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 102.1 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
102.1 °F
T = °C
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 2 tsp of an oral suspension every 12 hours for 7 days. The suspension comes in 150 mL bottles. Using 1 tsp = 5 mL, how many whole bottles N must be supplied so the course is complete?
2 tspevery 12 hours7 days150 mL1 tsp = 5 mL
N =
3.Dosage calculationsMedium
A dose of 250 mg is needed from a 5% (w/v) solution. What volume V contains this dose?
250 mg5% w/v
V = mL
4.Dosage calculationsHard
A patient weighs 85.8 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?
85.8 lb5 mg/kg250 mg/5 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 12 hours. After 5 hours you find that 980 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 / 12 hafter 5 h: 980 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 20 gtt/min through a set of 20 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
20 gtt/min20 gtt/mL400 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 8-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 10:30 at 80 mL/h. After 2 hours the rate is changed to 100 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 · 2 h100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 18 units/kg/h for a patient who weighs 98 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL18 units/kg/h98 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dobutamine infusion of 250 mg in 250 mL runs at 18 mL/h. The patient weighs 70 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
250 mg/250 mL18 mL/h70 kg
D = mcg/kg/min
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. What is the concentration C in mg/mL after reconstitution?
500 mg1.8 mL+0.2 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 180 mg. Draw up the dose: what volume V do you give?
500 mg4.5 mL + 0.5 mL180 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 38.9 °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
102.1 − 32 = 70.1
Multiply by 5/9
T = 70.1·5/9 = 38.94 ≈ 38.9 °C
Answer
T = 38.9 °C
2.Nursing math & unit conversions
Answer: N = 1
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.
Total volume
10 mL × 2 × 7 = 140 mL
Bottles
140/150 = 0.9333 → N = 1
Answer
N = 1
3.Dosage calculations
Answer: V = 5 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
5% = 50 mg/mL
Volume
V = 250/50 = 5 mL
Answer
V = 5 mL
4.Dosage calculations
Answer: V = 3.9 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
85.8/2.2 = 39 kg
Dose
5·39 = 195 mg
Volume
V = (195/250)·5 = 3.9 mL
Answer
V = 3.9 mL
5.IV infusion rates
Answer: R = 140 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
1500/12 = 125 mL/h
New rate
R = 980/7 = 140 mL/h
Answer
R = 140 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 6.7 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
20·60/20 = 60 mL/h
Time left
t = 400/60 = 6.667 ≈ 6.7 h
Answer
t = 6.7 h
7.IV fluids & fluid balance
Answer: B = 1370 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: 250 + 200 + 250 = 700 mL
ice chips: 240/2 = 120 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1920 mL
Total output
250 + 300 = 550 mL
Balance
B = 1920 − 550 = 1370 mL
Answer
B = 1370 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 5.4 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
80·2 = 160 mL
500 − 160 = 340 mL left
Second part
340/100 = 3.4 h
Total time
t = 2 + 3.4 = 5.4 h
Answer
t = 5.4 h
That is about 5 h 24 min, so the bag runs out at about 15:54.
9.Pediatric & critical-care dosing
Answer: R = 44.1 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
18·98 = 1 764 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1764/40 = 44.1 mL/h
Answer
R = 44.1 mL/h
10.Pediatric & critical-care dosing
Answer: D = 4.3 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
250 000/250 = 1000 mcg/mL
Micrograms per minute
18·1000 = 18000 mcg/h
18000/60 = 300 mcg/min
Per kilogram
D = 300/70 = 4.286 ≈ 4.3 mcg/kg/min
Answer
D = 4.3 mcg/kg/min
11.Pharmacy calculations
Answer: C = 250 mg/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
C = 500/2 = 250 mg/mL
Answer
C = 250 mg/mL
12.Pharmacy calculations
Answer: V = 1.8 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.