Lecture 5: More Medical Abbreviations and Dosage Calculations Using Body Weight and Surface Area

More Dosage Abbreviations: Route, Frequency, etc.

We have already learned how to write amounts in the metric, apothecary, and household systems. But every drug dosage order must contain more than just the name of the drug and the amount. In addition to the name and amount of a drug to be given, some additional information that would be necessary to determine how to give the dosage would be the route of administration or the frequency of doses, for example. Every order for a drug must actually contain:

Required Information for Every Drug Order

The name of the medication.
The amount of the medication to be given, with the units specified.
The route of administration to be used.
Remember that this is the way the medication is given. The most common routes are by mouth (p.o. or PO), or parenterally/by injection, which are: subcultaneously (subQ), intramuscularly (IM), or intravenously (IV). To review what these words mean, reread this section of lecture 3.
The frequency with which the medication is to be administered.
For example, some medications may be given only once a day, while others may be administered every 6 hours.
Any other information that could vary, depending upon what drug the order is for.
For example, if the drug must be reconsituted, the order might specify the type of diluent.
Or, if the order is for insulin, the order might specify the origin of the insulin.
Some medications might have special instructions, for example, to be taken with meals, or with a full glass of water, etc.
Also, for IV medications, which are given over an extended period of time, the length of time each dose should take or the rate at which each dose should be given will also need to be included (we will discuss this more in future chapters when we learn more about IVs).

So let's learn the abbreviations we will need. The only ones we have not yet learned are for the frequency with which they are to be given (and a few involving special instructions):

frequency

abbreviation

explanation

every day

q.d.

q is used to represent "every" (because the Latin for every is quisque)
d is used to represent "day" (because the Latin for day is diem)
We will see these two letters used this way in many of the abbreviations below.

every other day

every other day (q.o.d.)

Notice the use of q for every and d for day.
This abbreviation is now discouraged, because too often it was mistaken for "every day," so while you may still see it occasionally, you should always write out "every other day" instead of using q.o.d.

every hour

q.h.

Notice the use of q for every.
h is used to represent "hour"
We will also see these two letters used this way in many of the abbreviations below.

every 2 hours

every 3 hours

every 4 hours

etc...

q.2.h.

q.3.h.

q.4.h.

etc...

Notice the use of q for every and h for hour. The number of hours in between each dose always goes in the middle.

twice a day	b.i.d	b is used to represent "twice" (because the Latin prefix for 2 is bi - think bicycle)
three times a day	t.i.d	t is used to represent "three times " (because the Latin prefix for 3 is tri - think tricycle)
four times a day	q.i.d	q is used to represent "four times " (because the Latin prefix for 4 is quad- think quadruple )

every morning

q.a.m.

Notice the use of q for every.
Notice also that we use a.m. to represent morning (for the Latin ante meridiem meaning before noon)

at bedtime

h.s.

This stands for hour of sleep.

every bedtime

q.h.s.

Notice the use of q for every. This literally means "every hour of sleep"

before meals

a.c.

a stands for before (ante is the Latin for before - think of a.m. as in before noon)
c stands for meals (cibum is the Latin for meals - unfortunately, I can't think of a good memory aid for this one...)

after meals

p.c.

p stands for after (post is the Latin for after - think of p.m. as in after noon)
c stands for meals (cibum is the Latin for meals)

as desired

ad lib

short for ad libitum, Latin for "at one's pleasure" - in everyday English we often use this term to describe when someone is improvising dialog

as necessary

s.o.s.

short for si opus sit, Latin for "if it is necessary" (actually, it literally says, "if there is work", which in Latin is the phrase used to mean "if it is necessary")

when necessary/required

p.r.n.

short for pro re nata, Latin for "as occasion requires"

as much as required

q.s.

q stands for quantity (quantum is the Latin for quantity)

s stands for sufficient (sufficiat is the Latin for sufficient)

so literally, it means "a sufficient quantity"

immediately

stat

short for statim, which is Latin for "immediately'

with

c stands for with (cum is the Latin for with - think of "cum laude", which means "with honor")

before

a stands for before (ante is the Latin for before - think of a.m. as in before noon)

after

p stands for after (post is the Latin for after - think of p.m. as in after noon)

These are the most important abbreviations that you will need to know for now. However, there are many more medical abbreviations that may be found on a medication order. For more abbreviations, wee pages 128-129 of your book.

Let's look at a few examples where we can practice reading drug orders:

Example

Order: penicilin G 400,000 units IM b.i.d.

This means we are to give 400,000 units of penicilin G, intramuscularly, twice a day.

Notice that the order specifies the drug name, amount with units, route of administration, and frequency, as is required.

Example

Order: Velocef 700 mg IV q.i.d.

This means we are to give 700 mg of Velocef, intravenously, four times a day. (Not every other day or every day.)

Notice that the order specifies the drug name, amount with units, route of administration, and frequency, as is required.

Example

Order: Ilosone 1g p.o. q.6.h.

This means we are to give 1 gram of Ilosone, by mouth , every 6 hours.

Notice that the order specifies the drug name, amount with units, route of administration, and frequency, as is required.

