Table of Contents

### Unit conversions

*NB: prior to performing calculations, always convert all values the same units.*

### Drug dilutions and concentrations

**Ratios**= unit of solute*to*units of solvent__or__**Ratio = grams of drug in mls of solution***e.g. 1:10,000 adrenaline = 1 unit adrenaline to every 10,000 units saline*1g adrenaline in every 10,000ml saline__or__

**% 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*)

### Weight-dosage calculations

**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/rate

**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.*

**Infusion rate**(ml/hour) = dose rate (mg/hour) / concentration (mg/ml)*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 youâ€™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.*

### Test yourself

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?

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The IV injection needs to be diluted in normal saline at 10mg/ml. How many mls of normal saline is required?

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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)?

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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.

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