Ashar Pervaiz31 October 202630 Dosage Calculation Practice Problems, With the Working Shown
Thirty problems below, grouped by type, each with the full working rather than an answer key. Tablets, oral liquids, weight-based doses, infusion rates, drop rates, weight-based infusions, units, safe ranges, percentage and ratio strengths, and reconstitution. Work each one out before opening the answer, because reading a worked solution feels like understanding it and is not the same thing.
Two of the problems are orders that should not be given. They are not mistakes in the set. If you want the conversions to hand while you work, the nursing conversion chart has them, and the dose calculator will check a weight-based answer once you have your own.
How to Get Something Out of These
- Write your answer down before you open the working. An answer you only thought is an answer you cannot check.
- Convert every unit first, then calculate once. Converting midway is where factor errors hide.
- Before checking the arithmetic, ask whether the size of the answer is believable for the thing in your hand.
- If you get one wrong, redo it from the question rather than reading your working back. Re-reading reproduces the original mistake.
Tablets and Capsules
Dose divided by stock strength. The only trap is a unit change between the order and the packet.
1. Ordered: 750 mg. Stock: 250 mg tablets. How many tablets?
750 divided by 250 = 3.
Answer: 3 tablets
2. Ordered: 0.25 mg. Stock: 125 microgram tablets. How many tablets?
Convert first: 0.25 mg is 250 micrograms. Then 250 divided by 125 = 2. Converting after dividing gives 0.002, which is the classic thousandfold slip.
Answer: 2 tablets
3. Ordered: 1.5 g. Stock: 500 mg tablets. How many tablets?
1.5 g is 1,500 mg. 1,500 divided by 500 = 3.
Answer: 3 tablets
Oral Liquids
Dose divided by stock strength, multiplied by the volume that strength comes in. The volume is the step people drop.
4. Ordered: 180 mg. Stock: 125 mg in 5 mL. What volume?
180 divided by 125 = 1.44, multiplied by 5 = 7.2 mL. Reading the label as 125 mg/mL instead of per 5 mL gives 1.44 mL, a dose five times too small.
Answer: 7.2 mL
5. Ordered: 75 mg. Stock: 25 mg/mL. What volume?
75 divided by 25 = 3, multiplied by 1 mL = 3 mL.
Answer: 3 mL
6. Ordered: 400 mg. Stock: 250 mg in 5 mL. What volume?
400 divided by 250 = 1.6, multiplied by 5 = 8 mL.
Answer: 8 mL
Weight-Based Doses
Multiply the per-kilogram dose by the weight in kilograms. Check the weight is in kilograms before anything else.
7. Ordered: 15 mg/kg. Patient weighs 68 kg. What dose?
15 multiplied by 68 = 1,020 mg.
Answer: 1,020 mg
8. Ordered: 0.1 mg/kg. Child weighs 12.4 kg. What dose?
0.1 multiplied by 12.4 = 1.24 mg.
Answer: 1.24 mg
9. Ordered: 5 mg/kg. Patient weighs 154 lb. What dose?
154 divided by 2.2 = 70 kg. 70 multiplied by 5 = 350 mg. Using 154 as kilograms gives 770 mg, more than twice the dose.
Answer: 350 mg
10. Ordered: 20 mg/kg/day in four divided doses. Child weighs 18 kg. What is each dose?
20 multiplied by 18 = 360 mg per day. 360 divided by 4 = 90 mg per dose. Giving the daily total as a single dose is a fourfold overdose.
Answer: 90 mg per dose
Infusion Rates in mL per Hour
Total volume divided by the time in hours.
11. 1,000 mL over 8 hours. What rate?
1,000 divided by 8 = 125 mL/hour.
Answer: 125 mL/hour
12. 500 mL over 90 minutes. What rate?
90 minutes is 1.5 hours. 500 divided by 1.5 = 333.3 mL/hour. Dividing by 90 instead gives 5.6, which is per minute, not per hour.
Answer: 333.3 mL/hour
13. 250 mL over 30 minutes. What rate?
30 minutes is 0.5 hours. 250 divided by 0.5 = 500 mL/hour.