Example

Order: Novolin R 34 units subQ t.i.d. a.c.

This means we are to give 34 units of Novolin R insulin (regular action), subcultaneously, three times a day, before meals .

Notice that the order specifies the drug name, amount with units, route of administration, and frequency, as is required. It also specifies a few extra things, such as the action of the insulin, and the special directions that it is to be given before meals.

Example

Order: morphine 20 mg p.o. q.4.h. p.r.n. for pain

This means we are to give 20 milligrams of morphine, by mouth, every four hours , when needed for pain .

Notice that the order specifies the drug name, amount with units, route of administration, and frequency, as is required; notice that the frequency of every 4 hours specifies that this is the most often the drug can be taken - but it is only necessary for the patient to take it each time if they are actually in pain.

Common Mistakes to Avoid:

Be careful not to confuse the abbreviations q.o.d. for every other day with the abbreviation q.i.d. for four times a day with the abbreviation q.d. for every day. These are often confused, and this is why the abbreviation q.o.d. is no longer supposed to be used.
Remember never to write q.o.d.; rather, you should write out "every other day".

Calculating Dosages Based on Body Weight

Sometimes the dosage of a drug that a patient is supposed to receive depends upon how much they weigh. This is particularly the case with drugs that are given to children or infants, since their size will vary greatly from the size of an average adult, and often even varies a lot among children of the same age. This may also happen when we are dosing a patient with particularly sensitive drugs, so, for example, a patient in intensive care may be much more likely to be dosed by body weight. If we think about this, it makes sense that we would want to give people dosages of a drug that depend on how much you weigh: for example, a 350 lb man probably needs a different amount of a pain reliever than a 50 lb little girl (or even a 100 lb adult woman). For this reason, we need to know how to read drug orders that are given based on body weight. These drug orders will look just like any other drug order, for example:

Order: ampicillin susp. 400 mg p.o. q.6.h.

This looks like an ordinary order for a medication. However, if we look closely at the label for ampicillin, we notice that there are instructions about the usual dosage on the bottom right of the label. If, in this case, the person this drug is intended for is a child under 20 kg, then we will want to check this order to make sure that it is the correct amount for this particular child's weight. The doctor who wrote the order should have calculated this amount based on the child's weight, but we need to check just to be sure that this amount is safe.

We will use the information on the label and the weight of the patient to find either a recommended dosage, which is a single dosage amount that is the recommended amount for that patient, or to find a safe dosage range, which is a set of two numbers: a minimum safe dose and a maximum safe dose. Then we will want to compare the order that has been writen by the doctor to the recommended dosage or safe range:

When a label gives us the information needed to calculate a safe range, then the ordered dosage must fall within the range (i.e. between the minimum and the maximum) in order to be considered safe. Any dosage amount given in an order which falls outside of the range, even by a little bit, should be questioned.
When a label gives us the information needed to calculate a recommended dose, then the ordered dosage must be equal to (or fairly close to) the recommended dose in order to be considered safe. If the ordered dose is not exactly the same as the recommended dose, what do we do? Particular hospitals will have policies in place for particular drugs or calculations, but for the sake of simplicity, for all our calculations in this class, we will use the following rule: if the ordered dosage is within 10% of recommended dosage, then we will say it is safe, otherwise, we will say that the dosage is unsafe. This is a big generalization that will not be true for many medications in the real world, but we use it just to practice this idea in a simplistic way. Remember that you should always follow the policies of a particular hospital when determining whether or not a dosage is safe.

How can we tell if an ordered dosage is within 10% of the recommended dosage? Multiply the recommended dosage by 10%. The answer you get should be bigger than any difference between the recommended dosage and the ordered dosage. For example, if we have a recommended dosage of 150 mg, 10% of 150 mg is 15 mg. So an ordered dosage of 160 mg would be safe, since it is within 15 mg (10%) of the recommended dosage of 150 mg. But an ordered dosage of 170 mg would not be safe, because it is not within 15 mg (10%) of the recommended dosage of 150 mg.

So, how do we check that? Notice that the information on this label reads "100 mg/kg/day". This means that the child should get 100 mg of the drug for every kg they weigh. So, for example, if they weighed 10 kg, they should get 1000 mg per day, and if they weighed 15 kg, they should get 1500 mg per day; however, we must be careful, because if they weight over 20 kg, they should only receive "250 mg to 500 mg q.i.d. (four times a day). Notice that this is the amount to be given per DAY , NOT per dose. So, if there are supposed to be four doses a day (notice that the label says q.i.d.), the 10 kg child who gets 1000 mg per day should have that divided up into 4 equal doses, so we should divide 1000 mg by 4 to get 250 mg per dose. Likewise, the 15 kg child who will get 1500 mg per day should have that divided into 4 equal doses, so we should divide 1500 mg by 4 to get 375 mg per dose.

So, to check and see if the above order for "ampicillin susp. 400 mg p.o. q.6.h." is correct, we would begin by looking at the child's chart to get the child's weight. Let's suppose this child weighs 16 kg. We write down the important information below:

Example:

Is the following order safe for a 6 kg child?
Order: Principen 150 mg p.o. q.6.h.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 6 kg to the right of the equals sign, because we need to find the number of mg we need for a 6 kg patient:

_____ mg=6 kg

We can put 6 kg over 1 without changing it:

6 kg

If we look at the label, we see that it says that the safe dosage is 100 mg per kg per day.

