# How to Solve Drug Dosage Calculation Based on Body Weight I'm going to give a brief, no-fluff overview of calculating drug dose based on body weight. And then, we'll look at five carefully selected examples that illustrate the various ways in which you are likely to encounter calculating drug dose based on body weight.

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## Video Transcription Now, for most drugs, the usual dose is generally considered suitable for the majority of individuals taking the medication, and that is likely because of the wide therapeutic range of those drugs. But what we need to understand is the patient's weight actually plays an important factor when it comes to dosing. And that is because the size of the body influences drug concentration in the body fluids and at the site of action. And so, when it comes to dose in certain drugs for both adults and pediatric patients, it has actually become a standard to use what is known as a normalized dose. And so, a normalized dose is actually expressed as the specific quantity of a drug per unit of the patient's weight. Now, since most drugs are dosed in milligrams, you will normally see the normalized dose as mg/kg. So anytime you see kg or kilogram in the denominator, it's referring to body weight. Now, depending on the drug, the dosage form, and the route of administration, you may end up with different units of measure, you may end up with milliliters, micrograms, and so on. But all of these must be normalized to the body weight. And so you could have mcg/kg or ml/kg. And so why this is important is when you dose in this manner, you end up giving the quantity of drug which is specific to the weight of the patient being treated. And so you end up ensuring that you do not give too much or too little of the drug to the patient, so you don't end up with subtherapeutic or lethal doses of the drug that you're trying to administer. Now, there's a useful equation or formula when it comes to these types of calculations, and that will be the patient's dose in mg, being equal to the patient's weight in kg, times the ratio of the drug dose in mg/kg. And so just keep in mind that anywhere you see the milligrams, it could be a different unit of measure, it could be microlitres, it could be milliliters, it could be micrograms or kilograms. Just make sure that you're keeping your units consistent.

## Drug Dosage Calculations by Body Weight Examples

Now, for the examples in this tutorial, I'm going to be using dimensional analysis to actually solve those questions. And that is because if you really understand how dimensional analysis works, it's almost impossible to get a question wrong. But if you are an equation kind of person, then this equation will work really nicely for you. Now, we are going to look at the five powerful examples.

### Question 1 So let's take a look at this question, which says the usual initial dose of chlorambucil is of body weight. How many milligrams should be administered to a person weighing 154 lb? So here the first thing we want to do is identify the normalized dose. And in this question, the normalized dose is 150 mcg/kg. Now, because the answer requires us to find the amount of drug in mg, it may be a good idea to convert this normalized dose from mcg/kg to mg/kg. So we can do a quick conversion by saying that 1000 mcg makes 1 mg. So the mcg can cancel out. And we now have a normalized dose of 0.15 mg/kg. What this now means is that the 154 lb needs to be converted to kilograms. And so we can take the 154 lb and convert that to kilograms using the conversion factor, that 2.2 lb is 1 kg. So the pounds cancel out, and we end up with 70 kg. So what we can do now is we can take the normalized dose, which is 0.15 milligram per kg, and multiply that by the weight of the patient, which is 70 kg. The kilograms cancel out and we end up having 10.5 mg of chlorambucil.

### Question 2 Let's take a look at another question which says a patient needs 5 ml/kg fluid for dehydration. If a patient weighs 33 kg, how many tablespoons will they need? So here the first thing we want to do is identify the normalized dose, which would be 5 ml/kg. So we have 5 ml/kg, and we have the patient weight to be 33 kg. So we can multiply the normalized dose by the patient weight, 33 kg. The units of kilogram in the numerator will cancel out the units of kilogram in the denominator and that will end up giving us 165 ML. Now, we don't stop here because the question is asking for tablespoons. So we need to take the 165 ml, convert that to tbs. So the conversion factor is 15 ml makes one tbs, and so the milliliters cancel out and you end up having 11 tbs.

