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 newborn weighs 7 lb 8 oz. Using 1 lb = 16 oz and 1 kg = 2.2 lb, find the weight m in kilograms. Round to two decimal places.
7 lb 8 oz1 lb = 16 oz1 kg = 2.2 lb
m = kg
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). An infusion starts at 23:40 and finishes at 05:10 the next morning (24-hour clock). How many hours t did it run? Give the answer in hours as a decimal, rounded to two decimal places.
23:4005:10
t = h
3.Dosage calculationsMedium
A child weighing 8 kg is prescribed 10 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
8 kg10 mg/kg50 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 120 mg in 5 mL. What volume V do you give?
12 kg20 mg/kg120 mg/5 mL
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 10 hours. After 5 hours you find that 890 mL is still in the bag, and the order must still finish on time. To what rate R in mL/h must the pump be reset?
1500 mL / 10 hafter 5 h: 890 mL
R = mL/h
6.IV infusion ratesHard
A drip runs at 40 gtt/min through a set of 60 gtt/mL. There are 450 mL left in the bag. How many hours t until it is empty? Round to one decimal place.
40 gtt/min60 gtt/mL450 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 total intake I in mL.
milk: 100 mLwater: 240 mLIV infusion: 100 mL/h × 8 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 06:30 and runs by pump at 50 mL/h. How many mL V are left in the bag at 07:30?
1000 mL50 mL/h06:30 → 07:30
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). An infusion of 100 units of regular insulin in 250 mL runs at 2 mL/h. How many units per hour D does the patient receive?
100 units/250 mL2 mL/h
D = units/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 5 mcg/kg/min for a patient who weighs 102 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
250 mg/250 mL5 mcg/kg/min102 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:1000. You need 0.58 mg. Draw up the volume in the 1 mL syringe: what volume V is that?
1:10000.58 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You have 30 g of 20% zinc oxide ointment. How many grams m of plain ointment base (0%) must you add to make a 10% ointment? Round to the nearest whole gram.
30 g · 20%0%10%
m = g
3Solutions
1.Nursing math & unit conversions
Answer: m = 3.41 kg
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Ounces to pounds
8 oz/16 = 0.5 lb
7 + 0.5 = 7.5 lb
Pounds to kilograms
m = 7.5/2.2 = 3.409 ≈ 3.41 kg
Answer
m = 3.41 kg
2.Nursing math & unit conversions
Answer: t = 5.5 h
24-hour clock: from 1 PM onwards add 12 to the hour (3:45 PM = 15:45). Midnight to 12:59 AM is 00:00–00:59, and 12:00–12:59 PM stays 12:00–12:59. Going back, subtract 12 from hours 13–23 and add PM; hours 00 become 12 AM. Count time across midnight in two parts: up to 24:00 (00:00), then from 00:00 on.
Before midnight
23:40 → 24:00 = 20 min
After midnight
00:00 → 05:10 = 310 min
Total
20 + 310 = 330 min
t = 330/60 = 5.5 h
Answer
t = 5.5 h
3.Dosage calculations
Answer: V = 1.6 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 = 10·8 = 80 mg
Volume
V = 80/50 = 1.6 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 1.6 mL
4.Dosage calculations
Answer: V = 10 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 = (240/120)·5 = 10 mL
Answer
V = 10 mL
5.IV infusion rates
Answer: R = 178 mL/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.
Original rate
1500/10 = 150 mL/h
New rate
R = 890/5 = 178 mL/h
Answer
R = 178 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: t = 11.3 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
40·60/60 = 40 mL/h
Time left
t = 450/40 = 11.25 ≈ 11.3 h
Answer
t = 11.3 h
7.IV fluids & fluid balance
Answer: I = 1190 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: 100 + 240 = 340 mL
IV infusion: 100·8 = 800 mL
IV antibiotic: 1·50 = 50 mL
I = 1190 mL
Answer
I = 1190 mL
8.IV fluids & fluid balance
Answer: V = 950 mL
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.
Elapsed time
06:30 → 07:30 = 1 h
Volume infused
50·1 = 50 mL
Volume left
V = 1000 − 50 = 950 mL
Answer
V = 950 mL
9.Pediatric & critical-care dosing
Answer: D = 0.8 units/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
100/250 = 0.4 units/mL
Units per hour
D = 2·0.4 = 0.8 units/h
Answer
D = 0.8 units/h
10.Pediatric & critical-care dosing
Answer: R = 30.6 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
5·102 = 510 mcg/min
510·60 = 30600 mcg/h
Pump rate
R = 30600/1000 = 30.6 mL/h
Answer
R = 30.6 mL/h
11.Pharmacy calculations
Answer: V = 0.58 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 = 0.58/1 = 0.58 mL
Answer
V = 0.58 mL
12.Pharmacy calculations
Answer: m = 30 g
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.