Because this safe dosage is given per day, we should label our calculations "Safe dosage per day":

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 100 mg per kg as a fraction:

100 mg

1 kg

. In a safe dosage, 100 mg and 1 kg should be equal; we can multiply our equation by

100 mg

1 kg

, because:

The top of this fraction will be equal to the bottom in a safe dosage.
This fraction has kg on the bottom, which will cancel out the kg we want to get rid of on the top.

Safe dose per day: _____ mg=

6 kg

100 mg

1 kg

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Safe dosage per day: _____mg=

6 kg

100 mg

1 kg

Now we can multiply across to get:

Safe dosage per day: _____mg=

100 mg

600

So our safe dosage per day is:

600 mg

Because this amount is the safe amount per day, we must break this amount down to the safe amount per dose. The order says the frequency should be q.6.h., which means every 6 hours. Because there are 24 hours in a day, a dosage frequency of every 6 hours will result in a dosage 4 times per day.So in order to go from the safe dosage per day, 600 mg, to the safe dosage per dose, we must break the daily dosage up into 4 equal sized pieces.

So, we divide 600 mg by 4 to get the safe dosage per dose:

Safe amount per dose: 150 mg

The ordered amount is safe, because the ordered amount of 150 mg is within 10% of the safe amount per dose of 150 mg .

Example:

Is the following order safe for a 43 lb child? This child has a moderate infection.
Order: Kefzol 200 mg IM q.8.h.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 43 lb to the right of the equals sign, because we need to find the number of mg we need for a 43 lb patient:

_____ mg=43 lb

We can put 43 lb over 1 without changing it:

43 lb

Since the patient's weight is in lb and we want to use metric as a general rule, we need to convert lb to kg. So, we need to multiply by a fraction that is:

equal to one (where the top is equal to the bottom)
has lb on the bottom to cancel out the lb we want to get rid of on the top

Because we know that 1 kg=2.2 lb, we can then multiply by

1 kg

2.2 lb

because this has lb on the bottom to cancel out the lb on the top, and it is equal to one:

_____ mg=

43 lb

1 kg

2.2 lb

If we look at the label, we see that it says that the safe dosage is 25 to 50 mg per kg per day.
We choose this concentration instead of the others listed on the label because it is the one the label says we should use when This child has a moderate infection. , and the order states this.

Because this safe dosage is given per day, we should label our calculations "Safe dosage per day", and because the safe dosage given is a range, our answer must be a range, too, with a minimum safe amount, and a maximum safe amount:

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 25-50 mg per kg as two different fractions:

25 mg

1 kg

and

50 mg

1 kg

. In a minimum safe dosage, 25 mg and 1 kg should be equal and in a maximum safe dosage, 50 mg and 1 kg should be equal; we can multiply our equation for the minimum by

25 mg

1 kg

and our equation for the maximum by

50 mg

1 kg

, because:

The top of these fractions will be equal to the bottom in a safe minimum or maximum dosage.
Both fractions have kg on the bottom, which will cancel out the kg we want to get rid of on the top of each equation.

Minimum safe dose per day: _____ mg=

43 lb

1 kg

2.2 lb

25 mg

1 kg

Maximum safe dose per day: _____ mg=

43 lb

1 kg

2.2 lb

50 mg

1 kg

Now all we need to do is to simplify our fractions:

We begin by cancelling units that appear on both the top and the bottom to get:

Minimum safe dosage per day: _____mg=

43 lb

1 kg

2.2 lb

25 mg

1 kg

Maximum safe dosage per day: _____mg=

43 lb

1 kg

2.2 lb

50 mg

1 kg

Rewriting these gives us:

Minimum safe dosage per day: _____mg=

2.2

25 mg

Maximum safe dosage per day: _____mg=

2.2

50 mg

Now we need to get rid of the decimal in 2.2 on the bottom of the fraction in the right side of the equations. If we multiply 2.2 by 10, this will change 2.2 to 22, and therefore get rid of the decimal; but we can't multiply the bottom of the fraction by 10 unless we also multiply the top by 10, so we multiply

2.2

by 10 on both the top and the bottom to get

Minimum safe dosage per day: _____mg=

25 mg

Maximum safe dosage per day: _____mg=

50 mg

Now we notice that we can divide both 10 and 22 by 2, so we can reduce the right side of our equations by dividing 10 on the top and 22 on the bottom by 2:

Minimum safe dosage per day: _____mg=

10⁵

22₁₁

25 mg

Maximum safe dosage per day: _____mg=

10⁵

22₁₁

50 mg

Now there is nothing left to simplify, so we can multiply across to get:

Minimum safe dosage per day: _____mg=

25 mg

5375

Maximum safe dosage per day: _____mg=

50 mg

10750

Dividing 5375 by 11, we get our minimum safe dosage per day, which is:

Minimum:489 mg

Dividing 10750 by 11, we get our maximum safe dosage per day, which is:

Maximum:977 mg

Because this range is the safe range per day, we must break this minimum and maximum down to the safe range per dose. The order says the frequency should be q.8.h., which means every 8 hours. Because there are 24 hours in a day, a dosage frequency of every 8 hours will result in a dosage 3 times per day.So in order to go from the safe dosage range per day, 489-977 mg, to the safe dosage per dose, we must break the minimum daily dosage and the maximum daily dosage up into 3 equal sized pieces.

