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 36 °C. Convert it to degrees Fahrenheit T with °F = °C × 9/5 + 32. Round to one decimal place.
36 °C
T = °F
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 3 mcg/kg/min for a patient who weighs 77 kg. Express the dose rate D in mg/h. Round to two decimal places.
3 mcg/kg/min77 kg
D = mg/h
3.Dosage calculationsMedium
A vial contains 2 g of powder. The label says: add 7.4 mL of water for injection to give a total volume of 8 mL. The prescription is 200 mg. What volume V of the reconstituted solution do you give?
2 g+ 7.4 mL → 8 mL200 mg
V = mL
4.Dosage calculationsHard
You must prepare 100 mL of a 0.5% (w/v) solution from a 20% (w/v) stock solution. How much water W must be added to the stock?
C₁ = 20%C₂ = 0.5%V₂ = 100 mL
W = 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 15 mL/h. How many milligrams per hour D does the patient receive?
100 mg/250 mL15 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 total intake I in mL.
soup: 200 mLtea: 150 mLIV infusion: 75 mL/h × 12 hIV antibiotic: 2 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 120 mL/h. At 08:30, 150 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL150 mL infused120 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 20 units/kg/h for a patient who weighs 52 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL20 units/kg/h52 kg
R = mL/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 10 mcg/kg/min for a patient who weighs 63 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL10 mcg/kg/min63 kg
R = mL/h
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 750 mg. What volume V do you draw up? Round to one decimal place.
1000 mg3.5 mL+0.5 mL750 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 250 mg of powder. You add 4.8 mL of diluent, and the powder adds 0.2 mL of volume. The prescription is 145 mg. Draw up the dose: what volume V do you give?
250 mg4.8 mL + 0.2 mL145 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: T = 96.8 °F
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.
Multiply by 9/5
36·9/5 = 64.8
Add 32
T = 64.8 + 32 = 96.8 °F
Answer
T = 96.8 °F
2.Nursing math & unit conversions
Answer: D = 13.86 mg/h
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.
Set up the chain
D = 3 mcg/kg/min × 77 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 3·77·60/1000 = 13.86 mg/h
Answer
D = 13.86 mg/h
3.Dosage calculations
Answer: V = 0.8 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.
Concentration after mixing
2000 mg/8 mL = 250 mg/mL
Volume
V = 200/250 = 0.8 mL
Answer
V = 0.8 mL
4.Dosage calculations
Answer: W = 97.5 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.
Volume of stock
V₁ = 0.5·100/20 = 2.5 mL
Water to add
W = 100 − 2.5 = 97.5 mL
Answer
W = 97.5 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 = 6 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 = 0.4·15 = 6 mg/h
Answer
D = 6 mg/h
7.IV fluids & fluid balance
Answer: I = 1350 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 + 150 = 350 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 2·50 = 100 mL
I = 1350 mL
Answer
I = 1350 mL
8.IV fluids & fluid balance
Answer: t = 7.1 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 − 150 = 850 mL
Time
t = 850/120 = 7.083 ≈ 7.1 h
Answer
t = 7.1 h
That is about 7 h 05 min, so the bag runs out at about 15:35.
9.Pediatric & critical-care dosing
Answer: R = 26 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
20·52 = 1 040 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1040/40 = 26 mL/h
Answer
R = 26 mL/h
10.Pediatric & critical-care dosing
Answer: R = 37.8 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
10·63 = 630 mcg/min
630·60 = 37800 mcg/h
Pump rate
R = 37800/1000 = 37.8 mL/h
Answer
R = 37.8 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.
Final volume
3.5 + 0.5 = 4 mL
Concentration
1000/4 = 250 mg/mL
Volume to give
V = 750/250 = 3 mL
Answer
V = 3 mL
12.Pharmacy calculations
Answer: V = 2.9 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.