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 4 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.
4 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). An infusion starts at 17:05 and finishes at 05:05 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.
17:0505:05
t = h
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 9.6 mL of water for injection to give a total volume of 10 mL. The prescription is 120 mg. What volume V of the reconstituted solution do you give?
1 g+ 9.6 mL → 10 mL120 mg
V = mL
4.Dosage calculationsHard
A patient weighs 176 lb. The prescription is 2 mg/kg as a single dose, and the stock contains 40 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give?
176 lb2 mg/kg40 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 1500 mL over 10 hours with a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
1500 mL10 h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 200 mg of a drug in 100 mL and runs at 12 mL/h. How many milligrams per hour D does the patient receive?
200 mg/100 mL12 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 8-hour shift. The patient weighs 49 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 500 mL bag runs by pump at 120 mL/h. At 21:00, 250 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL250 mL infused120 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 50 units of regular insulin in 50 mL runs at 4 mL/h. How many units per hour D does the patient receive?
50 units/50 mL4 mL/h
D = units/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 24 mL/h. The patient weighs 84 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
500 mg/250 mL24 mL/h84 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.51 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.51 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 100 mg. Draw up the dose: what volume V do you give?
250 mg4.5 mL + 0.5 mL100 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: m = 1.93 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
4 + 0.25 = 4.25 lb
Pounds to kilograms
m = 4.25/2.2 = 1.932 ≈ 1.93 kg
Answer
m = 1.93 kg
2.Nursing math & unit conversions
Answer: t = 12 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
17:05 → 24:00 = 415 min
After midnight
00:00 → 05:05 = 305 min
Total
415 + 305 = 720 min
t = 720/60 = 12 h
Answer
t = 12 h
3.Dosage calculations
Answer: V = 1.2 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.
Concentration after mixing
1000 mg/10 mL = 100 mg/mL
Volume
V = 120/100 = 1.2 mL
Answer
V = 1.2 mL
4.Dosage calculations
Answer: V = 4 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
176/2.2 = 80 kg
Dose
2·80 = 160 mg
Volume
V = (160/40)·1 = 4 mL
Answer
V = 4 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.
Time in minutes
10·60 = 600 min
Drip rate
R = 1500·20/600 = 50 gtt/min
Answer
R = 50 gtt/min
6.IV infusion rates
Answer: D = 24 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
200/100 = 2 mg/mL
Dose rate
D = 2·12 = 24 mg/h
Answer
D = 24 mg/h
7.IV fluids & fluid balance
Answer: U = 2.36 mL/kg/h
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 urine
275 + 275 + 375 = 925 mL
Per kilogram per hour
U = 925/(49·8) = 2.36 mL/kg/h
Answer
U = 2.36 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 2.1 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 − 250 = 250 mL
Time
t = 250/120 = 2.083 ≈ 2.1 h
Answer
t = 2.1 h
That is about 2 h 05 min, so the bag runs out at about 23:05.
9.Pediatric & critical-care dosing
Answer: D = 4 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
50/50 = 1 units/mL
Units per hour
D = 4·1 = 4 units/h
Answer
D = 4 units/h
10.Pediatric & critical-care dosing
Answer: D = 9.5 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
24·2000 = 48000 mcg/h
48000/60 = 800 mcg/min
Per kilogram
D = 800/84 = 9.524 ≈ 9.5 mcg/kg/min
Answer
D = 9.5 mcg/kg/min
11.Pharmacy calculations
Answer: V = 0.51 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/1000 mL = 1 mg/mL
Volume
V = 0.51/1 = 0.51 mL
Answer
V = 0.51 mL
12.Pharmacy calculations
Answer: V = 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.