So, we divide 489 mg by 3 to get the minimum safe dosage per dose:

Minimum safe amount per dose: 163

And then we divide 977 mg by 3 to get the maximum safe dosage per dose:

Maximum safe amount per dose: 326

The ordered amount is safe, because the ordered amount of 200 mg is within the safe range per dose 163-326 mg.

Example:

Is the following order safe for a 150 lb child?
Order: Mithracin 350 mcg IV q.4.h.

We want our answer to be in mcg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mcg. So we begin by writing:

_____ mcg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 150 lb to the right of the equals sign, because we need to find the number of mcg we need for a 150 lb patient:

_____ mcg=150 lb

We can put 150 lb over 1 without changing it:

150 lb

Since the patient's weight is in lb and we want to use metric as a general rule, we need to convert lb to kg. So, we need to multiply by a fraction that is:

equal to one (where the top is equal to the bottom)
has lb on the bottom to cancel out the lb we want to get rid of on the top

Because we know that 1 kg=2.2 lb, we can then multiply by

1 kg

2.2 lb

because this has lb on the bottom to cancel out the lb on the top, and it is equal to one:

_____ mcg=

150 lb

1 kg

2.2 lb

If we look at the label, we see that it says that the safe dosage is 25 to 30 mcg per kg per day.

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 25-30 mcg per kg as two different fractions:

25 mcg

1 kg

and

30 mcg

1 kg

. In a minimum safe dosage, 25 mcg and 1 kg should be equal and in a maximum safe dosage, 30 mcg and 1 kg should be equal; we can multiply our equation for the minimum by

25 mcg

1 kg

and our equation for the maximum by

30 mcg

1 kg

, because:

The top of these fractions will be equal to the bottom in a safe minimum or maximum dosage.
Both fractions have kg on the bottom, which will cancel out the kg we want to get rid of on the top of each equation.

Minimum safe dose per day: _____ mcg=

150 lb

1 kg

2.2 lb

25 mcg

1 kg

Maximum safe dose per day: _____ mcg=

150 lb

1 kg

2.2 lb

30 mcg

1 kg

Now all we need to do is to simplify our fractions:

We begin by cancelling units that appear on both the top and the bottom to get:

Minimum safe dosage per day: _____mcg=

150 lb

1 kg

2.2 lb

25 mcg

1 kg

Maximum safe dosage per day: _____mcg=

150 lb

1 kg

2.2 lb

30 mcg

1 kg

Rewriting these gives us:

Minimum safe dosage per day: _____mcg=

150

2.2

25 mcg

Maximum safe dosage per day: _____mcg=

150

2.2

30 mcg

2.2

by 10 on both the top and the bottom to get

Minimum safe dosage per day: _____mcg=

150

25 mcg

Maximum safe dosage per day: _____mcg=

150

30 mcg

Now we notice that we can divide both 10 and 22 by 2, so we can reduce the right side of our equations by dividing 10 on the top and 22 on the bottom by 2:

Minimum safe dosage per day: _____mcg=

150

10⁵

22₁₁

25 mcg

Maximum safe dosage per day: _____mcg=

150

10⁵

22₁₁

30 mcg

Now there is nothing left to simplify, so we can multiply across to get:

Minimum safe dosage per day: _____mcg=

150

25 mcg

18750

mcg

Maximum safe dosage per day: _____mcg=

150

30 mcg

22500

mcg

Dividing 18750 by 11, we get our minimum safe dosage per day, which is:

Minimum:1705 mcg

Dividing 22500 by 11, we get our maximum safe dosage per day, which is:

Maximum:2045 mcg

Because this range is the safe range per day, we must break this minimum and maximum down to the safe range per dose. The order says the frequency should be q.4.h., which means every 4 hours. Because there are 24 hours in a day, a dosage frequency of every 4 hours will result in a dosage 6 times per day.So in order to go from the safe dosage range per day, 1705-2045 mcg, to the safe dosage per dose, we must break the minimum daily dosage and the maximum daily dosage up into 6 equal sized pieces.

So, we divide 1705 mcg by 6 to get the minimum safe dosage per dose:

Minimum safe amount per dose: 284

And then we divide 2045 mcg by 6 to get the maximum safe dosage per dose:

Maximum safe amount per dose: 341

The ordered amount is unsafe, and we should check with the physician who wrote the order and should not give the patient this dose, because the ordered amount of 350 mcg is not within the safe range per dose 284-341 mcg.

