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 is 4 ft 8 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
4 ft 8 in1 ft = 12 in1 in = 2.54 cm
h = cm
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ tbsp of liquid supplement, 1 fl oz of juice, 1½ cups of tea, 3 tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 tbsp = 15 mL1 fl oz = 30 mL1 cup = 8 fl oz = 240 mL1 tsp = 5 mL
V = mL
3.Dosage calculationsMedium
A child weighing 38 kg is prescribed 10 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
38 kg10 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A patient weighs 44 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 250 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
44 lb5 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 10 hours. After 8 hours you find that 330 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 / 10 hafter 8 h: 330 mL
R = mL/h
6.IV infusion ratesHard
1500 mL was ordered over 6 hours. After 4 hours you find that 580 mL is still in the bag, and the order must still finish on time. By what percentage Δ must the original pump rate be increased?
1500 mL / 6 hafter 4 h: 580 mL
Δ = %
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.
milk: 240 mLjelly: 100 mLIV infusion: 125 mL/h × 8 hIV antibiotic: 2 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 07:00 at 150 mL/h. After 4 hours the rate is changed to 75 mL/h and is not changed again. How many hours t after the start will the bag be empty? Round to one decimal place.
1000 mL150 mL/h · 4 h75 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 2 mL/h. How many units per hour D does the patient receive?
100 units/100 mL2 mL/h
D = units/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dobutamine 250 mg in 250 mL. The order is 2.5 mcg/kg/min for a patient who weighs 104 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL2.5 mcg/kg/min104 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 400 mg. What volume V do you draw up? Round to one decimal place.
500 mg1.8 mL+0.2 mL400 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 280 mg. Draw up the dose: what volume V do you give?
1000 mg4.2 mL + 0.8 mL280 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 142 cm
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.
Height in inches
4·12 + 8 = 56 in
Inches to centimetres
h = 56·2.54 = 142.2 ≈ 142 cm
Answer
h = 142 cm
2.Nursing math & unit conversions
Answer: V = 427.5 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 tbsp = 1.5·15 = 22.5 mL
1 fl oz = 1·30 = 30 mL
1½ cups = 1.5·240 = 360 mL
3 tsp = 3·5 = 15 mL
Add
V = 22.5 + 30 + 360 + 15 = 427.5 mL
Answer
V = 427.5 mL
3.Dosage calculations
Answer: V = 7.6 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 = 10·38 = 380 mg
Volume
V = 380/50 = 7.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 7.6 mL
4.Dosage calculations
Answer: V = 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.
Weight in kg
44/2.2 = 20 kg
Dose
5·20 = 100 mg
Volume
V = (100/250)·5 = 2 mL
Answer
V = 2 mL
5.IV infusion rates
Answer: R = 165 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
1500/10 = 150 mL/h
New rate
R = 330/2 = 165 mL/h
Answer
R = 165 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: Δ = 16 %
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
1500/6 = 250 mL/h
New rate
R = 580/2 = 290 mL/h
Percentage change
Δ = (290 − 250)/250·100% = 16%
Answer
Δ = 16%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: I = 1440 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: 240 + 100 = 340 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 2·50 = 100 mL
I = 1440 mL
Answer
I = 1440 mL
8.IV fluids & fluid balance
Answer: t = 9.3 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.
First part
150·4 = 600 mL
1000 − 600 = 400 mL left
Second part
400/75 = 5.333 h
Total time
t = 4 + 5.333 = 9.333 ≈ 9.3 h
Answer
t = 9.3 h
That is about 9 h 20 min, so the bag runs out at about 16:20.
9.Pediatric & critical-care dosing
Answer: D = 2 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 = 2·1 = 2 units/h
Answer
D = 2 units/h
10.Pediatric & critical-care dosing
Answer: R = 15.6 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
250 mg = 250 000 mcg
250 000/250 = 1000 mcg/mL
Dose per minute and per hour
2.5·104 = 260 mcg/min
260·60 = 15600 mcg/h
Pump rate
R = 15600/1000 = 15.6 mL/h
Answer
R = 15.6 mL/h
11.Pharmacy calculations
Answer: V = 1.6 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 = 400/250 = 1.6 mL
Answer
V = 1.6 mL
12.Pharmacy calculations
Answer: V = 1.4 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.