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 24.587 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
24.587 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads ½ tsp of an oral suspension every 8 hours for 10 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
½ tspevery 8 hours10 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A vial contains 2 g of powder. The label says: add 7.4 mL of water for injection to give a total volume of 8 mL. The prescription is 100 mg. What volume V of the reconstituted solution do you give?
2 g+ 7.4 mL → 8 mL100 mg
V = mL
4.Dosage calculationsHard
A patient is 135 cm tall and weighs 37 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
135 cm37 kg135 mg/m²
D = mg
5.IV infusion ratesMedium
A drip runs at 40 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 6 hours?
40 gtt/min15 gtt/mL6 h
V = mL
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 500 mL and runs at 30 mL/h. How many milligrams per hour D does the patient receive?
100 mg/500 mL30 mL/h
D = mg/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 fluid balance B = intake − output in mL (a negative answer means a net loss).
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 125 mL/h. At 11:30, 650 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL650 mL infused125 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 60 units/kg for a patient who weighs 79 kg. The vial contains 5 000 units/mL. What volume V do you draw up? Round to two decimal places.
60 units/kg79 kg5 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 69 kg has an order for nitroglycerin at 30 mcg/min. The bag contains 25 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
25 mg/250 mL30 mcg/min69 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.33 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.33 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 2.5% hydrocortisone ointment. How many grams m of 0.5% hydrocortisone ointment must you add to make a 1.5% ointment? Round to the nearest whole gram.
150 g · 2.5%0.5%1.5%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: x = 25 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
24.587 → 4
Only the next digit decides
24.587 → 5
5 is 5 or more, so round 4 up.
The digits after it (87) are ignored: round once, never step by step.
Round
x = 25 gtt/min
Answer
x = 25 gtt/min
2.Nursing math & unit conversions
Answer: V = 75 mL
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.
Volume per dose
½ tsp = 0.5·5 = 2.5 mL
Whole course
V = 2.5 mL × 3/day × 10 = 75 mL
Answer
V = 75 mL
3.Dosage calculations
Answer: V = 0.4 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.
Concentration after mixing
2000 mg/8 mL = 250 mg/mL
Volume
V = 100/250 = 0.4 mL
Answer
V = 0.4 mL
4.Dosage calculations
Answer: D = 159 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).
Body surface area
BSA = √(135·37/3600) = √1.387 = 1.178 m²
Dose
D = 135·1.178 = 159 mg
Answer
D = 159 mg
5.IV infusion rates
Answer: V = 960 mL
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
40·60/15 = 160 mL/h
Volume
V = 160·6 = 960 mL
Answer
V = 960 mL
6.IV infusion rates
Answer: D = 6 mg/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.
Concentration
100/500 = 0.2 mg/mL
Dose rate
D = 0.2·30 = 6 mg/h
Answer
D = 6 mg/h
7.IV fluids & fluid balance
Answer: B = 655 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: 300 + 200 + 180 = 680 mL
IV infusion: 100·12 = 1200 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1930 mL
Total output
375 + 250 + 500 + 150 = 1275 mL
Balance
B = 1930 − 1275 = 655 mL
Answer
B = 655 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 2.8 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 − 650 = 350 mL
Time
t = 350/125 = 2.8 h
Answer
t = 2.8 h
That is about 2 h 48 min, so the bag runs out at about 14:18.
9.Pediatric & critical-care dosing
Answer: V = 0.95 mL
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 needed
60·79 = 4 740 units
Volume
V = 4740/5000 = 0.948 ≈ 0.95 mL
Answer
V = 0.95 mL
10.Pediatric & critical-care dosing
Answer: R = 18 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
25 000/250 = 100 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
30·60 = 1800 mcg/h
Pump rate
R = 1800/100 = 18 mL/h
Answer
R = 18 mL/h
11.Pharmacy calculations
Answer: V = 0.33 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 = 0.33/1 = 0.33 mL
Answer
V = 0.33 mL
12.Pharmacy calculations
Answer: m = 150 g
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.