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 is charted at 22:15 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
22:15
110:15 PM
29:15 PM
312:15 PM
410:15 AM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 2 tsp of an oral suspension three times a day for 10 days. Using 1 tsp = 5 mL, how many mL V are needed for the whole course?
2 tspthree times a day10 days1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A child weighing 28 kg is prescribed 4 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
28 kg4 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 70.4 lb. The prescription is 2 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? Round to one decimal place.
70.4 lb2 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 6 hours. After 2 hours you find that 1080 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 / 6 hafter 2 h: 1080 mL
R = mL/h
6.IV infusion ratesHard
An infusion of 100 mg in 250 mL runs at 9 mL/h. How many micrograms per minute D does the patient receive?
100 mg/250 mL9 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 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 500 mL bag runs by pump at 120 mL/h. At 16:30, 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 100 units of regular insulin in 250 mL. The order is 5 units/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/250 mL5 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 28 mL/h. The patient weighs 60 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL28 mL/h60 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.4 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.4 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 115 mg. Draw up the dose: what volume V do you give?
250 mg9.6 mL + 0.4 mL115 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 10:15 PM
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Convert the hour
22 − 12 = 10 → PM
Answer
10:15 PM
Answer
10:15 PM
2.Nursing math & unit conversions
Answer: V = 300 mL
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.
Volume per dose
2 tsp = 2·5 = 10 mL
Whole course
V = 10 mL × 3/day × 10 = 300 mL
Answer
V = 300 mL
3.Dosage calculations
Answer: V = 2.8 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 = 4·28 = 112 mg
Volume
V = 112/40 = 2.8 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 2.8 mL
4.Dosage calculations
Answer: V = 1.3 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
70.4/2.2 = 32 kg
Dose
2·32 = 64 mg
Volume
V = (64/250)·5 = 1.28 ≈ 1.3 mL
Answer
V = 1.3 mL
5.IV infusion rates
Answer: R = 270 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
1500/6 = 250 mL/h
New rate
R = 1080/4 = 270 mL/h
Answer
R = 270 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: D = 60 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
100000 mcg/250 mL = 400 mcg/mL
Dose per hour
9·400 = 3600 mcg/h
Dose per minute
D = 3600/60 = 60 mcg/min
Answer
D = 60 mcg/min
7.IV fluids & fluid balance
Answer: B = 575 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 + 250 + 100 = 550 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1550 mL
Total output
450 + 375 + 150 = 975 mL
Balance
B = 1550 − 975 = 575 mL
Answer
B = 575 mL
Positive: more fluid went in than came out.
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 19:25.
9.Pediatric & critical-care dosing
Answer: R = 12.5 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
100/250 = 0.4 units/mL
Pump rate
R = 5/0.4 = 12.5 mL/h
Answer
R = 12.5 mL/h
10.Pediatric & critical-care dosing
Answer: D = 12.4 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
28·1600 = 44800 mcg/h
44800/60 = 746.7 mcg/min
Per kilogram
D = 746.7/60 = 12.44 ≈ 12.4 mcg/kg/min
Answer
D = 12.4 mcg/kg/min
11.Pharmacy calculations
Answer: V = 4 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/10 000 mL = 0.1 mg/mL
Volume
V = 0.4/0.1 = 4 mL
Answer
V = 4 mL
12.Pharmacy calculations
Answer: V = 4.6 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.