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 06:05 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
06:05
16:05 PM
25:05 AM
38:05 AM
46:05 AM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:35 and finishes at 06:55 the next morning (24-hour clock). How many minutes t did it run?
23:3506:55
t = min
3.Dosage calculationsMedium
How many milligrams of drug m are in 10 mL of a 10% (w/v) solution?
10% w/v10 mL
m = mg
4.Dosage calculationsHard
A patient is 125 cm tall and weighs 34 kg. The prescription is 50 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
125 cm34 kg50 mg/m²
D = mg
5.IV infusion ratesMedium
A drip runs at 20 gtt/min through a set of 20 gtt/mL. How many millilitres V does the patient receive in 3 hours?
20 gtt/min20 gtt/mL3 h
V = mL
6.IV infusion ratesHard
500 mg of a drug is diluted in 250 mL and given by gravity through a set of 15 gtt/mL. The order is 200 mg per hour. Find the drip rate R in drops per minute.
500 mg/250 mL200 mg/h15 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 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 runs by pump at 150 mL/h. At 16:00, 350 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL350 mL infused150 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 500 mL. The order is 16 units/kg/h for a patient who weighs 77 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL16 units/kg/h77 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 500 mg in 250 mL runs at 26 mL/h. The patient weighs 65 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL26 mL/h65 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.82 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.82 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 30% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%30%450 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 6:05 AM
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
06 → 6 AM
Answer
6:05 AM
Answer
6:05 AM
2.Nursing math & unit conversions
Answer: t = 440 min
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
23:35 → 24:00 = 25 min
After midnight
00:00 → 06:55 = 415 min
Total
t = 25 + 415 = 440 min
Answer
t = 440 min
3.Dosage calculations
Answer: m = 1000 mg
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
10% = 10 g/100 mL = 100 mg/mL
Mass of drug
m = 100·10 = 1000 mg
Answer
m = 1000 mg
4.Dosage calculations
Answer: D = 54.33 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Body surface area
BSA = √(125·34/3600) = √1.181 = 1.087 m²
Dose
D = 50·1.087 = 54.33 mg
Answer
D = 54.33 mg
5.IV infusion rates
Answer: V = 180 mL
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
20·60/20 = 60 mL/h
Volume
V = 60·3 = 180 mL
Answer
V = 180 mL
6.IV infusion rates
Answer: R = 25 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
500/250 = 2 mg/mL
Volume per hour
200/2 = 100 mL/h
Drip rate
R = 100·15/60 = 25 gtt/min
Answer
R = 25 gtt/min
7.IV fluids & fluid balance
Answer: B = 750 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: 240 + 100 + 240 = 580 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1640 mL
Total output
325 + 475 + 90 = 890 mL
Balance
B = 1640 − 890 = 750 mL
Answer
B = 750 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 4.3 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
1000 − 350 = 650 mL
Time
t = 650/150 = 4.333 ≈ 4.3 h
Answer
t = 4.3 h
That is about 4 h 20 min, so the bag runs out at about 20:20.
9.Pediatric & critical-care dosing
Answer: R = 24.6 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
16·77 = 1 232 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1232/50 = 24.64 ≈ 24.6 mL/h
Answer
R = 24.6 mL/h
10.Pediatric & critical-care dosing
Answer: D = 13.3 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
500 000/250 = 2000 mcg/mL
Micrograms per minute
26·2000 = 52000 mcg/h
52000/60 = 866.7 mcg/min
Per kilogram
D = 866.7/65 = 13.33 ≈ 13.3 mcg/kg/min
Answer
D = 13.3 mcg/kg/min
11.Pharmacy calculations
Answer: V = 8.2 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 = 0.82/0.1 = 8.2 mL
Answer
V = 8.2 mL
12.Pharmacy calculations
Answer: V = 150 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.