Answer: 500 mL/hour
Drop Rates
Volume multiplied by the drip factor, divided by the time in minutes. The drip factor is printed on the giving set packet, never assumed.
14. 1,000 mL over 8 hours, 20 drops/mL set. How many drops per minute?
8 hours is 480 minutes. 1,000 multiplied by 20 = 20,000, divided by 480 = 41.7, so 42 drops per minute.
Answer: 42 drops/min
15. 500 mL over 4 hours, 15 drops/mL set. How many drops per minute?
4 hours is 240 minutes. 500 multiplied by 15 = 7,500, divided by 240 = 31.3, so 31 drops per minute.
Answer: 31 drops/min
16. 100 mL over 30 minutes, 60 drops/mL microdrip set. How many drops per minute?
100 multiplied by 60 = 6,000, divided by 30 = 200 drops per minute. The arithmetic is right and the answer is unusable: nobody counts 200 drops a minute, which is the calculation telling you this needs a pump.
Answer: 200 drops/min, so use a pump
17. 1,500 mL over 12 hours, 10 drops/mL set. How many drops per minute?
12 hours is 720 minutes. 1,500 multiplied by 10 = 15,000, divided by 720 = 20.8, so 21 drops per minute.
Answer: 21 drops/min
Infusion Time
Volume divided by the rate.
18. 1,000 mL running at 125 mL/hour. How long will it take?
1,000 divided by 125 = 8 hours.
Answer: 8 hours
19. 250 mL running at 60 mL/hour. How long will it take?
250 divided by 60 = 4.17 hours. The decimal is not minutes: 0.17 of an hour is about 10 minutes, so 4 hours 10 minutes.
Answer: 4 hours 10 minutes
Weight-Based Infusions
Two conversions stacked: per-minute to per-hour, and micrograms to milligrams. Do them one at a time.
20. 5 mcg/kg/min for a 70 kg patient. Concentration 1 mg/mL. What rate in mL/hour?
5 multiplied by 70 = 350 mcg/min. Multiplied by 60 = 21,000 mcg/hour. Divided by 1,000 = 21 mg/hour. At 1 mg/mL that is 21 mL/hour.
Answer: 21 mL/hour
21. 3 mcg/kg/min for an 80 kg patient. Concentration 0.8 mg/mL. What rate in mL/hour?
3 multiplied by 80 = 240 mcg/min. Multiplied by 60 = 14,400 mcg/hour, which is 14.4 mg/hour. Divided by 0.8 = 18 mL/hour.
Answer: 18 mL/hour
Units: Insulin and Heparin
Units are not milligrams and do not convert to them. Work from the concentration printed on the vial or bag.
22. Ordered: 36 units of insulin. Stock: 100 units/mL. What volume?
36 divided by 100 = 0.36 mL. Insulin is drawn in an insulin syringe marked in units, so in practice you draw to 36 units rather than measuring 0.36 mL.
Answer: 0.36 mL (36 units on an insulin syringe)
23. Heparin 25,000 units in 250 mL. Ordered at 800 units/hour. What rate?
25,000 divided by 250 = 100 units/mL. 800 divided by 100 = 8 mL/hour.
Answer: 8 mL/hour
Safe Range: When the Answer Is to Stop
On these two the arithmetic works and the order does not. A calculator will return a confident number for both.
24. Reference range 25-50 mg/kg/day. Child weighs 14 kg. Ordered: 250 mg four times a day. Is this safe?
The range is 350 to 700 mg per day. The order totals 250 multiplied by 4 = 1,000 mg per day, which is above the maximum. Do not give it; check the order.
Answer: No. 1,000 mg/day against a 350-700 mg/day range
25. Reference range 10-15 mg/kg/dose. Child weighs 22 kg. Ordered: 400 mg. Is this safe?
The range is 220 to 330 mg per dose. 400 mg is above it. Do not give it; check the order.
Answer: No. 400 mg against a 220-330 mg range
Percentage and Ratio Strengths
A percentage is grams per 100 mL. A ratio is grams per that many millilitres. Convert both to mg/mL before using them.
