Pharmacology unit 2.2 page 1
RSPT 1213: Pharmacology for respiratory care: Unit 2.2 Drug calculations
By Elizabeth Kelley Buzbee A.A.S., R.R.T.-N.P.S., R.C.P.
Name:
Date:
2007
Why do we bother?
While drug calculation is not a routine activity for the RCP as it is for the RN, we do, on occasion, have
need to calculate drug doses. If a unit dose must be reduced to a smaller size for a patient, or if unit doses
have been back ordered and only multi-dose bottles are available, the RCP needs to know how to safely and
effectively treat his patient with the proper amount of the drug.
The problem with this is that 3 different multi-dose bottles can contain the same drug, each might be in
different strengths so that drawing up .5 ml in a syringe from one bottle may be exceeding the amount of
drug need while drawing up .5 ml from a different bottle will be much less drug that need. We need to
know how to convert drugs from one strength to another in this situation.
While one can use the simple ratio formula to calculate drugs, I have found this method to be the quickest
way not only to calculate, but to keep the units straight.
Drug Strengths
Drug Strengths are recorded in several manners:
1. weight/volume, such as gram/ml or micrograms/Liter
2. ratio, such as 1:20,000 or 6:300
3. percent solution, such as .25% solution or 15.5%
Because only wt/vol can be used to perform calculations, your first step may be to convert the drug from
ratio to wt/vol or from percent to wt/vol.
Wt/vol
When a liquid drug is mixed in the factory, usually a dry powder or a liquid is dissolved into another liquid
such as water or normal saline. The active drug is the solute while the liquid is the solvent-together they
are the solution. In the wt/vol method, the solution is listed as solute/solvent.
solute / solvent
Mg / mL
Gram /Liter
Micrograms / mL
If you have a drug that is recorded as having strength of 5 mg/10 ml, you have 5 mg of solute [active
ingredient] that is dissolved into 10 mL of solvent.
Complete the following:
1. Example: When you have a drug with a strength of 34 micrograms/1 liter, you have 34
micrograms of solute [active ingredient] that is dissolved into 1 liter of solvent.
2.
When you have a drug with a strength of 300 grams/300 ml you have ____of solute [active
ingredient] that is dissolved into _____ of solvent.
3.
When you have a drug with a strength of 2.5 mg/3 ml you have ____of solute [active ingredient]
that is dissolved into _____ of solvent.
4.
When you have a drug that is labeled 6grams/300ml , you know that you have
active ingredient dissolved into
of solvent.
Ratio
Another common way to express drug strength is to use ratio of solute to solvent.
of
Pharmacology unit 2.2 page 2
A drug with a ratio of 1:2 has 1 part solute to 2 part solution.
Complete the following:
1. Example: When you have a drug with a ratio of 1.25:750, you have 1.25 units of solute
[active ingredient] that is dissolved into 750 units of solvent.
2.
When you have a drug with a ratio of 25:75, you have ____units of solute [active ingredient] that
is dissolved into _____ units of solvent.
3.
When you have a drug with a ratio of 1:10,000, you have ____units of solute [active ingredient]
that is dissolved into _____ units of solvent.
4.
When you have a drug with a ratio of 10:100, you have ____units of solute [active ingredient] that
is dissolved into _____ units of solvent.
Unfortunately ratios are too inaccurate to use because the ratio contains no units. If you were to bake a
cake using ratios only, you would not know if your cake would feed 10 persons or 100. The cake
would come out ok, but you don’t know what sized pan to select.
That was the problem the apothecary had with ratios; he didn’t know if he was making up a solution
for a day or for a year.
So over the years, for pharmacology, the ratio got standardized to grams: mL--so if you have a ratio of
1:2, it is understood that you have 1 gram: 2 mL.
Based on this fact, complete the following:
1. Example When you have a drug with a ratio of 12.5:600, you have 12.5 grams of solute
[active ingredient] that is dissolved into 600 mL of solvent.
2. When you have a drug with a ratio of 25:75, you have ____grams of solute [active ingredient] that
is dissolved into _____ mL of solvent.
3. When you have a drug with a ratio of 1:10,000, you have ____grams of solute [active ingredient]
that is dissolved into _____ mL of solvent.
4. When you have a drug with a ratio of 12:120, you have ____grams of solute [active ingredient]
that is dissolved into _____ mL of solvent.
