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 6 lb 5 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
6 lb 5 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 18:35 and finishes at 06:25 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.
18:3506:25
t = h
3.Dosage calculationsMedium
A child weighing 32 kg is prescribed 2.5 mg/kg of a drug. The stock solution contains 40 mg/mL. Draw up the dose: what volume V do you give?
32 kg2.5 mg/kg40 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 16 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 120 mg in 5 mL. What volume V do you give? Round to one decimal place.
16 kg10 mg/kg120 mg/5 mL
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 12 hours. After 10 hours you find that 260 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 / 12 hafter 10 h: 260 mL
R = mL/h
6.IV infusion ratesHard
500 mg of a drug is diluted in 250 mL and given by gravity through a set of 20 gtt/mL. The order is 60 mg per hour. Find the drip rate R in drops per minute.
500 mg/250 mL60 mg/h20 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). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 100 mL/h. At 07:30, 600 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL600 mL infused100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 250 units of regular insulin in 250 mL runs at 7.5 mL/h. How many units per hour D does the patient receive?
250 units/250 mL7.5 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 3 mcg/kg/min for a patient who weighs 67 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL3 mcg/kg/min67 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 18.2 mL of diluent. The prescribed dose is 1 200 000 units. What volume V do you draw up? Round to one decimal place.
18.2 mL → 250 000 units/mL1 200 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 1500 mL of 8% 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%8%1500 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 2.87 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
5 oz/16 = 0.3125 lb
6 + 0.3125 = 6.313 lb
Pounds to kilograms
m = 6.313/2.2 = 2.869 ≈ 2.87 kg
Answer
m = 2.87 kg
2.Nursing math & unit conversions
Answer: t = 11.83 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
18:35 → 24:00 = 325 min
After midnight
00:00 → 06:25 = 385 min
Total
325 + 385 = 710 min
t = 710/60 = 11.83 h
Answer
t = 11.83 h
3.Dosage calculations
Answer: V = 2 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 = 2.5·32 = 80 mg
Volume
V = 80/40 = 2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 2 mL
4.Dosage calculations
Answer: V = 6.7 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.
Dose from weight
10·16 = 160 mg
Volume
V = (160/120)·5 = 6.667 ≈ 6.7 mL
Answer
V = 6.7 mL
5.IV infusion rates
Answer: R = 130 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
1500/12 = 125 mL/h
New rate
R = 260/2 = 130 mL/h
Answer
R = 130 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: R = 10 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
60/2 = 30 mL/h
Drip rate
R = 30·20/60 = 10 gtt/min
Answer
R = 10 gtt/min
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 + 100 = 540 mL
ice chips: 120/2 = 60 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·100 = 200 mL
total intake = 1760 mL
Total output
400 + 275 + 325 + 130 = 1130 mL
Balance
B = 1760 − 1130 = 630 mL
Answer
B = 630 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 4 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 − 600 = 400 mL
Time
t = 400/100 = 4 h
Answer
t = 4 h
That is about 4 h 00 min, so the bag runs out at about 11:30.
9.Pediatric & critical-care dosing
Answer: D = 7.5 units/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
250/250 = 1 units/mL
Units per hour
D = 7.5·1 = 7.5 units/h
Answer
D = 7.5 units/h
10.Pediatric & critical-care dosing
Answer: R = 7.5 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
3·67 = 201 mcg/min
201·60 = 12060 mcg/h
Pump rate
R = 12060/1600 = 7.537 ≈ 7.5 mL/h
Answer
R = 7.5 mL/h
11.Pharmacy calculations
Answer: V = 4.8 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.
Concentration from the label
18.2 mL → 250 000 units/mL
Volume to give
V = 1 200 000/250 000 = 4.8 mL
Answer
V = 4.8 mL
12.Pharmacy calculations
Answer: V = 1125 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.