Pharmacy school: Dosage calculations

Definitions & Key takeaways

Dosage calculations are an important part of pharmacy practice, as they help to figure out the right amount of medicine to give patients based on their particular needs. Different things can affect a patient's dosage requirements of a medicine, including age, weight, and laboratory values, or it may even depend on the medicine itself. Dosage calculations must be done with precision, accuracy, and attention to detail to ensure patient safety because both underdosing and overdosing can harm the patient.

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Dosage calculations are used to figure out the right amount of medicine to give a patient based on that particular patient's needs.

Different things can affect the patient's dosage requirements of a medicine including age weight, laboratory values, or it may even depend on the medicine itself.

Some calculations can be simple while others require conversions and use of proportions. This concept can be a bit intimidating at first.

But with a little practice, calculating doses will become second nature. Let's start out with some basic examples of calculations that you might encounter.

Let's say that we have a 140 kg person who needs a specific medication for an infection. The dosage for this medication is 6 mg per kilogram per dose.

What dose would this patient require in grams? We would start out by taking the person's weight which is 140 kg and multiply it by 6 mg per kilogram to get 840 mg per dose.

However, we aren't quite done to convert milligrams to grams. We know that for every 1 mg of a product, this is equal to 0.001 g of the same product since we know that this patient would need 840 mg of the medicine.

We can then take 840 mg and multiply this number by 0.001 which is the same as dividing by 1000 to get an answer of 0.84 g.

Now, there may be times when you or someone else has already selected a dose for a patient. But you need to figure out what that dose is per kilogram of the patient's weight.

Let's say that you receive a prescription for a man who's starting a medicine to treat a heart condition. This medicine comes in a concentration of 40 mg per milliliter and he's supposed to take 1 mL daily.

If he weighs 70 kg, what dose is he getting in milligrams per kilogram? We will first want to set up a proportion to figure out how many mgs he is getting per dose.

If we set up an equation that 40 mgs over 1 mL is equal to X migs over 1 mL, we know that the man is getting 40 mgs per dose to determine how many mgs per kilogram he is getting, we would then divide 40 mgs by 70 kg to get our answer of 0.57 M GS per kilogram per dose dosage.

Calculations also involve figuring out how many days a certain product will last for a patient. For example, let's say that we have a woman who buys a cough and cold medicine that has a concentration of 900 mg per 9 mL.

And this medicine comes in a bottle that has 100 mL total. She plans to take one teaspoon of this medicine two times a day.

How many days will this bottle last? Her?

We will first need to figure out how many milliliters she is taking of this medication per day. We know that one teaspoon is equal to approximately 5 mL.

So if she's taking one teaspoon per dose, this is equal to 5 mL per dose. Remember that since she's taking this medicine twice per day, she's actually taking 10 mL per day.

Next, we can divide 100 mL, which is the total amount in the bottle by 10 mL per day to get the number of days the medication will last, which is 10 days.

Sometimes we need to find out how much of a product will be needed to provide a patient with a 30 day supply of medicine.

So let's say that there is a man who is taking medication for seizures. If he takes two tablespoons of a medication, three times a day, how many liters does he need for a 30 day supply?

To figure this out. We first need to make sure that we are using consistent units of measure.

We know that one tablespoon is equal to approximately 15 mL. If this man takes two tablespoons per dose, we know that he's taking 30 mL per dose.

If he takes this medicine three times per day, then we will take 30 mL times three to get 90 mL per day. Now that we know his total daily dose, we can multiply 90 mL by 30 days to get a value of 2700 mL per 30 days.

Lastly, we want to convert this number from milliliters to liters. So we take 2700 mL times 0.001 or divide by 1000.

And we find out that he needs 2.7 L of the seizure medicine to last him 30 days. Now let's work on a problem that combines weight based dose and the amount needed for a certain number of days.

We have a woman who is 60 kg and she is starting an antibiotic that is dosed at 30 mgs per kilogram per day. And she will be taking this medicine for 10 days if the antibiotic comes in a concentration of 250 mgs per 5 mL.

How much of the antibiotic do you need to give her in milliliters? We first need to figure out how many milligrams of the medicine she needs per day.

If we multiply her weight of 60 kg by 30 mg per kilogram per day, we know that she needs 1800 mg of the antibiotic every day.