26. How many mg are in 1 mL of a 1:1,000 solution?
1 gram in 1,000 mL is 1,000 mg in 1,000 mL, which is 1 mg/mL. A 1:10,000 solution is 0.1 mg/mL.
Answer: 1 mg
27. How many mg of lidocaine are in 10 mL of a 2% solution?
2% is 2 g in 100 mL, which is 2,000 mg in 100 mL, which is 20 mg/mL. 20 multiplied by 10 = 200 mg.
Answer: 200 mg
28. How many grams of sodium chloride are in 500 mL of 0.9% saline?
0.9 g in 100 mL. 500 mL is five times that, so 0.9 multiplied by 5 = 4.5 g.
Answer: 4.5 g
Reconstitution
A powder has no concentration until it is made up, and the concentration depends on the volume actually added.
29. A 1 g vial is reconstituted to 4 mL. You need 600 mg. What volume?
1 g in 4 mL is 1,000 mg in 4 mL, which is 250 mg/mL. 600 divided by 250 = 2.4 mL.
Answer: 2.4 mL
30. A 500 mg vial is reconstituted to 2 mL. Ordered: 125 mg. What volume?
500 mg in 2 mL is 250 mg/mL. 125 divided by 250 = 0.5 mL.
Answer: 0.5 mL
Where These Go Wrong in Practice
The errors in a real drug round are not the ones a practice set punishes. An exam marks a wrong number; a ward produces a right number to the wrong question. The most common versions are a weight recorded in pounds and used as kilograms, a label read as mg/mL when it says mg per 5 mL, and a per-minute rate treated as per-hour. Each of those is covered above, and each one produces an answer that is internally consistent and wrong.
The practical defence is the plausibility check, then an independent second check by someone working from the prescription rather than from your answer. More on how those failures arise in how dosing errors actually happen, and the infusion-specific versions in the IV infusion guide.
Questions About Dosage Calculations
Which method should I use, formula or dimensional analysis?
Whichever one you can reproduce under pressure. The formula method (desired over have, multiplied by the volume) is quicker for single-step problems. Dimensional analysis carries the units through the working, so it catches a wrong conversion rather than silently producing a wrong number, which makes it safer for multi-step infusion problems. Most people use both and pick by the shape of the question.
Why do my answers come out by a factor of ten so often?
Because a factor error is what a unit mistake produces. An answer out by 10, 60, 100 or 1,000 is almost never arithmetic; it is a decimal point, a minutes-to-hours step missed, or micrograms read as milligrams. If the number is out by a round factor, look at the units before you look at the sums.
Should I round a drop rate up or down?
To the nearest whole drop, because a fraction of a drop cannot be delivered. Rounding 41.7 to 42 is right. What should not be rounded is an intermediate step: round once, at the end, or the error accumulates.
Is it safe to use a calculator for these in practice?
As a second opinion on a number you have already worked out, yes. As the only source, no. A calculator answers the question it was given. It cannot see the order, the vial, the patient's weight chart or the reference range, and it will return a confident answer to a question entered wrongly.
How do I know whether an answer is plausible?
Compare it to the thing you are holding. If the answer says draw 14 mL from a 2 mL ampoule, or give nine tablets, or run a drip at 200 drops a minute, the number is telling you something is wrong even when you cannot see where. Plausibility is the check that catches factor errors, and it takes a second.
What is a safe dosage range question actually testing?
Whether you will refuse. Two of the problems above are orders that exceed the reference range, and the expected answer is not a volume but a decision to check with the prescriber. Exams include them because the real failure mode is calculating the dose correctly and giving it anyway.
Do I convert units before or after calculating the dose?
Before, always. Converting partway through is where factor errors hide, because the working looks orderly and the mistake is invisible once it is folded into a larger number. Get everything into the same units, then calculate once.
Medically Reviewed
Dr. Syeda Khadija Akbar
PharmD (Doctor of Pharmacy) — Medical Reviewer
The formulas, dosing logic, unit handling, and safety wording on this page were reviewed for clinical accuracy by Dr. Syeda Khadija Akbar, PharmD. This page is an educational reference only — always confirm any clinical calculation independently before acting on it.