Med math
Dosage Calculation Practice Problems With Answers
These dosage calculation practice problems with answers cover every type nursing school and the NCLEX use: tablets, liquids, injections, IV pump rates, gravity drip rates, weight-based and pediatric divided doses, reconstitution and infusion time. Each one is worked with dimensional analysis, a single method that handles all of them, so you can check your setup as well as your answer.
Try each problem before reading the solution. The numbers are practice numbers, not doses to use at work. After the problems you will find the NCLEX rounding rules, the conversions to memorize and two calculation questions from the RN Basics bank.
How dimensional analysis works
Dimensional analysis writes the problem as one chain of fractions. Start with what was ordered, multiply by conversion factors arranged so each unit cancels the one before it, and stop when the only unit left is the unit of the answer (tablets, mL, mL/h or gtt/min). If a unit does not cancel, the setup is wrong before you touch the calculator.
- Write the answer unit first, so you know where you are going.
- Start with the order (for example 0.5 g).
- Convert units if the order and the supply differ (g to mg, lb to kg).
- Multiply by the supply as a fraction (1 tab per 250 mg, or 5 mL per 125 mg).
- Cancel units, then do the arithmetic once and round at the end.
- Ask whether the answer makes sense: four tablets or 12 mL for one injection means recheck.
Dosage calculation practice problems: oral and injection doses
1. Tablets with a unit conversion
Order: 0.5 g by mouth. On hand: 250 mg tablets. How many tablets? Setup: 0.5 g × 1,000 mg/1 g × 1 tab/250 mg. Grams cancel, milligrams cancel. Answer: 2 tablets.
2. Micrograms to milligrams
Order: 0.1 mg by mouth. On hand: 50 mcg tablets. Setup: 0.1 mg × 1,000 mcg/1 mg × 1 tab/50 mcg = 100 ÷ 50. Answer: 2 tablets. Mixing up mg and mcg is a 1,000-fold error, so convert before anything else.
3. Oral liquid
Order: 375 mg by mouth. On hand: 125 mg per 5 mL. Setup: 375 mg × 5 mL/125 mg = 1,875 ÷ 125. Answer: 15 mL.
4. Injection under 1 mL
Order: 4 mg IM. On hand: 10 mg/mL. Setup: 4 mg × 1 mL/10 mg. Answer: 0.4 mL, written with a leading zero.
IV rate practice problems: mL/h and gtt/min
5. Pump rate in mL/h
Order: 1,000 mL over 6 hours by pump. Setup: 1,000 mL/6 h = 166.666. Answer: 167 mL/h (pumps are usually set in whole mL/h unless the item asks for decimals).
6. Piggyback over minutes
Order: 100 mL over 30 minutes. Setup: 100 mL/30 min × 60 min/1 h. Answer: 200 mL/h.
7. Gravity drip with a drop factor
Order: 1,000 mL over 8 hours. Tubing: 20 gtt/mL. Setup: 1,000 mL/8 h × 1 h/60 min × 20 gtt/1 mL = 20,000 ÷ 480 = 41.67. Answer: 42 gtt/min (you cannot count part of a drop).
8. Microdrip tubing
Order: 50 mL/h. Tubing: 60 gtt/mL. Setup: 50 mL/1 h × 1 h/60 min × 60 gtt/1 mL. Answer: 50 gtt/min. With 60 gtt/mL tubing, gtt/min always equals mL/h.
| Tubing (drop factor) | Shortcut from mL/h to gtt/min |
|---|---|
| 10 gtt/mL | mL/h ÷ 6 |
| 15 gtt/mL | mL/h ÷ 4 |
| 20 gtt/mL | mL/h ÷ 3 |
| 60 gtt/mL (microdrip) | Same number as mL/h |
Weight-based and pediatric dose problems
9. Weight-based dose
Order: 2 mg/kg IV. Client: 154 lb. On hand: 40 mg/mL. Setup: 154 lb × 1 kg/2.2 lb × 2 mg/kg × 1 mL/40 mg. Steps: 70 kg, then 140 mg, then 3.5 mL. Answer: 3.5 mL.
10. Pediatric mg/kg/day in divided doses
Safe range: 30 to 50 mg/kg/day divided every 8 hours. Child: 33 lb. Order: 200 mg every 8 hours. On hand: 125 mg per 5 mL. Is the dose safe, and how many mL per dose?
- Weight: 33 lb ÷ 2.2 = 15 kg.
- Daily range: 30 × 15 = 450 mg to 50 × 15 = 750 mg per day.
- Per dose (every 8 hours is 3 doses a day): 150 to 250 mg.
- Ordered 200 mg per dose is inside the range, so it is safe to give.
- Volume: 200 mg × 5 mL/125 mg = 8 mL.