If we have a concentration of 250 mgs per 5 mL we can set up a proportion where 250 mg over 5 mL is equal to 1800 mg over X milliliters.

We will then multiply 5 mL by 1800 mg to get a value of 9000 and then divide this number by 250 mg to get an answer of 36 mL.

This means that the woman will need to take 36 mL of her medicine every day. If she needs to take this medicine for 10 days total, we can multiply 36 mL by 10 to get a value of 360 which is the total amount of antibiotic that you would need to give her to provide a 10 day supply of therapy.

In rare cases, like with chemotherapy, medicines are dosed based off of a person's body surface area or BSA. This is calculated based off of a person's weight in kilograms and height in centimeters and is expressed as meter squared or M squared.

Luckily, once you know a person's BSA, the calculation is pretty straightforward. For example, let's say that you have a woman who is 5 ft two inches and weighs 100 lbs.

She will be getting a medicine that is dosed at 300 mg per meter squared. We first want to figure out her height and weight in the correct units being 5 ft two inches is equal to 62 inches.

So we can multiply this number by 2.54 to know that she is 157 centimeters tall. To figure out her weight in kilograms, we will divide 100 lbs by 2.2 to get 45 kg.

Now, for some fun math to figure out her BSA, we will use the formula of height and centimeters multiplied by weight in kilograms.

We will divide this number by 3600 which is a constant number and then take the square root. This will give us our BSA which is in the units meters squared.

So for this patient, we'll multiply 155 centimeters by 45 kg and divide this number by 3600 we now have a value of 1.9 but we aren't done quite yet.

Our final step to figure out her BSA is to take the square root of 1.9 which is 1.4 m squared. Now that we know her BSA, we can figure out how much medicine she needs by taking 1.4 m squared and multiply this by 300 mg per meter squared to get an answer of 420 mg.

Now, a lot of medications have standard doses for adults. However, doses for Children can be very different.

This is because as a child grows from an infant to a teenager, their weight changes a lot. For this reason, you will typically see a lot of doses for Children described as weight based dosing ok, let's say we need to calculate the dosage of a medicine for an infant with a fever, for adults.

This particular medication is 500 mg per dose. However, for infants and Children, the dosage of this medicine is based on their weight which in this case is 15 lbs.

The prescription states it's dosed at 20 mg per kilogram per dose. So how much medicine should he get?

We first want to make sure that we are using the same units. Before we start calculating, we know that 1 kg is equal to 2.2 lbs.

So if we take 15 lbs and divide this number by 2.2 we get 6.8 kg. Now we want to figure out how much medicine he needs.

So we multiply 6.8 kg by 20 mg per kilogram and find that he needs 136 mg of the medicine for each dose. Since this is an infant, we'll likely need to give the medicine in liquid form.

If this medicine comes in a concentration of 60 mg per 0.6 mL. How many milliliters does he need for each dose?

We already know that he needs 136 mg of the medicine. So we just need to make a proportion to figure out how much he will need in milliliters.

We will set up our proportion. So that 60 mg over 0.6 mL is equal to 136 mg over X milliliters.

Next we cross multiply so we get 60 mgs times X milliliters equals 136 mgs times 0.6 mL. To get X, we simply divide both sides by 60 mgs and we get an answer of 1.36 mL.

A lot of dosages for Children are expressed in ranges rather than having one specific weight based dose. You may see doses described a little more loosely.

For example, a common dose for a certain medication may be described as 10 to 15 mgs per kilogram per dose. This means that 10 mg per kilogram per dose can be thought of as the lower dosage threshold.

Whereas 15 mg per kilogram per dose can be thought of as the upper dosage threshold. Let's say we want to give this medicine to an infant that weighs 7 kg.

We would take 10 mg per kilogram and multiply this by 7 kg to get 70 mg as our lower dosage threshold. Then we would take 15 mg per kilogram and multiply this by 7 kg to get 105 mg as our upper dosage threshold.

Therefore, this child can safely receive between 70 to 105 mg per dose of this medicine. So to recap remember that dosing calculations can be used to figure out a dose and can be useful for weight based dosing calculations like in Children as well as body surface area calculations like in chemotherapy they're also helpful in figuring out the volume of a medication that's needed as well as the overall amount of the medication supply that a patient will need over the course of the