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 4 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 4 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 1½ tsp of an oral suspension every 12 hours for 5 days. The suspension comes in 50 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
1½ tspevery 12 hours5 days50 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A patient weighs 25 kg and is prescribed 15 mg/kg as a single dose. Find the dose D in mg.
25 kg15 mg/kg
D = mg
4.Dosage calculationsHard
An infusion contains 20000 units of a drug in 500 mL. The prescription is 2000 units per hour. At what rate R do you set the pump, in mL/h?
20000 units/500 mL2000 units/h
R = mL/h
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 100 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
500 mg/100 mL10 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 was started at 09:45 and runs by pump at 80 mL/h. How many mL V are left in the bag at 16:45?
1000 mL80 mL/h09:45 → 16:45
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 50 mL. The order is 0.1 units/kg/h for a patient who weighs 90 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/50 mL0.1 units/kg/h90 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 57 kg has an order for norepinephrine at 10 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL10 mcg/min57 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. What is the concentration C in mg/mL after reconstitution?
500 mg1.8 mL+0.2 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 2000 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 440 mg. Draw up the dose: what volume V do you give?
2000 mg4.2 mL + 0.8 mL440 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 4.66 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
4 oz/16 = 0.25 lb
10 + 0.25 = 10.25 lb
Pounds to kilograms
m = 10.25/2.2 = 4.659 ≈ 4.66 kg
Answer
m = 4.66 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
7.5 mL × 2 × 5 = 75 mL
Bottles
75/50 = 1.5 → N = 2
Answer
N = 2
3.Dosage calculations
Answer: D = 375 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.
Dose
15·25 = 375 mg
Answer
D = 375 mg
4.Dosage calculations
Answer: R = 50 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
20000/500 = 40 units/mL
Pump rate
R = 2000/40 = 50 mL/h
Answer
R = 50 mL/h
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 = 50 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
500/100 = 5 mg/mL
Dose rate
D = 5·10 = 50 mg/h
Answer
D = 50 mg/h
7.IV fluids & fluid balance
Answer: B = 630 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: 200 + 240 + 250 = 690 mL
IV infusion: 125·12 = 1500 mL
IV antibiotic: 2·100 = 200 mL
total intake = 2390 mL
Total output
350 + 325 + 500 + 275 + 110 + 200 = 1760 mL
Balance
B = 2390 − 1760 = 630 mL
Answer
B = 630 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 440 mL
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.
Elapsed time
09:45 → 16:45 = 7 h
Volume infused
80·7 = 560 mL
Volume left
V = 1000 − 560 = 440 mL
Answer
V = 440 mL
9.Pediatric & critical-care dosing
Answer: R = 9 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
0.1·90 = 9 units/h
Concentration
50/50 = 1 units/mL
Pump rate
R = 9/1 = 9 mL/h
Answer
R = 9 mL/h
10.Pediatric & critical-care dosing
Answer: R = 18.8 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/32 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
11.Pharmacy calculations
Answer: C = 250 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
1.8 + 0.2 = 2 mL
Concentration
C = 500/2 = 250 mg/mL
Answer
C = 250 mg/mL
12.Pharmacy calculations
Answer: V = 1.1 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.