NCLEX-style dosage calculations: cram pack

Formula sheets, the key method steps for every topic and 10 practice problems, with full solutions at the back.

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1Formulas and methods

Dosage calculations

Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg

Method

  1. Convert the ordered dose and the stock strength to the same unit.
  2. Use desired over have times quantity: (D/H) × Q.
  3. For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
  4. Estimate first and check that the answer is reasonable.

IV infusion rates

Pump rate
mL/h = volume (mL)/time (h)
Drip rate
drops/min = volume (mL) × drop factor / time (min)
Infusion time
time (h) = volume (mL)/rate (mL/h)

Method

  1. Pump rate in mL/h: volume divided by time in hours.
  2. Drip rate in drops/min: volume × drop factor divided by time in minutes.
  3. For time remaining: volume left divided by the rate.
  4. Round as the question or the equipment requires.

Pediatric & critical-care dosing

Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg

IV fluids & fluid balance

Holliday–Segar per hour
4 mL/kg (first 10 kg) + 2 mL/kg (next 10 kg) + 1 mL/kg (each kg above 20)
Holliday–Segar per day
100 / 50 / 20 mL/kg for the same bands
Fluid balance
intake − output
Ice chips
count as half their volume
Urine output
mL/kg/h = mL / (kg × h)
Infusion time
time (h) = volume left (mL) / rate (mL/h)
Volume infused
mL = rate × time

Nursing math & unit conversions

Metric steps
1 kg = 1000 g, 1 g = 1000 mg, 1 mg = 1000 mcg, 1 L = 1000 mL
Weight and length
1 kg = 2.2 lb, 1 lb = 16 oz, 1 in = 2.54 cm, 1 ft = 12 in
Household measures
1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 8 fl oz = 240 mL
Temperature
°C = (°F − 32)·5/9, °F = °C·9/5 + 32
24-hour clock
PM hours 1–11: add 12; 12 AM = 00:xx; 12 PM = 12:xx
Dose rate
mcg/min × 60/1000 = mg/h
Laboratory factors
glucose 1 mmol/L = 18 mg/dL; creatinine 1 mg/dL = 88.4 µmol/L; Hb 1 g/dL = 10 g/L

Method

  1. Write the given quantity with its unit and the unit you want.
  2. Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
  3. Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
  4. Check the direction: a smaller unit gives a bigger number.
  5. Round only the final answer, to the precision the question names.

2Practice problems

1.Dosage calculationsMedium
80 kg20 mg/kg/day2× per dayD = ? mg

A patient weighs 80 kg. The prescribed dose is 20 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?

80 kg20 mg/kg/day2× per day
D = mg
2.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 0.46 mg. The ampoule contains 500 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

0.46 mg500 mcg/mL
V = mL
3.IV infusion ratesMedium
250 mL10 gtt/mL5 h? gtt/min

Infuse 250 mL over 5 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.

250 mL5 h10 gtt/mL
R = gtt/min
4.IV infusion ratesHard
100 mg250 mL24 mL/h? mcg/min

An infusion of 100 mg in 250 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?

100 mg/250 mL24 mL/h
D = mcg/min
5.Pediatric & critical-care dosingMedium
250 units250 mLregular insulin6 mL/h? units/h

Practice exercise (made-up values, not clinical guidance). An infusion of 250 units of regular insulin in 250 mL runs at 6 mL/h. How many units per hour D does the patient receive?

250 units/250 mL6 mL/h
D = units/h
6.Pediatric & critical-care dosingHard
400 mg250 mLdopamine? mL/h107 kg10 mcg/kg/min

Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 10 mcg/kg/min for a patient who weighs 107 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.

