Write the given quantity with its unit and the unit you want.
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.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
2Practice problems
1.Dosage calculationsMedium
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
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
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
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
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
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
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.
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
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
115:05
203:05
314:05
416:05
10.Nursing math & unit conversionsHard
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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