Example:

Is the following order safe for a 35 lb child?
Order: Velocef 300 mg IV q.i.d.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 35 lb to the right of the equals sign, because we need to find the number of mg we need for a 35 lb patient:

_____ mg=35 lb

We can put 35 lb over 1 without changing it:

35 lb

Since the patient's weight is in lb and we want to use metric as a general rule, we need to convert lb to kg. So, we need to multiply by a fraction that is:

equal to one (where the top is equal to the bottom)
has lb on the bottom to cancel out the lb we want to get rid of on the top

Because we know that 1 kg=2.2 lb, we can then multiply by

1 kg

2.2 lb

because this has lb on the bottom to cancel out the lb on the top, and it is equal to one:

_____ mg=

35 lb

1 kg

2.2 lb

If we look at the label, we see that it says that the safe dosage is 50 to 100 mg per kg per day.

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 50-100 mg per kg as two different fractions:

50 mg

1 kg

and

100 mg

1 kg

. In a minimum safe dosage, 50 mg and 1 kg should be equal and in a maximum safe dosage, 100 mg and 1 kg should be equal; we can multiply our equation for the minimum by

50 mg

1 kg

and our equation for the maximum by

100 mg

1 kg

, because:

The top of these fractions will be equal to the bottom in a safe minimum or maximum dosage.
Both fractions have kg on the bottom, which will cancel out the kg we want to get rid of on the top of each equation.

Minimum safe dose per day: _____ mg=

35 lb

1 kg

2.2 lb

50 mg

1 kg

Maximum safe dose per day: _____ mg=

35 lb

1 kg

2.2 lb

100 mg

1 kg

Now all we need to do is to simplify our fractions:

We begin by cancelling units that appear on both the top and the bottom to get:

Minimum safe dosage per day: _____mg=

35 lb

1 kg

2.2 lb

50 mg

1 kg

Maximum safe dosage per day: _____mg=

35 lb

1 kg

2.2 lb

100 mg

1 kg

Rewriting these gives us:

Minimum safe dosage per day: _____mg=

2.2

50 mg

Maximum safe dosage per day: _____mg=

2.2

100 mg

2.2

by 10 on both the top and the bottom to get

Minimum safe dosage per day: _____mg=

50 mg

Maximum safe dosage per day: _____mg=

100 mg

Now we notice that we can divide both 10 and 22 by 2, so we can reduce the right side of our equations by dividing 10 on the top and 22 on the bottom by 2:

Minimum safe dosage per day: _____mg=

10⁵

22₁₁

50 mg

Maximum safe dosage per day: _____mg=

10⁵

22₁₁

100 mg

Now there is nothing left to simplify, so we can multiply across to get:

Minimum safe dosage per day: _____mg=

50 mg

8750

Maximum safe dosage per day: _____mg=

100 mg

17500

Dividing 8750 by 11, we get our minimum safe dosage per day, which is:

Minimum:795 mg

Dividing 17500 by 11, we get our maximum safe dosage per day, which is:

Maximum:1591 mg

Because this range is the safe range per day, we must break this minimum and maximum down to the safe range per dose. The order says the frequency should be q.i.d., which means four times a day. So in order to go from the safe dosage range per day, 795-1591 mg, to the safe dosage per dose, we must break the minimum daily dosage and the maximum daily dosage up into 4 equal sized pieces.

So, we divide 795 mg by 4 to get the minimum safe dosage per dose:

Minimum safe amount per dose: 199

And then we divide 1591 mg by 4 to get the maximum safe dosage per dose:

Maximum safe amount per dose: 398

The ordered amount is safe, because the ordered amount of 300 mg is within the safe range per dose 199-398 mg.

Example:

Is the following order safe for a 33 kg child? This child has bacterial meningitis.
Order: Zinacef 2.5 g IV t.i.d.

We want our answer to be in g, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in g. So we begin by writing:

_____ g=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's weight, we begin by putting 33 kg to the right of the equals sign, because we need to find the number of g we need for a 33 kg patient:

_____ g=33 kg

We can put 33 kg over 1 without changing it:

33 kg

If we look at the label, we see that it says that the safe dosage is 200 to 240 mg per kg per day.
We choose this concentration instead of the others listed on the label because it is the one the label says we should use when This child has bacterial meningitis. , and the order states this.

Now we want to get rid of the kg on the top of the right side of the equation, and we notice that we can write 200-240 mg per kg as two different fractions:

200 mg

1 kg

and

240 mg

1 kg

. In a minimum safe dosage, 200 mg and 1 kg should be equal and in a maximum safe dosage, 240 mg and 1 kg should be equal; we can multiply our equation for the minimum by

200 mg

1 kg

and our equation for the maximum by

240 mg

1 kg

, because:

The top of these fractions will be equal to the bottom in a safe minimum or maximum dosage.
Both fractions have kg on the bottom, which will cancel out the kg we want to get rid of on the top of each equation.

