NB: prior to performing calculations, always convert all values the same units.
Drug dilutions and concentrations
Ratios = unit of solute to units of solventor grams of solvent in mls of solution (because 1g = 1ml)
Ratio = grams of drug in mls of solution
e.g. 1:10,000 adrenaline = 1 unit adrenaline to every 10,000 units saline or 1g adrenaline in every 10,000ml saline
% solutions = grams of solvent per 100ml solute (because 1ml = 1g)
% = grams of drug per 100ml of solution
e.g. 0.01% adrenaline = 0.01g adrenaline per 100ml saline (or 1g adrenaline per 10,000ml)
Dose required (mg) = weight-dosage (mg/kg) x weight (kg)
e.g. the weight-dosage of a phenytoin infusion in status epilepticus is 20mg/kg and the patient weighs 80kg. The dose required is therefore 20 x 80, which is 1600mg.
Infusion rate calculations
Infusion time (minutes) = total dose required (mg) / drug rate required (mg/min)
e.g. the infusion rate of phenytoin in status epilepticus is 50mg/minute and the total dose required for an 80kg patient is 1.44g (1600mg). The infusion time is therefore 1600 / 50, which is 32 minutes.
e.g. a 5g (5000mg) magnesium infusion is prescribed to run at 1g/hour (1000mg/hour). The 500ml infusion bag contains magnesium at a concentration of 10mg/ml. The infusion rate is therefore 1000 / 10, which is 100ml/hour.
Infusion set drop rate
Drops per minute = total drops in bag / infusion time (minutes)
Where total drops in bag = bag volume (ml) x drops per ml (usually 20 but depends on giving set)
e.g. a 1L (1000ml) bag of normal saline is prescribed over 8 hours (480 minutes). The giving set runs fluid through at 20 drops per ml and so the total drops in the bag are 1000 x 20, which is 20,000. To run the infusion over 8 hours, the rate required in drops per minute is 20,000 / 480, which is 42 drops per minute. This is approximately 10 drops in 15 seconds (42 / 4), and the giving set clamp can be adjusted to give that rate.
Number of tablets/liquids needed
What you need to give (number of tablets or ml) = dose you want / dose of what you’ve got (dose per tab or dose per ml)
What you need tp gove = dose you want / dose of what you have
e.g. you want to give 40mg prednisolone. Only 5mg tablets are available. The amount you need to give is therefore 40 / 5, which is 8 tablets.
You would like to load a patient with IV phenytoin for status epilepticus. The patient has a low BMI and weighs 37.5kg. You look up the phenytoin loading dose and it is 20mg/kg.
How many milligrams of phenytoin does this patient require?
The IV injection needs to be diluted in normal saline at 10mg/ml. How many mls of normal saline is required?
You look up the rate and determine the infusion should be administered at 50mg/minute. At what rate should you set the infusion machine to run the infusion at (in ml/minute)?
If an infusion machine was not available, how many drops per minute would you set the infusion giving set to run at? The giving set specifies 20 drops/ml.