Frequently for most respiratory drugs these units need to be converted from grams: ml to mg: mL
1 gram = 1000 mg
Express the following ratios as wt/vol and then convent from grams to mg
ratio
Grams: mL
Mg: mL
1:25
1 gram: 25 mL
1000 mg: 25 mL
1:2.5
1:100
2:25
6: 300
100:100
10:10,000
Pharmacology unit 2.2 page 3
Reduce the ratio
Imagine you are a red-shirt on the Enterprise and Spock turns to tell Captain Kirk to tell him that the
Romulans out-numbered us 45,000: 450,000.
Bones would yell at him. “Simplify that ratio, you green-blooded hobgoblin! I’m a doctor—not a
calculator!”
We have to agree with the good doctor, because--- like Captain Kirk--- we humans understand ratios better
if the ratio had been reduced to one in which one of the numbers is 1. When we do this reduction of the
ratio, we discover that the Romulans out-number us 1:10. Now, you know you are in serious trouble
because you are a red-shirt and know that the red-shirt always dies in these situation.
To make the numbers easier to understand and to calculate most ratios need to be reduced to a form in
which the solute is 1. To do this we divide both the solute and the solvent by the solute.
600 : 900 =
[get rid of extra zeros!]
6
: 9
6 : 9=
6
6
1: 1.5
Reduce the following ratios [watch out for the decimals]
ratio
Reduce to 1:X
10:25
1 : 2.5
Grams: mL
1 gram : 2.5 ml
120:180
2:100
2.5:5.0
600: 300
500:100
.1:10,000
Now if we need out solute in mg, we need to reduce adding this step.
Reduce the following ratios [watch out for the decimals]
ratio
Reduce to 1:X
Grams: mL
.10:2.5
1 :25
12.0:18.0
2:1000
20.5:500.0
15:12,000
1 gram : 25 ml
Mg: mL
1000 mg: 25 ml
Pharmacology unit 2.2 page 4
Look at the fourth column of the above table. The problem with converting from grams to mg is that now
we have huge numbers again, so it is permissible to again reduce the numbers by dividing both sides by
100 to get the solution easier to understand.
Reduce the following ratios [watch out for the decimals]
ratio
Reduce to 1:X
Grams: mL
Mg: mL
.10:2.5
1 :25
1 gram : 25 ml
1000 mg: 25 ml
Mg: mL
100 mg: 2.5 ml
or
10 mg: .25 ml
or
1.0mg : .025 ml
12.0:18.0
2:1000
20.5:500.0
6.00: 3.00
50.0:1000
15:12,000
Because the point of the table is to get the number easier to understand it is not always necessary to reduce
the solution to this last step, but sometime it is easier if it is done.
Convert from ratio to wt/vol.
ratio
Reduce to 1:X
Grams: mL
Mg: mL
Wt /: Volume
120.5:500
1 gram: 4.166
1000 mg: 4.166
100mg/ 4.166 mL
1: 4.166
mL
mL
16.00: 30.00
150:100
1.5:350
Pharmacology unit 2.2 page 5
Percentages
These are the easiest conversions to wt/vol, because the solute [in grams] is always in a solvent that is 100
ml. so 5% solution is 5grams/100 mL. Because there will be so many zeroes in this answer, reduction might
help.
convert these percentages to wt/vol
percent
ratio
Wt / vol
Reduce 100 mL
to 1mL
50%
50:100
50gram/100mL
.5 gram/1 ml
or
or
50,000 mg in 100 mL
500 mg/1 ml
4.5%
12.5%
75%
.5%
Calculation of drug dosages
As stated at the beginning of this lecture, we must convert our drug labeled in Percentage or in ratio to the
wt/vol format before we can calculate a drug dose. We are now ready for the drug calculation.
These are the steps:
1. discover the question being asked and the units in which the answer must appear
2. conversion to wt/vol
3. set up the equation
4. solve the equation
1. Discover the question being asked and the units in which the answer must appear
In word questions, sometimes the hardest thing to determine is the actual information the situation asks for.
In drug calculations, generally, there are only two possible bits of information need:
[1]
you have a multi-dose bottle and need to know how many mL [or Liters] you must
draw up.
[2]
you need to know in grams [or mg] how much active ingredient is present in a given
volume [mL or Liters] of a solution.
