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 15 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 15 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tsp of an oral suspension every 6 hours for 10 days. The suspension comes in 150 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
1 tspevery 6 hours10 days150 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A patient weighs 70 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
70 kg10 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
A patient weighs 68.2 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
68.2 lb1 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 2 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
500 mL2 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
100 mg of a drug is diluted in 100 mL and given by gravity through a set of 60 gtt/mL. The order is 75 mg per hour. Find the drip rate R in drops per minute.
100 mg/100 mL75 mg/h60 gtt/mL
R = gtt/min
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 total intake I in mL. Count ice chips as half their volume.
tea: 200 mLjelly: 100 mLice chips: 200 mLIV infusion: 80 mL/h × 8 hIV antibiotic: 2 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 75 mL/h. At 14:30, 300 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL300 mL infused75 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 70 units/kg for a patient who weighs 56 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
70 units/kg56 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 22 mL/h. The patient weighs 73 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL22 mL/h73 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. What is the concentration C in mg/mL after reconstitution?
750 mg7.2 mL+0.3 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 150 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 6% ointment? Round to the nearest whole gram.
150 g · 10%2%6%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.7 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
15 oz/16 = 0.9375 lb
5 + 0.9375 = 5.938 lb
Pounds to kilograms
m = 5.938/2.2 = 2.699 ≈ 2.7 kg
Answer
m = 2.7 kg
2.Nursing math & unit conversions
Answer: N = 2
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.
Total volume
5 mL × 4 × 10 = 200 mL
Bottles
200/150 = 1.333 → N = 2
Answer
N = 2
3.Dosage calculations
Answer: D = 233.3 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
10·70 = 700 mg
Per dose
D = 700/3 = 233.3 mg
Answer
D = 233.3 mg
4.Dosage calculations
Answer: V = 0.62 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
68.2/2.2 = 31 kg
Dose
1·31 = 31 mg
Volume
V = (31/250)·5 = 0.62 mL
Answer
V = 0.62 mL
5.IV infusion rates
Answer: R = 83 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
2·60 = 120 min
Drip rate
R = 500·20/120 = 83.33 ≈ 83 gtt/min
Answer
R = 83 gtt/min
At the bedside you round to the nearest whole drop: 83 gtt/min.
6.IV infusion rates
Answer: R = 75 gtt/min
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
100/100 = 1 mg/mL
Volume per hour
75/1 = 75 mL/h
Drip rate
R = 75·60/60 = 75 gtt/min
Answer
R = 75 gtt/min
7.IV fluids & fluid balance
Answer: I = 1140 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: 200 + 100 = 300 mL
ice chips: 200/2 = 100 mL
IV infusion: 80·8 = 640 mL
IV antibiotic: 2·50 = 100 mL
I = 1140 mL
Answer
I = 1140 mL
8.IV fluids & fluid balance
Answer: t = 2.7 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 − 300 = 200 mL
Time
t = 200/75 = 2.667 ≈ 2.7 h
Answer
t = 2.7 h
That is about 2 h 40 min, so the bag runs out at about 17:10.
9.Pediatric & critical-care dosing
Answer: V = 3.9 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
70·56 = 3 920 units
Volume
V = 3920/1000 = 3.92 ≈ 3.9 mL
Answer
V = 3.9 mL
10.Pediatric & critical-care dosing
Answer: D = 8 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
22·1600 = 35200 mcg/h
35200/60 = 586.7 mcg/min
Per kilogram
D = 586.7/73 = 8.037 ≈ 8 mcg/kg/min
Answer
D = 8 mcg/kg/min
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
7.2 + 0.3 = 7.5 mL
Concentration
C = 750/7.5 = 100 mg/mL
Answer
C = 100 mg/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.