A child weighing 22 kg is prescribed amoxicillin 45 mg/kg/day divided into two doses. The suspension contains 400 mg per 5 mL. How many milliliters should the nurse give per dose?
- 2.5 mL
- 6.2 mL
- 12.4 mL
- 3.1 mL
Show the answer and rationale
Answer: B
- A. Incorrect calculation.
- B. Correct. 45 × 22 = 990 mg/day; ÷ 2 = 495 mg/dose; 495 ÷ 400 × 5 = 6.19 mL, rounded to 6.2 mL.
- C. That is the whole day’s dose.
- D. That is half a dose.
Weight-based pediatric dosing: multiply mg/kg/day by weight, divide by the number of doses, then convert to volume using the concentration. Round to the nearest tenth for volumes over 1 mL and hundredth for volumes under 1 mL, use an oral syringe, and check the result against the safe dose range.
Bottom line: For pediatric doses, multiply mg/kg/day by weight, divide by doses per day, convert to volume, and check against the safe range.
Sources: Wong's Care of Infants & Children, 12th ed.; Potter & Perry Fundamentals, 12th ed.
Walk-through: the order is per day, so find the daily total first (weight times mg/kg/day), split it into the number of doses, and only then convert to mL with the concentration. The wrong answers come from skipping the split or using the whole day's dose.
Reconstitution, heparin and infusion time
11. Reconstituted powder
A 2 g vial label says: add diluent to make 10 mL. Order: 750 mg. Concentration: 2,000 mg/10 mL = 200 mg/mL. Setup: 750 mg × 1 mL/200 mg = 3.75. Answer: 3.8 mL. Use the final concentration on the label, not the volume of diluent, because the powder adds volume.
12. Units per hour to mL/h
Bag: 25,000 units in 500 mL. Order: 1,000 units/h. Concentration: 50 units/mL. Setup: 1,000 units/h × 1 mL/50 units. Answer: 20 mL/h.
A heparin infusion of 25,000 units in 250 mL of dextrose 5% is running at 12 mL per hour. How many units per hour is the client receiving?
- 2,400 units per hour
- 600 units per hour
- 120 units per hour
- 1,200 units per hour
Show the answer and rationale
Answer: D
- A. Double the correct value.
- B. Half the correct value.
- C. Off by a factor of 10.
- D. Correct. 25,000 ÷ 250 = 100 units/mL; 100 × 12 = 1,200 units/h.
Weight-based heparin protocols: bolus (80 units/kg), initial infusion (18 units/kg/h), aPTT or anti-Xa every 6 hours until therapeutic, then daily, with rate adjustments per nomogram. Calculate the concentration (units/mL) first, then multiply by the rate; independent double checks are required for every change.
Bottom line: To find units per hour, calculate the concentration in units/mL first, then multiply by the infusion rate in mL/h.
Sources: Potter & Perry Fundamentals, 12th ed.; Lehne's Pharmacology for Nursing, 12th ed.
Walk-through: this one runs backward, from the pump rate to the dose. Find units per mL from the bag, then multiply by the mL per hour. Checking the dose a running infusion delivers is a routine safety step at handoff.
13. Infusion time
1,000 mL running at 125 mL/h, started at 0700. Time: 1,000 ÷ 125 = 8 hours. Answer: it finishes at 1500. When the answer has a decimal, multiply the decimal by 60 to get minutes: 6.5 hours is 6 hours 30 minutes.
Rounding rules and conversions
- NCLEX: round once, at the end of the calculation, never at each step.
- NCLEX: the item tells you whether to answer with a whole number or one or two decimal places; when decimals are asked, the decimal point must be entered.
- When nothing is stated, follow your program's or agency's rule. A common one: volumes over 1 mL to tenths, under 1 mL to hundredths; drops to whole numbers.
- Write a leading zero (0.4 mL, not .4 mL) and no trailing zero (2 mg, not 2.0 mg) in orders and notes.
| Unit | Equals |
|---|---|
| 1 kg | 2.2 lb |
| 1 g | 1,000 mg |
| 1 mg | 1,000 mcg |
| 1 L | 1,000 mL |
| 1 tsp / 1 tbsp | 5 mL / 15 mL |
| 1 fl oz | 30 mL |
Frequently asked questions
What is the easiest way to do dosage calculations?
Use one method for everything. Dimensional analysis sets up every problem as a chain of fractions that cancel units, so the same steps work for tablets, drip rates and weight-based doses.
How do you round dosage calculations on the NCLEX?
Round only at the end, to the number of decimal places the item asks for, and type the decimal point when decimals are requested.
What is the formula for drops per minute?
Total mL times the drop factor (gtt/mL), divided by the time in minutes. Round to a whole drop.
How do you calculate a pediatric dose in mg/kg/day?
Convert the weight to kg, multiply by the mg/kg/day to get the daily dose or range, divide by the number of doses per day, then compare with the ordered dose before working out the volume.
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