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 9:10 AM. Which entry is the same time on the 24-hour clock? Click it.
9:10 AM
110:10
208:10
321:10
409:10
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ tsp of cough syrup, 1 tbsp of liquid supplement, ½ fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 tbsp = 15 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
A patient weighs 45 kg. The prescribed dose is 20 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
45 kg20 mg/kg/day3× per day
D = mg
4.Dosage calculationsHard
An infusion contains 25000 units of a drug in 1000 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?
25000 units/1000 mL1500 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 250 mL over 4 hours with a giving set of 60 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL4 h60 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 30 gtt/min through a set of 60 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty?
30 gtt/min60 gtt/mL450 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 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 75 mL/h. At 20:00, 450 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL450 mL infused75 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 250 mL. The order is 20 units/kg/h for a patient who weighs 64 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL20 units/kg/h64 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 90 kg has an order for norepinephrine at 10 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 mL10 mcg/min90 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. The prescribed dose is 300 mg. What volume V do you draw up? Round to one decimal place.
500 mg1.8 mL+0.2 mL300 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 60 g of 5% coal tar ointment. How many grams m of 1% coal tar ointment must you add to make a 3% ointment? Round to the nearest whole gram.
60 g · 5%1%3%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: 09:10
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
9 AM → 09
Answer
09:10
Answer
09:10
2.Nursing math & unit conversions
Answer: V = 37.5 mL
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.
Each item in mL
1½ tsp = 1.5·5 = 7.5 mL
1 tbsp = 1·15 = 15 mL
½ fl oz = 0.5·30 = 15 mL
Add
V = 7.5 + 15 + 15 = 37.5 mL
Answer
V = 37.5 mL
3.Dosage calculations
Answer: D = 300 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
20·45 = 900 mg
Per dose
D = 900/3 = 300 mg
Answer
D = 300 mg
4.Dosage calculations
Answer: R = 60 mL/h
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
25000/1000 = 25 units/mL
Pump rate
R = 1500/25 = 60 mL/h
Answer
R = 60 mL/h
5.IV infusion rates
Answer: R = 63 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
4·60 = 240 min
Drip rate
R = 250·60/240 = 62.5 ≈ 63 gtt/min
Answer
R = 63 gtt/min
At the bedside you round to the nearest whole drop: 63 gtt/min.
6.IV infusion rates
Answer: t = 15 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
30·60/60 = 30 mL/h
Time left
t = 450/30 = 15 h
Answer
t = 15 h
7.IV fluids & fluid balance
Answer: B = 675 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 + 120 = 560 mL
IV infusion: 60·12 = 720 mL
IV antibiotic: 2·100 = 200 mL
total intake = 1480 mL
Total output
475 + 300 + 30 = 805 mL
Balance
B = 1480 − 805 = 675 mL
Answer
B = 675 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 7.3 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 − 450 = 550 mL
Time
t = 550/75 = 7.333 ≈ 7.3 h
Answer
t = 7.3 h
That is about 7 h 20 min, so the bag runs out at about 03:20.
9.Pediatric & critical-care dosing
Answer: R = 12.8 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
20·64 = 1 280 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 1280/100 = 12.8 mL/h
Answer
R = 12.8 mL/h
10.Pediatric & critical-care dosing
Answer: R = 37.5 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
4 000/250 = 16 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/16 = 37.5 mL/h
Answer
R = 37.5 mL/h
11.Pharmacy calculations
Answer: V = 1.2 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.
Final volume
1.8 + 0.2 = 2 mL
Concentration
500/2 = 250 mg/mL
Volume to give
V = 300/250 = 1.2 mL
Answer
V = 1.2 mL
12.Pharmacy calculations
Answer: m = 60 g
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.