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 patient’s temperature is 99.8 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
99.8 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A serum creatinine result is 1.5 mg/dL. Using 1 mg/dL = 88.4 µmol/L for creatinine, find c in µmol/L to the nearest whole number.
1.5 mg/dL1 mg/dL = 88.4 µmol/L
c = µmol/L
3.Dosage calculationsMedium
A patient weighing 14 kg has a body surface area of 0.68 m². The prescription is 175 mg/m². Find the dose D in mg.
14 kgBSA = 0.68 m²175 mg/m²
D = mg
4.Dosage calculationsHard
The prescription is 0.28 mg. The ampoule contains 2000 micrograms per mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
0.28 mg2000 mcg/mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 4 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL4 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
An infusion of 100 mg in 250 mL runs at 10 mL/h. How many micrograms per minute D does the patient receive?
100 mg/250 mL10 mL/h
D = mcg/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 8-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
tea: 200 mLwater: 240 mLice chips: 240 mLIV infusion: 100 mL/h × 8 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 500 mL infusion starts at 12:00 at 80 mL/h. After 4 hours the rate is changed to 50 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 mL80 mL/h · 4 h50 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 100 mL runs at 8 mL/h. How many units per hour D does the patient receive?
100 units/100 mL8 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 31 mL/h. The patient weighs 57 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL31 mL/h57 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. The prescribed dose is 800 mg. What volume V do you draw up? Round to one decimal place.
1000 mg3.5 mL+0.5 mL800 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 3.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 425 mg. Draw up the dose: what volume V do you give?
1000 mg3.4 mL + 0.6 mL425 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 37.7 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
99.8 − 32 = 67.8
Multiply by 5/9
T = 67.8·5/9 = 37.67 ≈ 37.7 °C
Answer
T = 37.7 °C
2.Nursing math & unit conversions
Answer: c = 133 µmol/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 = 1.5·88.4 = 132.6 ≈ 133 µmol/L
Answer
c = 133 µmol/L
3.Dosage calculations
Answer: D = 119 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).
Dose
D = 175·0.68 = 119 mg
Answer
D = 119 mg
4.Dosage calculations
Answer: V = 0.14 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.
Same units
0.28 mg = 280 mcg
Volume
V = 280/2000 = 0.14 mL
Answer
V = 0.14 mL
5.IV infusion rates
Answer: R = 16 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 = 250·15/240 = 15.63 ≈ 16 gtt/min
Answer
R = 16 gtt/min
At the bedside you round to the nearest whole drop: 16 gtt/min.
6.IV infusion rates
Answer: D = 66.67 mcg/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
100000 mcg/250 mL = 400 mcg/mL
Dose per hour
10·400 = 4000 mcg/h
Dose per minute
D = 4000/60 = 66.67 mcg/min
Answer
D = 66.67 mcg/min
7.IV fluids & fluid balance
Answer: I = 1560 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.
Add the intake
oral: 200 + 240 = 440 mL
ice chips: 240/2 = 120 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 2·100 = 200 mL
I = 1560 mL
Answer
I = 1560 mL
8.IV fluids & fluid balance
Answer: t = 7.6 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
80·4 = 320 mL
500 − 320 = 180 mL left
Second part
180/50 = 3.6 h
Total time
t = 4 + 3.6 = 7.6 h
Answer
t = 7.6 h
That is about 7 h 36 min, so the bag runs out at about 19:36.
9.Pediatric & critical-care dosing
Answer: D = 8 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
100/100 = 1 units/mL
Units per hour
D = 8·1 = 8 units/h
Answer
D = 8 units/h
10.Pediatric & critical-care dosing
Answer: D = 14.5 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
31·1600 = 49600 mcg/h
49600/60 = 826.7 mcg/min
Per kilogram
D = 826.7/57 = 14.5 mcg/kg/min
Answer
D = 14.5 mcg/kg/min
11.Pharmacy calculations
Answer: V = 3.2 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
3.5 + 0.5 = 4 mL
Concentration
1000/4 = 250 mg/mL
Volume to give
V = 800/250 = 3.2 mL
Answer
V = 3.2 mL
12.Pharmacy calculations
Answer: V = 1.7 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.