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 drip-rate calculation gives 167.954 gtt/min. The rule in this exercise is that drip rates are rounded to the nearest whole drop. What value x do you record?
167.954 gtt/min
x = gtt/min
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion delivers 10 mg/h. Express this dose rate D in mcg/min. Round to one decimal place.
10 mg/h1 mg = 1000 mcg1 h = 60 min
D = mcg/min
3.Dosage calculationsMedium
A child weighing 36 kg is prescribed 5 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
36 kg5 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 28 kg is prescribed 10 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?
28 kg10 mg/kg250 mg/5 mL
V = mL
5.IV infusion ratesMedium
Infuse 250 mL over 5 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
250 mL5 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A drip runs at 25 gtt/min through a set of 15 gtt/mL. There are 400 mL left in the bag. How many hours t until it is empty?
25 gtt/min15 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 1000 mL infusion starts at 13:30 at 80 mL/h. After 4 hours the rate is changed to 60 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 mL80 mL/h · 4 h60 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 54 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/h54 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 12 mcg/kg/min for a patient who weighs 87 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL12 mcg/kg/min87 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains cefazolin 1000 mg as a powder. The practice label says to add 4.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
1000 mg4.5 mL+0.5 mL
C = mg/mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 1.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 300 mg. Draw up the dose: what volume V do you give?
1000 mg1.4 mL + 0.6 mL300 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 168 gtt/min
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 ones place
167.954 → 7
Only the next digit decides
167.954 → 9
9 is 5 or more, so round 7 up.
The digits after it (54) are ignored: round once, never step by step.
Round
x = 168 gtt/min
Answer
x = 168 gtt/min
2.Nursing math & unit conversions
Answer: D = 166.7 mcg/min
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 mg/h × (1000 mcg/1 mg) × (1 h/60 min)
Calculate
D = 10000/60 = 166.7 mcg/min
Answer
D = 166.7 mcg/min
3.Dosage calculations
Answer: V = 3.6 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 = 5·36 = 180 mg
Volume
V = 180/50 = 3.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 3.6 mL
4.Dosage calculations
Answer: V = 5.6 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.
Dose from weight
10·28 = 280 mg
Volume
V = (280/250)·5 = 5.6 mL
Answer
V = 5.6 mL
5.IV infusion rates
Answer: R = 8 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 = 250·10/300 = 8.333 ≈ 8 gtt/min
Answer
R = 8 gtt/min
At the bedside you round to the nearest whole drop: 8 gtt/min.
6.IV infusion rates
Answer: t = 4 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
25·60/15 = 100 mL/h
Time left
t = 400/100 = 4 h
Answer
t = 4 h
7.IV fluids & fluid balance
Answer: B = 975 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 + 200 = 400 mL
ice chips: 100/2 = 50 mL
IV infusion: 125·8 = 1000 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1550 mL
Total output
250 + 325 = 575 mL
Balance
B = 1550 − 575 = 975 mL
Answer
B = 975 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: t = 15.3 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
80·4 = 320 mL
1000 − 320 = 680 mL left
Second part
680/60 = 11.33 h
Total time
t = 4 + 11.33 = 15.33 ≈ 15.3 h
Answer
t = 15.3 h
That is about 15 h 20 min, so the bag runs out at about 04:50.
9.Pediatric & critical-care dosing
Answer: R = 27 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
20·54 = 1 080 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 1080/40 = 27 mL/h
Answer
R = 27 mL/h
10.Pediatric & critical-care dosing
Answer: R = 39.2 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
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
12·87 = 1044 mcg/min
1044·60 = 62640 mcg/h
Pump rate
R = 62640/1600 = 39.15 ≈ 39.2 mL/h
Answer
R = 39.2 mL/h
11.Pharmacy calculations
Answer: C = 200 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
4.5 + 0.5 = 5 mL
Concentration
C = 1000/5 = 200 mg/mL
Answer
C = 200 mg/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.