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 07:45 (24-hour clock). Which entry is the same time on the 12-hour clock? Click it.
07:45
17:45 PM
26:45 AM
37:45 AM
49:45 AM
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A blood glucose result is 356 mg/dL. Using 1 mmol/L = 18 mg/dL for glucose, find c in mmol/L. Round to one decimal place.
356 mg/dL1 mmol/L = 18 mg/dL
c = mmol/L
3.Dosage calculationsMedium
A patient weighs 30 kg. The prescribed dose is 2 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
30 kg2 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
The prescription is 3900 units of a drug that comes as 5000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
3900 units5000 units/mL
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 100 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.
100 mL/h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 100 mg of a drug in 250 mL and runs at 20 mL/h. How many milligrams per hour D does the patient receive?
100 mg/250 mL20 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 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 500 mL infusion starts at 07:00 at 100 mL/h. After 2 hours the rate is changed to 80 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
500 mL100 mL/h · 2 h80 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 12 units/kg/h for a patient who weighs 71 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL12 units/kg/h71 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 2 mcg/kg/min for a patient who weighs 88 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min88 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 8.2 mL of diluent. The prescribed dose is 1 500 000 units. What volume V do you draw up? Round to one decimal place.
8.2 mL → 500 000 units/mL1 500 000 units
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 10% salicylic acid ointment. How many grams m of 2% salicylic acid ointment must you add to make a 5% ointment? Round to the nearest whole gram.
30 g · 10%2%5%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: 7:45 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
07 → 7 AM
Answer
7:45 AM
Answer
7:45 AM
2.Nursing math & unit conversions
Answer: c = 19.8 mmol/L
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Convert
c = 356/18 = 19.78 ≈ 19.8 mmol/L
Answer
c = 19.8 mmol/L
3.Dosage calculations
Answer: D = 30 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
2·30 = 60 mg
Per dose
D = 60/2 = 30 mg
Answer
D = 30 mg
4.Dosage calculations
Answer: V = 0.78 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.
Volume
V = 3900/5000 = 0.78 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.78 mL
5.IV infusion rates
Answer: R = 25 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
100/60 = 1.667 mL/min
Drip rate
R = 1.667·15 = 25 gtt/min
Answer
R = 25 gtt/min
6.IV infusion rates
Answer: D = 8 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
100/250 = 0.4 mg/mL
Dose rate
D = 0.4·20 = 8 mg/h
Answer
D = 8 mg/h
7.IV fluids & fluid balance
Answer: B = 85 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: 150 + 150 + 240 = 540 mL
ice chips: 120/2 = 60 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 1·100 = 100 mL
total intake = 1600 mL
Total output
450 + 350 + 200 + 475 + 40 = 1515 mL
Balance
B = 1600 − 1515 = 85 mL
Answer
B = 85 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 5.8 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.
First part
100·2 = 200 mL
500 − 200 = 300 mL left
Second part
300/80 = 3.75 h
Total time
t = 2 + 3.75 = 5.75 ≈ 5.8 h
Answer
t = 5.8 h
That is about 5 h 45 min, so the bag runs out at about 12:45.
9.Pediatric & critical-care dosing
Answer: R = 8.5 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
12·71 = 852 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 852/100 = 8.52 ≈ 8.5 mL/h
Answer
R = 8.5 mL/h
10.Pediatric & critical-care dosing
Answer: R = 6.6 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
2·88 = 176 mcg/min
176·60 = 10560 mcg/h
Pump rate
R = 10560/1600 = 6.6 mL/h
Answer
R = 6.6 mL/h
11.Pharmacy calculations
Answer: V = 3 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
8.2 mL → 500 000 units/mL
Volume to give
V = 1 500 000/500 000 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: m = 50 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.