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 6:35 AM. Which entry is the same time on the 24-hour clock? Click it.
6:35 AM
107:35
206:35
318:35
405:35
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A blood glucose result is 16.3 mmol/L. Using 1 mmol/L = 18 mg/dL for glucose, find c in mg/dL to the nearest whole number.
16.3 mmol/L1 mmol/L = 18 mg/dL
c = mg/dL
3.Dosage calculationsMedium
A child weighing 30 kg is prescribed 15 mg/kg of a drug. The stock solution contains 50 mg/mL. Draw up the dose: what volume V do you give?
30 kg15 mg/kg50 mg/mL
V = mL
4.Dosage calculationsHard
An infusion contains 25000 units of a drug in 500 mL. The prescription is 1000 units per hour. At what rate R do you set the pump, in mL/h?
25000 units/500 mL1000 units/h
R = mL/h
5.IV infusion ratesMedium
Infuse 1000 mL over 3 hours with a giving set of 10 gtt/mL. Find the drip rate R in drops per minute. Round to the nearest whole number.
1000 mL3 h10 gtt/mL
R = gtt/min
6.IV infusion ratesHard
A bag contains 4 g of a drug in 500 mL. The order is 3 mg per minute. At what rate R do you set the pump, in mL/h?
4 g/500 mL3 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 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the total intake I in mL. Count ice chips as half their volume.
juice: 200 mLtea: 150 mLice chips: 240 mLIV infusion: 50 mL/h × 12 hIV antibiotic: 1 × 50 mL
I = mL
8.IV fluids & fluid balanceHard
Practice exercise (made-up values, not clinical guidance). A 1000 mL infusion starts at 19:00 at 150 mL/h. After 3 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 mL150 mL/h · 3 h60 mL/h
t = h
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 25 000 units of heparin in 250 mL. The order is 12 units/kg/h for a patient who weighs 80 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
25 000 units/250 mL12 units/kg/h80 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 800 mg in 500 mL. The order is 2 mcg/kg/min for a patient who weighs 77 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
800 mg/500 mL2 mcg/kg/min77 kg
R = mL/h
11.Pharmacy calculationsMedium
A solution has a ratio strength of 1:10 000. You need 0.38 mg. Draw up the volume in the 10 mL syringe: what volume V is that?
1:10 0000.38 mg
V = mL
12.Pharmacy calculationsHard
A vial holds 1000 mg of powder. You add 9.6 mL of diluent, and the powder adds 0.4 mL of volume. The prescription is 470 mg. Draw up the dose: what volume V do you give?
1000 mg9.6 mL + 0.4 mL470 mg
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: 06:35
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
6 AM → 06
Answer
06:35
Answer
06:35
2.Nursing math & unit conversions
Answer: c = 293 mg/dL
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 = 16.3·18 = 293.4 ≈ 293 mg/dL
Answer
c = 293 mg/dL
3.Dosage calculations
Answer: V = 9 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 = 15·30 = 450 mg
Volume
V = 450/50 = 9 mL
On the syringe
On this 10 mL syringe every small line is 0.2 mL.
Answer
V = 9 mL
4.Dosage calculations
Answer: R = 20 mL/h
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
25000/500 = 50 units/mL
Pump rate
R = 1000/50 = 20 mL/h
Answer
R = 20 mL/h
5.IV infusion rates
Answer: R = 56 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
3·60 = 180 min
Drip rate
R = 1000·10/180 = 55.56 ≈ 56 gtt/min
Answer
R = 56 gtt/min
At the bedside you round to the nearest whole drop: 56 gtt/min.
6.IV infusion rates
Answer: R = 22.5 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
3·60 = 180 mg/h
Pump rate
R = 180/8 = 22.5 mL/h
Answer
R = 22.5 mL/h
7.IV fluids & fluid balance
Answer: I = 1120 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 + 150 = 350 mL
ice chips: 240/2 = 120 mL
IV infusion: 50·12 = 600 mL
IV antibiotic: 1·50 = 50 mL
I = 1120 mL
Answer
I = 1120 mL
8.IV fluids & fluid balance
Answer: t = 12.2 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.
First part
150·3 = 450 mL
1000 − 450 = 550 mL left
Second part
550/60 = 9.167 h
Total time
t = 3 + 9.167 = 12.17 ≈ 12.2 h
Answer
t = 12.2 h
That is about 12 h 10 min, so the bag runs out at about 07:10.
9.Pediatric & critical-care dosing
Answer: R = 9.6 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
12·80 = 960 units/h
Concentration
25 000/250 = 100 units/mL
Pump rate
R = 960/100 = 9.6 mL/h
Answer
R = 9.6 mL/h
10.Pediatric & critical-care dosing
Answer: R = 5.8 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
800 mg = 800 000 mcg
800 000/500 = 1600 mcg/mL
Dose per minute and per hour
2·77 = 154 mcg/min
154·60 = 9240 mcg/h
Pump rate
R = 9240/1600 = 5.775 ≈ 5.8 mL/h
Answer
R = 5.8 mL/h
11.Pharmacy calculations
Answer: V = 3.8 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 = 0.38/0.1 = 3.8 mL
Answer
V = 3.8 mL
12.Pharmacy calculations
Answer: V = 4.7 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.