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 is charted at 9:00 PM. Which entry is the same time on the 24-hour clock? Click it.
9:00 PM
120:00
209:00
322:00
421:00
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A blood glucose result is 173 mg/dL. Using 1 mmol/L = 18 mg/dL for glucose, find c in mmol/L. Round to one decimal place.
173 mg/dL1 mmol/L = 18 mg/dL
c = mmol/L
3.Dosage calculationsMedium
A vial contains 1 g of powder. The label says: add 4.2 mL of water for injection to give a total volume of 5 mL. The prescription is 200 mg. What volume V of the reconstituted solution do you give?
1 g+ 4.2 mL → 5 mL200 mg
V = mL
4.Dosage calculationsHard
A child weighing 12 kg is prescribed 12.5 mg/kg per dose of an oral suspension that contains 250 mg in 5 mL. What volume V do you give?
12 kg12.5 mg/kg250 mg/5 mL
V = mL
5.IV infusion ratesMedium
1500 mL was ordered over 10 hours. After 3 hours you find that 1200 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 3 h: 1200 mL
R = mL/h
6.IV infusion ratesHard
A bag contains 4 g of a drug in 500 mL. The order is 4 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/500 mL4 mg/min
R = mL/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).
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag runs by pump at 100 mL/h. At 10:30, 100 mL have already been infused. How many hours t until the bag is empty? Round to one decimal place.
1000 mL100 mL infused100 mL/h
t = h
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 8 mL/h. How many units per hour D does the patient receive?
100 units/250 mL8 mL/h
D = units/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 36 mL/h. The patient weighs 56 kg. What dose D in mcg/kg/min is the patient receiving? Round to one decimal place.
800 mg/500 mL36 mL/h56 kg
D = mcg/kg/min
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.76 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.76 mg
V = mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 200 mL of 3% hydrogen peroxide from a 30% stock and purified water. How many mL V of water do you need? Round to the nearest whole mL.
30%0%3%200 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 21:00
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.
Convert the hour
9 PM → 9 + 12 = 21
Answer
21:00
Answer
21:00
2.Nursing math & unit conversions
Answer: c = 9.6 mmol/L
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.
Convert
c = 173/18 = 9.611 ≈ 9.6 mmol/L
Answer
c = 9.6 mmol/L
3.Dosage calculations
Answer: V = 1 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.
Concentration after mixing
1000 mg/5 mL = 200 mg/mL
Volume
V = 200/200 = 1 mL
Answer
V = 1 mL
4.Dosage calculations
Answer: V = 3 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
12.5·12 = 150 mg
Volume
V = (150/250)·5 = 3 mL
Answer
V = 3 mL
5.IV infusion rates
Answer: R = 171.4 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 = 1200/7 = 171.4 mL/h
Answer
R = 171.4 mL/h
Many hospitals allow such an adjustment up to 25% without a new order; check local policy.
6.IV infusion rates
Answer: R = 30 mL/h
Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).
Concentration
4000 mg/500 mL = 8 mg/mL
Dose per hour
4·60 = 240 mg/h
Pump rate
R = 240/8 = 30 mL/h
Answer
R = 30 mL/h
7.IV fluids & fluid balance
Answer: B = −205 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
IV infusion: 80·8 = 640 mL
IV antibiotic: 1·50 = 50 mL
total intake = 1070 mL
Total output
250 + 400 + 375 + 150 + 100 = 1275 mL
Balance
B = 1070 − 1275 = −205 mL
Answer
B = −205 mL
Negative: the patient lost more fluid than went in.
8.IV fluids & fluid balance
Answer: t = 9 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 − 100 = 900 mL
Time
t = 900/100 = 9 h
Answer
t = 9 h
That is about 9 h 00 min, so the bag runs out at about 19:30.
9.Pediatric & critical-care dosing
Answer: D = 3.2 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 = 8·0.4 = 3.2 units/h
Answer
D = 3.2 units/h
10.Pediatric & critical-care dosing
Answer: D = 17.1 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
36·1600 = 57600 mcg/h
57600/60 = 960 mcg/min
Per kilogram
D = 960/56 = 17.14 ≈ 17.1 mcg/kg/min
Answer
D = 17.1 mcg/kg/min
11.Pharmacy calculations
Answer: V = 7.6 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 = 0.76/0.1 = 7.6 mL
Answer
V = 7.6 mL
12.Pharmacy calculations
Answer: V = 180 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.
Alligation parts
30%: 3 − 0 = 3 parts
0%: 30 − 3 = 27 parts
total: 30 parts
Water
V = 200·27/30 = 180 mL
Answer
V = 180 mL
Check: 20 mL of 30% contains 6 g of drug, which is 3% of 200 mL.