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.
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
Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
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
Pump rate in mL/h: volume divided by time in hours.
Drip rate in drops/min: volume × drop factor divided by time in minutes.
For time remaining: volume left divided by the rate.
Round as the question or the equipment requires.
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
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
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
2Practice problems
1.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A drip-rate calculation gives 223.263 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
223.263 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:20 and finishes at 07:45 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
18:2007:45
t = h
3.Dosage calculationsMedium
A patient weighs 60 kg. The prescribed dose is 20 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
60 kg20 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
The prescription is 2750 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
2750 units5000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 8 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL8 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 2 g of a drug in 250 mL. The order is 2 mg per minute. At what rate R do you set the pump, in mL/h?
2 g/250 mL2 mg/min
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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
water: 150 mLjuice: 150 mLmilk: 200 mLIV infusion: 50 mL/h × 12 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 80 mL/h. At 22:00, 600 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL600 mL infused80 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 93 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL18 units/kg/h93 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 84 kg has an order for nitroglycerin at 20 mcg/min. The bag contains 50 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
50 mg/250 mL20 mcg/min84 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ceftriaxone 1000 mg as a powder. The practice label says to add 9.6 mL of sterile water; the powder adds 0.4 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg9.6 mL+0.4 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 82.5 mg. Draw up the dose: what volume V do you give?
250 mg9.2 mL + 0.8 mL82.5 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 223 gtt/min
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the ones place
223.263 → 3
Only the next digit decides
223.263 → 2
2 is 4 or less, so 3 stays.
The digits after it (63) are ignored: round once, never step by step.
Round
x = 223 gtt/min
Answer
x = 223 gtt/min
2.Nursing math & unit conversions
Answer: t = 13.42 h
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.
Before midnight
18:20 → 24:00 = 340 min
After midnight
00:00 → 07:45 = 465 min
Total
340 + 465 = 805 min
t = 805/60 = 13.42 h
Answer
t = 13.42 h
3.Dosage calculations
Answer: D = 400 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
20·60 = 1200 mg
Per dose
D = 1200/3 = 400 mg
Answer
D = 400 mg
4.Dosage calculations
Answer: V = 0.55 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.
Volume
V = 2750/5000 = 0.55 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.55 mL
5.IV infusion rates
Answer: R = 10 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
8·60 = 480 min
Drip rate
R = 500·10/480 = 10.42 ≈ 10 gtt/min
Answer
R = 10 gtt/min
At the bedside you round to the nearest whole drop: 10 gtt/min.
6.IV infusion rates
Answer: R = 15 mL/h
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
2000 mg/250 mL = 8 mg/mL
Dose per hour
2·60 = 120 mg/h
Pump rate
R = 120/8 = 15 mL/h
Answer
R = 15 mL/h
7.IV fluids & fluid balance
Answer: I = 1150 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.
Add the intake
oral: 150 + 150 + 200 = 500 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·50 = 50 mL
I = 1150 mL
Answer
I = 1150 mL
8.IV fluids & fluid balance
Answer: t = 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
1000 − 600 = 400 mL
Time
t = 400/80 = 5 h
Answer
t = 5 h
That is about 5 h 00 min, so the bag runs out at about 03:00.
9.Pediatric & critical-care dosing
Answer: R = 33.5 mL/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.
Units per hour
18·93 = 1 674 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1674/50 = 33.48 ≈ 33.5 mL/h
Answer
R = 33.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 6 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
50 000/250 = 200 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
20·60 = 1200 mcg/h
Pump rate
R = 1200/200 = 6 mL/h
Answer
R = 6 mL/h
11.Pharmacy calculations
Answer: C = 100 mg/mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Final volume
9.6 + 0.4 = 10 mL
Concentration
C = 1000/10 = 100 mg/mL
Answer
C = 100 mg/mL
12.Pharmacy calculations
Answer: V = 3.3 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.