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 31.8059 kg. The rule in this exercise is that weights are rounded to the nearest tenth of a kilogram. What value x do you record?
31.8059 kg
x = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An order reads 2.5 mcg/kg/min for a patient who weighs 93 kg. Express the dose rate D in mg/h. Round to two decimal places.
2.5 mcg/kg/min93 kg
D = mg/h
3.Dosage calculationsMedium
A child weighing 26 kg is prescribed 5 mg/kg of a drug. The stock solution contains 25 mg/mL. Draw up the dose: what volume V do you give?
26 kg5 mg/kg25 mg/mL
V = mL
4.Dosage calculationsHard
A child weighing 12 kg is prescribed 20 mg/kg per dose of an oral suspension that contains 100 mg in 5 mL. What volume V do you give?
12 kg20 mg/kg100 mg/5 mL
V = mL
5.IV infusion ratesMedium
A drip runs at 20 gtt/min through a set of 15 gtt/mL. How many millilitres V does the patient receive in 12 hours?
20 gtt/min15 gtt/mL12 h
V = mL
6.IV infusion ratesHard
A drip runs at 40 gtt/min through a set of 15 gtt/mL. There are 300 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
40 gtt/min15 gtt/mL300 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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL.
milk: 200 mLtea: 240 mLIV infusion: 75 mL/h × 12 hIV antibiotic: 2 × 100 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 125 mL/h. At 20:00, 600 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL600 mL infused125 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion contains 50 units of regular insulin in 100 mL. The order is 0.05 units/kg/h for a patient who weighs 90 kg. Find the pump rate R in mL/h. Round to one decimal place.
50 units/100 mL0.05 units/kg/h90 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A dopamine infusion of 800 mg in 500 mL runs at 23 mL/h. The patient weighs 77 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL23 mL/h77 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.64 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.64 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 450 mL of 20% dextrose by mixing 70% and 10% dextrose. How many mL V of the 70% solution do you need? Round to the nearest whole mL.
70%10%20%450 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: x = 31.8 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
31.8059 → 8
Only the next digit decides
31.8059 → 0
0 is 4 or less, so 8 stays.
The digits after it (59) are ignored: round once, never step by step.
Round
x = 31.8 kg
Answer
x = 31.8 kg
2.Nursing math & unit conversions
Answer: D = 13.95 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 = 2.5 mcg/kg/min × 93 kg × (60 min/1 h) × (1 mg/1000 mcg)
Calculate
D = 2.5·93·60/1000 = 13.95 mg/h
Answer
D = 13.95 mg/h
3.Dosage calculations
Answer: V = 5.2 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 = 5·26 = 130 mg
Volume
V = 130/25 = 5.2 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 5.2 mL
4.Dosage calculations
Answer: V = 12 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
20·12 = 240 mg
Volume
V = (240/100)·5 = 12 mL
Answer
V = 12 mL
5.IV infusion rates
Answer: V = 960 mL
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
20·60/15 = 80 mL/h
Volume
V = 80·12 = 960 mL
Answer
V = 960 mL
6.IV infusion rates
Answer: t = 1.9 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
40·60/15 = 160 mL/h
Time left
t = 300/160 = 1.875 ≈ 1.9 h
Answer
t = 1.9 h
7.IV fluids & fluid balance
Answer: I = 1540 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 + 240 = 440 mL
IV infusion: 75·12 = 900 mL
IV antibiotic: 2·100 = 200 mL
I = 1540 mL
Answer
I = 1540 mL
8.IV fluids & fluid balance
Answer: t = 3.2 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 − 600 = 400 mL
Time
t = 400/125 = 3.2 h
Answer
t = 3.2 h
That is about 3 h 12 min, so the bag runs out at about 23:12.
9.Pediatric & critical-care dosing
Answer: R = 9 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
0.05·90 = 4.5 units/h
Concentration
50/100 = 0.5 units/mL
Pump rate
R = 4.5/0.5 = 9 mL/h
Answer
R = 9 mL/h
10.Pediatric & critical-care dosing
Answer: D = 8 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
800 000/500 = 1600 mcg/mL
Micrograms per minute
23·1600 = 36800 mcg/h
36800/60 = 613.3 mcg/min
Per kilogram
D = 613.3/77 = 7.965 ≈ 8 mcg/kg/min
Answer
D = 8 mcg/kg/min
11.Pharmacy calculations
Answer: V = 6.4 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 = 0.64/0.1 = 6.4 mL
Answer
V = 6.4 mL
12.Pharmacy calculations
Answer: V = 75 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.