Minimum safe dose per day: _____ g=

33 kg

200 mg

1 kg

Maximum safe dose per day: _____ g=

33 kg

240 mg

1 kg

Now we notice that the units we have on the top right of our equation are mg, but we need our answer to be in g. Because we know that 1 g=1000 mg, we can multiply our equation by

1 g

1000 mg

, which is a good fraction to multiply by because it has mg on the bottom, which will cancel out the mg which we want to get rid of on the top at the right of our equation:

Minimum safe dose per day: _____ g=

33 kg

200 mg

1 kg

1 g

1000 mg

Maximum safe dose per day: _____ g=

33 kg

240 mg

1 kg

1 g

1000 mg

Now all we need to do is to simplify our fractions:

We begin by cancelling units that appear on both the top and the bottom to get:

Minimum safe dosage per day: _____g=

33 kg

200 mg

1 kg

1 g

1000 mg

Maximum safe dosage per day: _____g=

33 kg

240 mg

1 kg

1 g

1000 mg

Rewriting this gives us:

Minimum safe dosage per day: _____g=

200

1000

Maximum safe dosage per day: _____g=

240

1000

We can divide both 200 on the top and 1000 on the bottom by 200:

Safe dosage per day: _____g=

~~200~~¹

~~1000~~₅

Rewriting this yields:

Minimum safe dosage per day: _____g=

We can divide both 240 on the top and 1000 on the bottom by 40:

Safe dosage per day: _____g=

~~240~~⁶

~~1000~~₂₅

Rewriting this yields:

Maximum safe dosage per day: _____g=

Now there is nothing to simplify, so we can multiply across to get:

Minimum safe dosage per day: _____g=

Maximum safe dosage per day: _____g=

Dividing 0 by 5, we get our minimum safe dosage per day which is:

6.6 g

Dividing 0 by 25, we get our maximum safe dosage per day which is:

7.92 g

Because this range is the safe range per day, we must break this minimum and maximum down to the safe range per dose. The order says the frequency should be t.i.d., which means three times a day. So in order to go from the safe dosage range per day, 6.6-7.92 g, to the safe dosage per dose, we must break the minimum daily dosage and the maximum daily dosage up into 3 equal sized pieces.

So, we divide 6.6 g by 3 to get the minimum safe dosage per dose:

Minimum safe amount per dose: 2

And then we divide 7.92 g by 3 to get the maximum safe dosage per dose:

Maximum safe amount per dose: 3

The ordered amount is safe, because the ordered amount of 2.5 g is within the safe range per dose 2-3 g.

Calculating Dosages Based on Body Surface Area

Sometimes using a person's weight to determine how much of a drug they receive isn't the best method. For example, someone who is 4 ft 10 in tall and someone who is 6 ft 4in tall might both be 150 lbs, but they may need more or less of a drug, depending on what portion of their weight is fat, or muscle, or retained fluid, etc. Some ways of dealing with this might include determining a person's dosage not on their actual weight, but on their "ideal" body weight - the weight that would be healthy for someone of their height and build; a hospital should have a chart that would allow us to calculate what this is. However, another way to address this issue is to determine how much drug a person should get by their body surface area, rather than their weight.

What is Body Surface Area and How Do We Calculate It?

The body surface area is precisely what it sounds like: the surface area of a person's body. You have probably calculated the surface areas of more regular shapes, like cubes and balls and pyramids in a previous math class. A person's surface area would be the area that the skin would take up if we could lay it out flat. Obviously this would be difficult to measure, as people are made up of a lot of irregular shapes, so to determine a person's body surface area, or BSA, we use formulas or charts based on their height and weight.

The book gives two formulas to determine a person's BSA. If we know someone's height and weight in the metric system in kg and cm we use this formula:

BSA (in m²)=

weight (in kg)×height (in cm)

3600

If we know someone's height and weight in lb (pounds) and in (inches) we use this formula:

BSA (in m²)=

weight (in lb)×height (in in)

3131

Notice that our BSA is always in square meters, no matter which formula we use. The BSA of a person will always be below 3 m². The BSA of a child will generally be below 1.5 m², and the BSA of an adult will usually be above 1.5 m². We will always round BSA to the nearest hundredth. Let's look at a few examples that will show us how to calculate BSA:

Example:

Calculate the BSA for someone who weighs 5 lb and is 12 in tall.

Because this question gives us the height and weight in lb and in, we must use the formula for these units:

BSA (in m²)=

weight (in lb)×height (in in)

3131

Plugging the weight and height into the formula gives us:
BSA (in m²)=

5 lb × 12 in

3131

Multiplying 5 lb × 12 in yields:
BSA (in m²)=

60

3131

Dividing 60 by 3131 yields:
BSA (in m²)=

0.019163206643245

Taking the square root of 0.019163206643245 yields:
BSA=0.13843123434848 m²
Rounding to two decimal places yields:
BSA=0.14 m²

Example:

Calculate the BSA for someone who weighs 43 kg and is 61 cm tall.

Because this question gives us the height and weight in kg and cm, we must use the formula for these units:

BSA (in m²)=

weight (in kg)×height (in cm)

3600

Plugging the weight and height into the formula gives us:
BSA (in m²)=

43 kg × 61 cm

3600

Multiplying 43 kg × 61 cm yields:
BSA (in m²)=

2623

3600

Dividing 2623 by 3600 yields:
BSA (in m²)=

0.72861111111111

Taking the square root of 0.72861111111111 yields:
BSA=0.85358720182013 m²
Rounding to two decimal places yields:
BSA=0.85 m²

Example:

Calculate the BSA for someone who weighs 87 lb and is 40 in tall.

