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 16.126 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
16.126 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 3 mcg/min. Express this dose rate D in mg/h.
3 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A patient weighing 49 kg has a body surface area of 1.33 m². The prescription is 175 mg/m². Find the dose D in mg.
49 kgBSA = 1.33 m²175 mg/m²
D = mg
4.Dosage calculationsHard
A patient weighs 178.2 lb. The prescription is 0.5 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to two decimal places.
178.2 lb0.5 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 90 mL/h, but no pump is available. It runs by gravity through a giving set of 60 gtt/mL. Find the drip rate R in drops per minute.
90 mL/h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 42 gtt/min through a set of 15 gtt/mL. There are 200 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
42 gtt/min15 gtt/mL200 mL
t = 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 patient weighs 69 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
69 kg12 hurine: 150 mLurine: 150 mLwound drain: 150 mL
U = mL/kg/h
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 19:30 at 125 mL/h. After 3 hours the rate is changed to 200 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL125 mL/h · 3 h200 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 250 mL runs at 3 mL/h. How many units per hour D does the patient receive?
100 units/250 mL3 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 26 mL/h. The patient weighs 96 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL26 mL/h96 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.12 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.12 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 3.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 450 mg. Draw up the dose: what volume V do you give?
2000 mg3.6 mL + 0.4 mL450 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 16 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
16.126 → 6
Only the next digit decides
16.126 → 1
1 is 4 or less, so 6 stays.
The digits after it (26) are ignored: round once, never step by step.
Round
x = 16 gtt/min
Answer
x = 16 gtt/min
2.Nursing math & unit conversions
Answer: D = 0.18 mg/h
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Set up the chain
D = 3 mcg/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 3·60/1000 = 0.18 mg/h
Answer
D = 0.18 mg/h
3.Dosage calculations
Answer: D = 232.8 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Dose
D = 175·1.33 = 232.8 mg
Answer
D = 232.8 mg
4.Dosage calculations
Answer: V = 0.41 mL
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.
Weight in kg
178.2/2.2 = 81 kg
Dose
0.5·81 = 40.5 mg
Volume
V = (40.5/100)·1 = 0.405 ≈ 0.41 mL
Answer
V = 0.41 mL
5.IV infusion rates
Answer: R = 90 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.
Millilitres per minute
90/60 = 1.5 mL/min
Drip rate
R = 1.5·60 = 90 gtt/min
Answer
R = 90 gtt/min
With a microdrip set (60 gtt/mL), gtt/min equals mL/h.
6.IV infusion rates
Answer: t = 1.2 h
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.
Rate in mL/h
42·60/15 = 168 mL/h
Time left
t = 200/168 = 1.19 ≈ 1.2 h
Answer
t = 1.2 h
7.IV fluids & fluid balance
Answer: U = 0.36 mL/kg/h
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 urine
150 + 150 = 300 mL
Per kilogram per hour
U = 300/(69·12) = 0.3623 ≈ 0.36 mL/kg/h
Answer
U = 0.36 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 3.6 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.
First part
125·3 = 375 mL
500 − 375 = 125 mL left
Second part
125/200 = 0.625 h
Total time
t = 3 + 0.625 = 3.625 ≈ 3.6 h
Answer
t = 3.6 h
That is about 3 h 38 min, so the bag runs out at about 23:08.
9.Pediatric & critical-care dosing
Answer: D = 1.2 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
100/250 = 0.4 units/mL
Units per hour
D = 3·0.4 = 1.2 units/h
Answer
D = 1.2 units/h
10.Pediatric & critical-care dosing
Answer: D = 7.2 mcg/kg/min
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
800 000/500 = 1600 mcg/mL
Micrograms per minute
26·1600 = 41600 mcg/h
41600/60 = 693.3 mcg/min
Per kilogram
D = 693.3/96 = 7.222 ≈ 7.2 mcg/kg/min
Answer
D = 7.2 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.12 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.12/1 = 0.12 mL
Answer
V = 0.12 mL
12.Pharmacy calculations
Answer: V = 0.9 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.