.
  7. Conclude SAFE or UNSAFE; only then calculate administration volume if asked.

7. Critical-Care Drip Workflow

Order → pump rate (mL/hr):

  1. Convert to a common time base (per min or per hr).
  2. Multiply by weight (kg) for kg-based orders (mcg/kg/min, mg/kg/hr).
  3. Convert drug mass to volume using concentration (mg/mL or mcg/mL).
  4. Ensure only mL/hr remains.

Pump rate → actual dose (reverse):

  1. mL/hr → drug/hr using concentration.
  2. ÷ weight (kg).
  3. 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):

AvoidUse
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 / MgSO4spell 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.

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Sources & references

  1. The Joint Commission — "Do Not Use" List of Abbreviations.
  2. ISMP (Institute for Safe Medication Practices) — List of Error-Prone Abbreviations, Symbols, and Dose Designations.
  3. ISMP — High-Alert Medications in Acute Care Settings.
  4. FDA — Medication Guides / drug labeling.
  5. USP — General Chapter <7> Labeling and pharmaceutical compounding references (as applicable).
  6. CDC — Vaccine administration / injection-safety references (as applicable).
  7. Official manufacturer labeling — drug-specific concentrations, reconstitution, stability, and beyond-use information (accessed per drug via DailyMed).

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