Because this question gives us the height and weight in lb and in, we must use the formula for these units:

BSA (in m²)=

weight (in lb)×height (in in)

3131

Plugging the weight and height into the formula gives us:
BSA (in m²)=

87 lb × 40 in

3131

Multiplying 87 lb × 40 in yields:
BSA (in m²)=

3480

3131

Dividing 3480 by 3131 yields:
BSA (in m²)=

1.1114659853082

Taking the square root of 1.1114659853082 yields:
BSA=1.0542608715627 m²
Rounding to two decimal places yields:
BSA=1.05 m²

Example:

Calculate the BSA for someone who weighs 48 kg and is 111 cm tall.

Because this question gives us the height and weight in kg and cm, we must use the formula for these units:

BSA (in m²)=

weight (in kg)×height (in cm)

3600

Plugging the weight and height into the formula gives us:
BSA (in m²)=

48 kg × 111 cm

3600

Multiplying 48 kg × 111 cm yields:
BSA (in m²)=

5328

3600

Dividing 5328 by 3600 yields:
BSA (in m²)=

1.48

Taking the square root of 1.48 yields:
BSA=1.2165525060596 m²
Rounding to two decimal places yields:
BSA=1.22 m²

Example:

Calculate the BSA for someone who weighs 172 lb and is 172 in tall.

Because this question gives us the height and weight in lb and in, we must use the formula for these units:

BSA (in m²)=

weight (in lb)×height (in in)

3131

Plugging the weight and height into the formula gives us:
BSA (in m²)=

172 lb × 172 in

3131

Multiplying 172 lb × 172 in yields:
BSA (in m²)=

29584

3131

Dividing 29584 by 3131 yields:
BSA (in m²)=

9.4487384222293

Taking the square root of 9.4487384222293 yields:
BSA=3.0738800272993 m²
Rounding to two decimal places yields:
BSA=3.07 m²

How to Use BSA to Calculate Dosages

We use BSA just like weight when we want to calculate a dosage. Notice how similar these examples are to the ones we had for dosages calculated by weight:

Example:

Is the following order safe for a 0.55 m² child? This is the child's fifth dose.
Order: vinblastine sulfate 3.75 mg IV

Before we can calculate anything, we must first calculate the patient's BSA. If you don't remember how to do this, scroll up to the examples earlier in the lecture where BSA was calculated.

The patient's BSA is given as 0.55 m².

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's BSA, we begin by putting 0.55 m² to the right of the equals sign, because we need to find the number of mg we need for a 0.55 m² patient:

_____ mg=0.55 m²

We can put 0.55 m² over 1 without changing it:

0.55 m²

If we look at the label, we see that it says that the safe dosage is 7.5 mg per m² per dose.
We choose this concentration instead of the others listed on the label because it is the one the label says we should use when This is the child's fifth dose. , and the order states this.

Because this safe dosage is given per dose, we should label our calculations "Safe dosage per dose":

Now we want to get rid of the m² on the top of the right side of the equation, and we notice that we can write 7.5 mg per m² as a fraction:

7.5 mg

1 m²

. In a safe dosage, 7.5 mg and 1 m² should be equal; we can multiply our equation by

7.5 mg

1 m²

, because:

The top of this fraction will be equal to the bottom in a safe dosage.
This fraction has m² on the bottom, which will cancel out the m² we want to get rid of on the top.

Safe dose per dose: _____ mg=

0.55 m²

7.5 mg

1 m²

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Safe dosage per dose: _____mg=

0.55 m²

7.5 mg

1 m²

Now we can multiply across to get:

Safe dosage per dose: _____mg=

0.55

7.5 mg

4.125

So our safe dosage per dose is:

4.125 mg

This is our safe amount per dose, so we can compare it with the ordered dose 3.75 mg.

The ordered amount is safe, because the ordered amount of 3.75 mg is within 10% of the safe amount per dose of 4.125 mg .

Example:

Is the following order safe for a 1.98 m² child?
Order: BiCNU 350 mg IV

Before we can calculate anything, we must first calculate the patient's BSA. If you don't remember how to do this, scroll up to the examples earlier in the lecture where BSA was calculated.

The patient's BSA is given as 1.98 m².

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's BSA, we begin by putting 1.98 m² to the right of the equals sign, because we need to find the number of mg we need for a 1.98 m² patient:

_____ mg=1.98 m²

We can put 1.98 m² over 1 without changing it:

1.98 m²

If we look at the label, we see that it says that the safe dosage is 150 to 200 mg per m² per dose.
We choose this concentration instead of the others listed on the label because it is the one the label says we should use when , and the order states this.

Because this safe dosage is given per dose, we should label our calculations "Safe dosage per dose", and because the safe dosage given is a range, our answer must be a range, too, with a minimum safe amount, and a maximum safe amount:

Now we want to get rid of the m² on the top of the right side of the equation, and we notice that we can write 150-200 mg per m² as two different fractions:

150 mg

1 m²

and

200 mg

1 m²

. In a minimum safe dosage, 150 mg and 1 m² should be equal and in a maximum safe dosage, 200 mg and 1 m² should be equal; we can multiply our equation for the minimum by

150 mg

1 m²

and our equation for the maximum by

200 mg

1 m²

, because:

The top of these fractions will be equal to the bottom in a safe minimum or maximum dosage.
Both fractions have m² on the bottom, which will cancel out the m² we want to get rid of on the top of each equation.

