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 dose calculation for a small injection gives 0.95952 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.95952 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 4 tbsp of liquid supplement, 2 cups of tea, 1½ tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 cup = 8 fl oz = 240 mL1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A child weighing 32 kg is prescribed 15 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
32 kg15 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A patient is 135 cm tall and weighs 53 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
135 cm53 kg50 mg/m²
D = mg
5.IV infusion ratesMedium
1500 mL was ordered over 8 hours. After 6 hours you find that 490 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1500 mL / 8 hafter 6 h: 490 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 32 gtt/min through a set of 20 gtt/mL. There are 750 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
32 gtt/min20 gtt/mL750 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 8-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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 120 mL/h. At 08:30, 150 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL150 mL infused120 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 250 units of regular insulin in 250 mL. The order is 4 units/h. Find the pump rate R in mL/h. Round to one decimal place.
250 units/250 mL4 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 500 mg in 250 mL. The order is 5 mcg/kg/min for a patient who weighs 71 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
500 mg/250 mL5 mcg/kg/min71 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.59 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.59 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 40% dextrose by mixing 70% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
70%10%40%200 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 0.96 mL
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 hundredths place
0.95952 → 5
Only the next digit decides
0.95952 → 9
9 is 5 or more, so round 5 up.
The digits after it (52) are ignored: round once, never step by step.
Round
x = 0.96 mL
Answer
x = 0.96 mL
2.Nursing math & unit conversions
Answer: V = 547.5 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
4 tbsp = 4·15 = 60 mL
2 cups = 2·240 = 480 mL
1½ tsp = 1.5·5 = 7.5 mL
Add
V = 60 + 480 + 7.5 = 547.5 mL
Answer
V = 547.5 mL
3.Dosage calculations
Answer: V = 9.6 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.
Dose from body weight
D = 15·32 = 480 mg
Volume
V = 480/50 = 9.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9.6 mL
4.Dosage calculations
Answer: D = 70.49 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 = √(135·53/3600) = √1.988 = 1.41 m²
Dose
D = 50·1.41 = 70.49 mg
Answer
D = 70.49 mg
5.IV infusion rates
Answer: R = 245 mL/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.
Original rate
1500/8 = 187.5 mL/h
New rate
R = 490/2 = 245 mL/h
Answer
R = 245 mL/h
This is more than a 25% increase: most hospitals require you to contact the prescriber instead of catching up, and to assess the patient for fluid overload.
6.IV infusion rates
Answer: t = 7.8 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
32·60/20 = 96 mL/h
Time left
t = 750/96 = 7.813 ≈ 7.8 h
Answer
t = 7.8 h
7.IV fluids & fluid balance
Answer: B = −310 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: 240 + 180 + 120 = 540 mL
ice chips: 200/2 = 100 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1540 mL
Total output
475 + 475 + 400 + 500 = 1850 mL
Balance
B = 1540 − 1850 = −310 mL
Answer
B = −310 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: t = 2.9 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
500 − 150 = 350 mL
Time
t = 350/120 = 2.917 ≈ 2.9 h
Answer
t = 2.9 h
That is about 2 h 55 min, so the bag runs out at about 11:25.
9.Pediatric & critical-care dosing
Answer: R = 4 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.
Concentration
250/250 = 1 units/mL
Pump rate
R = 4/1 = 4 mL/h
Answer
R = 4 mL/h
10.Pediatric & critical-care dosing
Answer: R = 10.7 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
500 mg = 500 000 mcg
500 000/250 = 2000 mcg/mL
Dose per minute and per hour
5·71 = 355 mcg/min
355·60 = 21300 mcg/h
Pump rate
R = 21300/2000 = 10.65 ≈ 10.7 mL/h
Answer
R = 10.7 mL/h
11.Pharmacy calculations
Answer: V = 0.59 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 = 0.59/1 = 0.59 mL
Answer
V = 0.59 mL
12.Pharmacy calculations
Answer: V = 100 mL
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.