### Question 3 Let's take a look at another example. This question says a patient who is taking theophylline 0.8 mg/kg by mouth twice a day, just found out he has a CrCl of 27 so his theophylline will have to be renally adjusted. If he weighs 210 lb and his dose needs to be decreased by 20%, what is his new daily dose? So, in analyzing the question, the first thing we want to identify is the normalized dose. And in this question, it is given a 0.8 mg/kg. Now, if you read the question carefully, the 0.8 mg/kg is for a single dose, okay? And you are given the theophylline twice a day. So you actually have two doses in one day. And so the doses can cancel out, and you actually end up having the 0.8 times the 2, which gives you 1.6 mg/kg/day. And that's important because the question is asking for the daily dose. Now, this is the normalized dose for a patient with normal CrCl. However, because this patient has a CrCl of 27, you have to decrease the dose by 20%, which means the actual dose that will be given to the patient is 80% of the 1.6, and 80% is 80 divided by 100. So that is the same as multiplying this dose by 0.8. And we are doing this because you want to know the actual normalized dose that is going to be used for this particular patient. So if we multiply the 1.6 by the 0.8, we end up having 1.28 mg/kg/day. And the next thing we actually need is the weight of the patient. So we can take the 210 lb and convert that to kg. The conversion factor is 2.2 lb, make 1 kg. So the pounds cancel out and you end up with 95.46 kg. So what we will do is we'll take the normalized dose for this particular patient, which is the 1.28 mg/kg/day, and we'll multiply that by the weight of the patient, which is 95.46 kg. The kilograms cancel out and we end up with 122.2 mg.

### Question 4 Let's take a look at another example. And this question says JG was admitted to the hospital for severe chest pain. The doctor ordered metoprolol 5 mg/kg, and he was given 200 mg by mouth of metoprolol. If JG weighs 175 lb, how many mg over/under was the given dose? So, in analyzing this question, we want to identify the normalized dose, and that would be the 5 mg/kg. Now, because it's normalized to kg, we want to take the patient's weight, which is 175 lb, and convert that to kg. So the conversion factor is 2.2 lb, make 1 kg. So the pounds cancel out and you end up with 79.55 kilogram. And so now what we will do is we'll take the normalized dose, which is 5 mg/kg, and multiply that by the body weight in kilograms, which is 79.55 kg. The kilograms cancel out and you end up with 397.55 mg. Now, notice that the patient was given 200 mg, which is less than the 397.55. So already we know that the patient was given an amount which was under the dose that was required. So to determine exactly how much the patient was underdosed, we're going to take the 397.55 mg and subtract from that  200 mg which was given, and we end up with 197.55 mg. So, to answer the question specifically, what we will say is the given dose was 197.55 mg under.

### Question 5 Let's take a look at another example which says a 54 lb child was found to have a fungal infection. So the doctor prescribed griseofulvin 6 mg/kg every 6 hours for six weeks. The pharmacy has a 480 ml bottle of griseofulvin, 400 mg / 5 ml. How many days will the bottle last? So, in our analysis, the first thing we want to identify is what is the normalized dose? And so, in the question, the normalized dose is 6 mg/kg, but it's every 6 hours. So, because we know we are normalized to kg, the first thing we want to do is to take the patient's weight, which is 54 lb, and we want to convert that to kg. So we go ahead and use the conversion factor of 2.2 lb, make 1 kg. The pounds cancel out, and you end up with 24.55 kg. So that's the weight of the patient in kg. So we can now go ahead and take the normalized dose, which is 6 mg/kg every 6 hours. And because we are concerned about how many days, we would use the fact that there are 24 hours in one day, to determine the normalized dose on a daily basis. Okay, so the hours cancel out, the 6 cancel out, and now your daily normalized dose is going to be 24 mg/kg/day. So the next thing we can do is figure out exactly how many mg the patient needs a day. So we take the 24 mg/kg/day and multiply that by the patient's weight, which is 24.55 kg. The kilograms cancel out and you end up with 589.2 mg/day. So now the next piece that we need is to actually find out how many mg of griseofulvin is present in the 480 ml bottle. And so we will take the concentration that has been given, which would be 400 mg of griseofulvin per 5 ml, and multiply that by the total volume in the bottle, which is 480 ml. So the milliliters cancel out, and you end up with 38,400 mg. And so the next thing that we will do is we will take the total quantity of griseofulvin in the bottle, which is the 38,400 mg, and we will divide that by the amount that the patient needs per day, which would be the 589.2 mg/day. The milligrams cancel out, and the day flips to the numerator and you end up with 65 days.

So I hope you found this tutorial useful. Thank you so much, and I will see you in the next blog.

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