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 patient’s temperature is 97.9 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
97.9 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 22:40 and finishes at 00:10 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
22:4000:10
t = h
3.Dosage calculationsMedium
A patient weighs 22 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
22 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
The prescription is 435 micrograms. The ampoule contains 0.5 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
435 mcg0.5 mg/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 200 mL/h, but no pump is available. It runs by gravity through a giving set of 15 gtt/mL. Find the drip rate R in drops per minute.
200 mL/h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 50 gtt/min through a set of 20 gtt/mL. There are 750 mL left in the bag. How many hours t until it is empty?
50 gtt/min20 gtt/mL750 mL
t = 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 11:45 and runs by pump at 100 mL/h. How many mL V are left in the bag at 14:15?
1000 mL100 mL/h11:45 → 14:15
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A practice protocol calls for a heparin bolus of 80 units/kg for a patient who weighs 92 kg. The vial contains 1 000 units/mL. What volume V do you draw up? Round to one decimal place.
80 units/kg92 kg1 000 units/mL
V = mL
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 74 kg has an order for norepinephrine at 12 mcg/min. The bag contains 4 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
4 mg/250 mL12 mcg/min74 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.88 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.88 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 500 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
23%3%5%500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 36.6 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
97.9 − 32 = 65.9
Multiply by 5/9
T = 65.9·5/9 = 36.61 ≈ 36.6 °C
Answer
T = 36.6 °C
2.Nursing math & unit conversions
Answer: t = 1.5 h
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.
Before midnight
22:40 → 24:00 = 80 min
After midnight
00:00 → 00:10 = 10 min
Total
80 + 10 = 90 min
t = 90/60 = 1.5 h
Answer
t = 1.5 h
3.Dosage calculations
Answer: D = 22 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
2·22 = 44 mg
Per dose
D = 44/2 = 22 mg
Answer
D = 22 mg
4.Dosage calculations
Answer: V = 0.87 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.
Same units
0.5 mg/mL = 500 mcg/mL
Volume
V = 435/500 = 0.87 mL
Answer
V = 0.87 mL
5.IV infusion rates
Answer: R = 50 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.
Millilitres per minute
200/60 = 3.333 mL/min
Drip rate
R = 3.333·15 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: t = 5 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.
Rate in mL/h
50·60/20 = 150 mL/h
Time left
t = 750/150 = 5 h
Answer
t = 5 h
7.IV fluids & fluid balance
Answer: B = 260 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 = 450 mL
ice chips: 120/2 = 60 mL
IV infusion: 75·8 = 600 mL
IV antibiotic: 2·100 = 200 mL
total intake = 1310 mL
Total output
200 + 425 + 275 + 150 = 1050 mL
Balance
B = 1310 − 1050 = 260 mL
Answer
B = 260 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 750 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
11:45 → 14:15 = 2.5 h
Volume infused
100·2.5 = 250 mL
Volume left
V = 1000 − 250 = 750 mL
Answer
V = 750 mL
9.Pediatric & critical-care dosing
Answer: V = 7.4 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
80·92 = 7 360 units
Volume
V = 7360/1000 = 7.36 ≈ 7.4 mL
Answer
V = 7.4 mL
10.Pediatric & critical-care dosing
Answer: R = 45 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
12·60 = 720 mcg/h
Pump rate
R = 720/16 = 45 mL/h
Answer
R = 45 mL/h
11.Pharmacy calculations
Answer: V = 8.8 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 = 0.88/0.1 = 8.8 mL
Answer
V = 8.8 mL
12.Pharmacy calculations
Answer: V = 450 mL
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.