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 dose calculation for an injection gives 9.5029 mL. The rule in this exercise is that volumes of 1 mL or more are rounded to the nearest tenth of a mL. What value x do you record?
9.5029 mL
x = mL
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 10 mcg/kg/min for a patient who weighs 65 kg. Express the dose rate D in mg/h. Round to two decimal places.
10 mcg/kg/min65 kg
D = mg/h
3.Dosage calculationsMedium
A patient weighs 25 kg. The prescribed dose is 30 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
25 kg30 mg/kg/day2× per day
D = mg
4.Dosage calculationsHard
A patient weighs 46.2 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 40 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to two decimal places.
46.2 lb1 mg/kg40 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
Infuse 1500 mL over 10 hours with a giving set of 15 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1500 mL10 h15 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 1000 mg of a drug in 500 mL and runs at 10 mL/h. How many milligrams per hour D does the patient receive?
1000 mg/500 mL10 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 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 bag runs by pump at 100 mL/h. At 11:00, 250 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
500 mL250 mL infused100 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 100 units of regular insulin in 100 mL. The order is 1 unit/h. Find the pump rate R in mL/h. Round to one decimal place.
100 units/100 mL1 units/h
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 400 mg in 250 mL runs at 14 mL/h. The patient weighs 81 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
400 mg/250 mL14 mL/h81 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.86 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.86 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 500 mg of powder. You add 1.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 150 mg. Draw up the dose: what volume V do you give?
500 mg1.6 mL + 0.4 mL150 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 9.5 mL
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
9.5029 → 5
Only the next digit decides
9.5029 → 0
0 is 4 or less, so 5 stays.
The digits after it (29) are ignored: round once, never step by step.
Round
x = 9.5 mL
Answer
x = 9.5 mL
2.Nursing math & unit conversions
Answer: D = 39 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 = 10 mcg/kg/min × 65 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 10·65·60/1000 = 39 mg/h
Answer
D = 39 mg/h
3.Dosage calculations
Answer: D = 375 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.
Total per day
30·25 = 750 mg
Per dose
D = 750/2 = 375 mg
Answer
D = 375 mg
4.Dosage calculations
Answer: V = 0.53 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
46.2/2.2 = 21 kg
Dose
1·21 = 21 mg
Volume
V = (21/40)·1 = 0.525 ≈ 0.53 mL
Answer
V = 0.53 mL
5.IV infusion rates
Answer: R = 38 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
10·60 = 600 min
Drip rate
R = 1500·15/600 = 37.5 ≈ 38 gtt/min
Answer
R = 38 gtt/min
At the bedside you round to the nearest whole drop: 38 gtt/min.
6.IV infusion rates
Answer: D = 20 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
1000/500 = 2 mg/mL
Dose rate
D = 2·10 = 20 mg/h
Answer
D = 20 mg/h
7.IV fluids & fluid balance
Answer: B = 5 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: 200 + 180 = 380 mL
ice chips: 100/2 = 50 mL
IV infusion: 50·8 = 400 mL
IV antibiotic: 1·100 = 100 mL
total intake = 930 mL
Total output
275 + 400 + 250 = 925 mL
Balance
B = 930 − 925 = 5 mL
Answer
B = 5 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 2.5 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
500 − 250 = 250 mL
Time
t = 250/100 = 2.5 h
Answer
t = 2.5 h
That is about 2 h 30 min, so the bag runs out at about 13:30.
9.Pediatric & critical-care dosing
Answer: R = 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.
Concentration
100/100 = 1 units/mL
Pump rate
R = 1/1 = 1 mL/h
Answer
R = 1 mL/h
10.Pediatric & critical-care dosing
Answer: D = 4.6 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
400 000/250 = 1600 mcg/mL
Micrograms per minute
14·1600 = 22400 mcg/h
22400/60 = 373.3 mcg/min
Per kilogram
D = 373.3/81 = 4.609 ≈ 4.6 mcg/kg/min
Answer
D = 4.6 mcg/kg/min
11.Pharmacy calculations
Answer: V = 8.6 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.
Strength in mg/mL
1000 mg/10 000 mL = 0.1 mg/mL
Volume
V = 0.86/0.1 = 8.6 mL
Answer
V = 8.6 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.