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 weight conversion gives 45.0352 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
45.0352 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 3 mcg/min. Express this dose rate D in mg/h.
3 mcg/min1 h = 60 min1 mg = 1000 mcg
D = mg/h
3.Dosage calculationsMedium
A patient weighs 22 kg and is prescribed 30 mg/kg as a single dose. Find the dose D in mg.
22 kg30 mg/kg
D = mg
4.Dosage calculationsHard
The prescription is 620 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
620 units1000 units/mL
V = mL
5.IV infusion ratesMedium
Infuse 500 mL over 5 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute.
500 mL5 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
500 mL was ordered over 10 hours. After 3 hours you find that 400 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?
500 mL / 10 hafter 3 h: 400 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 12-hour shift. The patient weighs 108 kg. Find the average urine output U in mL/kg/h. Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 60 mL/h. At 06:30, 700 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL700 mL infused60 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 500 mL. The order is 14 units/kg/h for a patient who weighs 74 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/500 mL14 units/kg/h74 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A patient who weighs 60 kg has an order for norepinephrine at 10 mcg/min. The bag contains 8 mg in 250 mL. Find the pump rate R in mL/h. Round to one decimal place.
8 mg/250 mL10 mcg/min60 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.86 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.86 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
1000 mg1.6 mL + 0.4 mL300 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 45 kg
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the tenths place
45.0352 → 0
Only the next digit decides
45.0352 → 3
3 is 4 or less, so 0 stays.
The digits after it (52) are ignored: round once, never step by step.
Round
x = 45 kg
Answer
x = 45 kg
2.Nursing math & unit conversions
Answer: D = 0.18 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/min × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 3·60/1000 = 0.18 mg/h
Answer
D = 0.18 mg/h
3.Dosage calculations
Answer: D = 660 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.
Dose
30·22 = 660 mg
Answer
D = 660 mg
4.Dosage calculations
Answer: V = 0.62 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 = 620/1000 = 0.62 mL
On the syringe
On this 1 mL syringe every small line is 0.01 mL.
Answer
V = 0.62 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.
Time in minutes
5·60 = 300 min
Drip rate
R = 500·15/300 = 25 gtt/min
Answer
R = 25 gtt/min
6.IV infusion rates
Answer: Δ = 14.29 %
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
500/10 = 50 mL/h
New rate
R = 400/7 = 57.14 mL/h
Percentage change
Δ = (57.14 − 50)/50·100% = 14.29%
Answer
Δ = 14.29%
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
7.IV fluids & fluid balance
Answer: U = 0.91 mL/kg/h
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 urine
325 + 325 + 375 + 150 = 1175 mL
Per kilogram per hour
U = 1175/(108·12) = 0.9066 ≈ 0.91 mL/kg/h
Answer
U = 0.91 mL/kg/h
8.IV fluids & fluid balance
Answer: t = 5 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 − 700 = 300 mL
Time
t = 300/60 = 5 h
Answer
t = 5 h
That is about 5 h 00 min, so the bag runs out at about 11:30.
9.Pediatric & critical-care dosing
Answer: R = 20.7 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
14·74 = 1 036 units/h
Concentration
25 000/500 = 50 units/mL
Pump rate
R = 1036/50 = 20.72 ≈ 20.7 mL/h
Answer
R = 20.7 mL/h
10.Pediatric & critical-care dosing
Answer: R = 18.8 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
8 000/250 = 32 mcg/mL
Dose per hour
The order is per minute for the whole patient, so the weight is not needed.
10·60 = 600 mcg/h
Pump rate
R = 600/32 = 18.75 ≈ 18.8 mL/h
Answer
R = 18.8 mL/h
11.Pharmacy calculations
Answer: V = 0.86 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.
Strength in mg/mL
1000 mg/1000 mL = 1 mg/mL
Volume
V = 0.86/1 = 0.86 mL
Answer
V = 0.86 mL
12.Pharmacy calculations
Answer: V = 0.6 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.