Minimum safe dose per dose: _____ mg=

1.98 m²

150 mg

1 m²

Maximum safe dose per dose: _____ mg=

1.98 m²

200 mg

1 m²

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Minimum safe dosage per dose: _____mg=

1.98 m²

150 mg

1 m²

Maximum safe dosage per dose: _____mg=

1.98 m²

200 mg

1 m²

Now we can multiply across to get:

Minimum safe dosage per dose: _____mg=

1.98

150 mg

297

Maximum safe dosage per dose: _____mg=

1.98

200 mg

396

So our safe dosage range per dose is:

297-396 mg

This is our safe amount per dose, so we can compare it with the ordered dose 350 mg.

The ordered amount is safe, because the ordered amount of 350 mg is within the safe range per dose 297-396 mg.

Example:

Is the following order safe for a child who weighs 194 lb and is 70 tall?
Order: Mutamycin 35 mg IV

Before we can calculate anything, we must first calculate the patient's BSA. If you don't remember how to do this, scroll up to the examples earlier in the lecture where BSA was calculated.

We know that the patient weighs 194 lb and is 70 in tall. By plugging these numbers into the correct formula, we get that their BSA is 2.08.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's BSA, we begin by putting 2.08 m² to the right of the equals sign, because we need to find the number of mg we need for a 2.08 m² patient:

_____ mg=2.08 m²

We can put 2.08 m² over 1 without changing it:

2.08 m²

If we look at the label, we see that it says that the safe dosage is 20 mg per m² per dose.

Because this safe dosage is given per dose, we should label our calculations "Safe dosage per dose":

Now we want to get rid of the m² on the top of the right side of the equation, and we notice that we can write 20 mg per m² as a fraction:

20 mg

1 m²

. In a safe dosage, 20 mg and 1 m² should be equal; we can multiply our equation by

20 mg

1 m²

, because:

The top of this fraction will be equal to the bottom in a safe dosage.
This fraction has m² on the bottom, which will cancel out the m² we want to get rid of on the top.

Safe dose per dose: _____ mg=

2.08 m²

20 mg

1 m²

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Safe dosage per dose: _____mg=

2.08 m²

20 mg

1 m²

Now we can multiply across to get:

Safe dosage per dose: _____mg=

2.08

20 mg

41.6

So our safe dosage per dose is:

41.6 mg

This is our safe amount per dose, so we can compare it with the ordered dose 35 mg.

The ordered amount is unsafe, and we should check with the physician who wrote the order and should not give the patient this dose, because the ordered amount of 35 mg is not within 10% of the safe amount per dose 41.6 mg .

Example:

Is the following order safe for a child who weighs 59 kg and is 160 tall?
Order: Paraplatin 550 mg IV

Before we can calculate anything, we must first calculate the patient's BSA. If you don't remember how to do this, scroll up to the examples earlier in the lecture where BSA was calculated.

We know that the patient weighs 59 kg and is 160 cm tall. By plugging these numbers into the correct formula, we get that their BSA is 1.62.

We want our answer to be in mg, because our goal is to calculate the safe dosage and compare it to the given order, which measures the drug in mg. So we begin by writing:

_____ mg=

Now we need to find something to put on the right side of the equation that will help us determine a safe dosage for this patient. Since the dosage range depends on the patient's BSA, we begin by putting 1.62 m² to the right of the equals sign, because we need to find the number of mg we need for a 1.62 m² patient:

_____ mg=1.62 m²

We can put 1.62 m² over 1 without changing it:

1.62 m²

If we look at the label, we see that it says that the safe dosage is 360 mg per m² per dose.

Because this safe dosage is given per dose, we should label our calculations "Safe dosage per dose":

Now we want to get rid of the m² on the top of the right side of the equation, and we notice that we can write 360 mg per m² as a fraction:

360 mg

1 m²

. In a safe dosage, 360 mg and 1 m² should be equal; we can multiply our equation by

360 mg

1 m²

, because:

The top of this fraction will be equal to the bottom in a safe dosage.
This fraction has m² on the bottom, which will cancel out the m² we want to get rid of on the top.

Safe dose per dose: _____ mg=

1.62 m²

360 mg

1 m²

Now all we need to do is to simplify our fractions:

None of the numbers will cancel, but we can cancel units that appear on both the top and the bottom to get:

Safe dosage per dose: _____mg=

1.62 m²

360 mg

1 m²

Now we can multiply across to get:

Safe dosage per dose: _____mg=

1.62

360 mg

583.2

So our safe dosage per dose is:

583.2 mg

This is our safe amount per dose, so we can compare it with the ordered dose 550 mg.

The ordered amount is safe, because the ordered amount of 550 mg is within 10% of the safe amount per dose of 583.2 mg .