400 mg/250 mL10 mcg/kg/min107 kg
R = mL/h
7.IV fluids & fluid balanceMedium
IntakeOutput8-hour shiftjuice100 mLsoup180 mLtea150 mLice chips240 mLIV infusion60 mL/h × 8 hIV antibiotic2 × 50 mLurine175 mLurine325 mLurine150 mLwound drain80 mL

Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss). Count ice chips as half their volume.

juice: 100 mLsoup: 180 mLtea: 150 mLice chips: 240 mLIV infusion: 60 mL/h × 8 hIV antibiotic: 2 × 50 mLurine: 175 mLurine: 325 mLurine: 150 mLwound drain: 80 mL
B = mL
8.IV fluids & fluid balanceHard
500 mL50 mL infused60 mL/h14:00t = ? h

Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 60 mL/h. At 14:00, 50 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.

500 mL50 mL infused60 mL/h
t = h
9.Nursing math & unit conversionsMedium
1234567891011123:05 PM?15:0503:0514:0516:05

Practice exercise (made-up values, not clinical guidance). A dose is charted at 3:05 PM. Which entry is the same time on the 24-hour clock? Click it.

3:05 PM
  1. 115:05
  2. 203:05
  3. 314:05
  4. 416:05
10.Nursing math & unit conversionsHard
2 tbsp? mL1 tsp? mL1 fl oz? mLΣ = ? mL

Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 2 tbsp of liquid supplement, 1 tsp of cough syrup, 1 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.

1 tbsp = 15 mL1 tsp = 5 mL1 fl oz = 30 mL
V = mL

3Solutions

1.Dosage calculations

Answer: D = 800 mg

Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.

Total per day

20·80 = 1600 mg

Per dose

D = 1600/2 = 800 mg

Answer

D = 800 mg
2.Dosage calculations

Answer: V = 0.92 mL

Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.

Same units

0.46 mg = 460 mcg

Volume

V = 460/500 = 0.92 mL

Answer

V = 0.92 mL
3.IV infusion rates

Answer: R = 8 gtt/min

Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.

Time in minutes

5·60 = 300 min

Drip rate

R = 250·10/300 = 8.333 ≈ 8 gtt/min

Answer

R = 8 gtt/min

At the bedside you round to the nearest whole drop: 8 gtt/min.

4.IV infusion rates

Answer: D = 160 mcg/min

Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).

Concentration

100000 mcg/250 mL = 400 mcg/mL

Dose per hour

24·400 = 9600 mcg/h

Dose per minute

D = 9600/60 = 160 mcg/min

Answer

D = 160 mcg/min
5.Pediatric & critical-care dosing

Answer: D = 6 units/h

Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Concentration

250/250 = 1 units/mL

Units per hour

D = 6·1 = 6 units/h

Answer

D = 6 units/h
6.Pediatric & critical-care dosing

Answer: R = 40.1 mL/h

Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Concentration

400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL

Dose per minute and per hour

10·107 = 1070 mcg/min
1070·60 = 64200 mcg/h

Pump rate

R = 64200/1600 = 40.13 ≈ 40.1 mL/h

Answer

R = 40.1 mL/h
7.IV fluids & fluid balance

Answer: B = 400 mL

Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Total intake

oral: 100 + 180 + 150 = 430 mL
ice chips: 240/2 = 120 mL
IV infusion: 60·8 = 480 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1130 mL

Total output

175 + 325 + 150 + 80 = 730 mL

Balance

B = 1130 − 730 = 400 mL

Answer

B = 400 mL

Positive: more fluid went in than came out.

8.IV fluids & fluid balance

Answer: t = 7.5 h

Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Volume left

500 − 50 = 450 mL

Time

t = 450/60 = 7.5 h

Answer

t = 7.5 h

That is about 7 h 30 min, so the bag runs out at about 21:30.

9.Nursing math & unit conversions

Answer: 15:05

24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.

Convert the hour

3 PM → 3 + 12 = 15

Answer

15:05

Answer

15:05
10.Nursing math & unit conversions

Answer: V = 65 mL

Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.

Each item in mL

2 tbsp = 2·15 = 30 mL
1 tsp = 1·5 = 5 mL
1 fl oz = 1·30 = 30 mL

Add

V = 30 + 5 + 30 = 65 mL

Answer

V = 65 mL

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