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 10 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.
10 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 blood glucose result is 308 mg/dL. Using 1 mmol/L = 18 mg/dL for glucose, find c in mmol/L. Round to one decimal place.
308 mg/dL1 mmol/L = 18 mg/dL
c = mmol/L
3.Dosage calculationsMedium
A patient weighs 22 kg. The prescribed dose is 5 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
22 kg5 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
An infusion contains 25000 units of a drug in 500 mL. The prescription is 500 units per hour. At what rate R do you set the pump, in mL/h?
25000 units/500 mL500 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 250 mL over 4 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL4 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 25 mg in 250 mL runs at 24 mL/h. How many micrograms per minute D does the patient receive?
25 mg/250 mL24 mL/h
D = mcg/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.
water: 240 mLtea: 200 mLIV infusion: 100 mL/h × 8 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 20:00 at 100 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.
1000 mL100 mL/h · 3 h200 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 14 units/kg/h for a patient who weighs 93 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL14 units/kg/h93 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 36 mL/h. The patient weighs 65 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL36 mL/h65 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.46 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.46 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
30 g · 5%1%3%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: m = 4.91 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
10 + 0.8125 = 10.81 lb
Pounds to kilograms
m = 10.81/2.2 = 4.915 ≈ 4.91 kg
Answer
m = 4.91 kg
2.Nursing math & unit conversions
Answer: c = 17.1 mmol/L
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
c = 308/18 = 17.11 ≈ 17.1 mmol/L
Answer
c = 17.1 mmol/L
3.Dosage calculations
Answer: D = 36.67 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
5·22 = 110 mg
Per dose
D = 110/3 = 36.67 mg
Answer
D = 36.67 mg
4.Dosage calculations
Answer: R = 10 mL/h
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
25000/500 = 50 units/mL
Pump rate
R = 500/50 = 10 mL/h
Answer
R = 10 mL/h
5.IV infusion rates
Answer: R = 63 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
4·60 = 240 min
Drip rate
R = 250·60/240 = 62.5 ≈ 63 gtt/min
Answer
R = 63 gtt/min
At the bedside you round to the nearest whole drop: 63 gtt/min.
6.IV infusion rates
Answer: D = 40 mcg/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
25000 mcg/250 mL = 100 mcg/mL
Dose per hour
24·100 = 2400 mcg/h
Dose per minute
D = 2400/60 = 40 mcg/min
Answer
D = 40 mcg/min
7.IV fluids & fluid balance
Answer: I = 1290 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: 240 + 200 = 440 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 1·50 = 50 mL
I = 1290 mL
Answer
I = 1290 mL
8.IV fluids & fluid balance
Answer: t = 6.5 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
100·3 = 300 mL
1000 − 300 = 700 mL left
Second part
700/200 = 3.5 h
Total time
t = 3 + 3.5 = 6.5 h
Answer
t = 6.5 h
That is about 6 h 30 min, so the bag runs out at about 02:30.
9.Pediatric & critical-care dosing
Answer: R = 32.6 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
14·93 = 1 302 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1302/40 = 32.55 ≈ 32.6 mL/h
Answer
R = 32.6 mL/h
10.Pediatric & critical-care dosing
Answer: D = 14.8 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
36·1600 = 57600 mcg/h
57600/60 = 960 mcg/min
Per kilogram
D = 960/65 = 14.77 ≈ 14.8 mcg/kg/min
Answer
D = 14.8 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.46 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 = 0.46/1 = 0.46 mL
Answer
V = 0.46 mL
12.Pharmacy calculations
Answer: m = 30 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.