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 newborn weighs 5 lb 13 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
5 lb 13 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A haemoglobin result is 126 g/L. Express it in g/dL Hb.
126 g/L1 L = 10 dL
Hb = g/dL
3.Dosage calculationsMedium
A patient weighs 45 kg. The prescribed dose is 15 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?
45 kg15 mg/kg/day4× per day
D = mg
4.Dosage calculationsHard
The prescription is 240 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
240 units1000 units/mL
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 10 hours. After 3 hours you find that 1160 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 / 10 hafter 3 h: 1160 mL
R = mL/h
6.IV infusion ratesHard
A bag contains 500 mg of a drug in 500 mL and runs at 5 mL/h. How many milligrams per hour D does the patient receive?
500 mg/500 mL5 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 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).
soup: 180 mLmilk: 200 mLIV infusion: 60 mL/h × 8 hIV antibiotic: 2 × 50 mLurine: 325 mLurine: 225 mL
B = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 13:30 at 100 mL/h. After 4 hours the rate is changed to 50 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL100 mL/h · 4 h50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 250 mL. The order is 0.1 units/kg/h for a patient who weighs 69 kg. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL0.1 units/kg/h69 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 38 mL/h. The patient weighs 93 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL38 mL/h93 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 320 mg. Draw up the dose: what volume V do you give?
1000 mg4.4 mL + 0.6 mL320 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.64 kg
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.
Ounces to pounds
13 oz/16 = 0.8125 lb
5 + 0.8125 = 5.813 lb
Pounds to kilograms
m = 5.813/2.2 = 2.642 ≈ 2.64 kg
Answer
m = 2.64 kg
2.Nursing math & unit conversions
Answer: Hb = 12.6 g/dL
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.
Convert
Hb = 126 g/L × (1 L/10 dL) = 12.6 g/dL
Answer
Hb = 12.6 g/dL
3.Dosage calculations
Answer: D = 168.8 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
15·45 = 675 mg
Per dose
D = 675/4 = 168.8 mg
Answer
D = 168.8 mg
4.Dosage calculations
Answer: V = 0.24 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 = 240/1000 = 0.24 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.24 mL
5.IV infusion rates
Answer: R = 165.7 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
1500/10 = 150 mL/h
New rate
R = 1160/7 = 165.7 mL/h
Answer
R = 165.7 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: D = 5 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
500/500 = 1 mg/mL
Dose rate
D = 1·5 = 5 mg/h
Answer
D = 5 mg/h
7.IV fluids & fluid balance
Answer: B = 410 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: 180 + 200 = 380 mL
IV infusion: 60·8 = 480 mL
IV antibiotic: 2·50 = 100 mL
total intake = 960 mL
Total output
325 + 225 = 550 mL
Balance
B = 960 − 550 = 410 mL
Answer
B = 410 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 16 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
100·4 = 400 mL
1000 − 400 = 600 mL left
Second part
600/50 = 12 h
Total time
t = 4 + 12 = 16 h
Answer
t = 16 h
That is about 16 h 00 min, so the bag runs out at about 05:30.
9.Pediatric & critical-care dosing
Answer: R = 17.3 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
0.1·69 = 6.9 units/h
Concentration
100/250 = 0.4 units/mL
Pump rate
R = 6.9/0.4 = 17.25 ≈ 17.3 mL/h
Answer
R = 17.3 mL/h
10.Pediatric & critical-care dosing
Answer: D = 13.6 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
38·2000 = 76000 mcg/h
76000/60 = 1267 mcg/min
Per kilogram
D = 1267/93 = 13.62 ≈ 13.6 mcg/kg/min
Answer
D = 13.6 mcg/kg/min
11.Pharmacy calculations
Answer: C = 160 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
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
12.Pharmacy calculations
Answer: V = 1.6 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.