After you have determined which question has been asked, you find out what units are required. This will
determine how much you reduce your figures prior to calculation or if you even need to reduce it.
For example, you are asked how much active ingredient is in a bottle labeled 1: 3. You are not asked how
many mg, so you could leave the answer in grams rather than go through the steps of converting from
grams to mg.
Another example is that the doctor has ordered 2 mg of a drug. You have a bottle labeled 2% so you will
have to convert this 2% into 2000 mg/100 ml and reduce it to 20 mg/1 ml in order to discover how many
ml will yield 2 mg.
2.
conversion to wt/vol
Once you have discovered the information you need, you convert the unit to wt/vol, and then reduce as
needed to get the units the question requires.
Pharmacology unit 2.2 page 6
For example, you are asked how much active ingredient is in a bottle labeled 5%. You are not asked how
many mg, so could convert from 5% to 5gram/100 ml in order to do the next step.
But if your doctor has ordered 2.5 mg from a bottle labeled .5%, you must first convert the .5% to
.5grams/100 ml and then to 500 mg/100 ml and even 5 mg/1 ml to calculate your answer.
If your doctors orders 2.5 mg from a bottle labeled 12:75, you would be better to reduce the ratio from
12:75 into 1:6.25, then 1 gram: 6.25 ml, before converting to 1000 mg/6.25 mL.
3.
set up the equation
While you could answer a lot of these questions by just setting up a ratio, some folks use the following
formula:
A. doctor’s order [include the unit]
B. dose on hand [in units you need]
Nothing goes here
C. Dose on hand [in same units as the doctor’s
order.
We multiply A and B, the divide the answer by C.
Example A:
Your doctor has ordered 2.5 mg from a bottle labeled .5%. We know that .5% is .5gram/100ml but we
need mg so we convert to 500 mg/100 ml
A. 2.5 mg
B. 100 ml
Nothing goes here
C. 500 mg
[2.5 mg x 100 ml]
500 mg
[the mg cancel out and we are left with ml]
250.0 ml /500
.5 ml need to be drawn up to give 2.5 mg
Example B: you are asked how much active ingredient is in a bottle labeled 25% if you draw up 5 ml.
you convert 2.5% to 2.5grams/100 mL, because the question was not asked in terms of mg, we can stay
with grams.
A. 5 ml
B. 2.5 grams
Nothing goes here
C. 100 mL.
5 ml x 2.5 grams
100 ml
[the ml cancel out and we are left with grams]
12.5 grams / 100 = .125 grams of active ingredient are present in 5 ml of 25% solution
Pharmacology unit 2.2 page 7
Now it is your turn. Answer the following questions:
1.
How much do you draw up to administer 3.0 mg of a 10% solution?
2.
How much do you draw up to administer 20 mg of a .5% solution?
3.
How much do you draw up to administer 4.6 grams of a 25% solution?
4.
How much do you draw up to administer 2.5 grams of a 10:10,000 solution?
5.
Your doctor orders 3 mg from a drug labeled 3:600 solution. How much do you draw up?
6.
How much do you draw up to administer 45.3 mg of a 1:3 solution?
7.
How much do you draw up to administer 3 mg of a 3.5 mg: 1ml solution?
8.
How much do you draw up to administer 5 grams of a 60 gram:10 ml solution?
9.
How much do you draw up to administer .25 gram of a 5.5 gram:100 ml solution?
10.
Your doctor orders 3 mg of a drug that is labeled 4grams/ml. How much do you draw up?
11.
Correction You want to know how much active ingredient is found in 50 ml of a 1:10,000
solution
12.
Correction You want to know how much active ingredient is found in 1.550 ml of a 50:250
solution
13.
Correction You want to know how much active ingredient is found in 150 ml of a 1:30
solution.
14.
Correction You want to know how much active ingredient is found in 100 ml of a 2.5%
solution
15.
Correction You want to know how much active ingredient is found in 50 ml of a 38% solution
16.
Correction You want to know how much active ingredient is found in 10 ml of a 50% solution
17.
You want to know how much active ingredient is found in 1.5 ml of a 300mg/ 1ml solution
18.
You want to know how much active ingredient is found in 250 ml of a 150mg/ 10ml solution
19.
You want to know how much active ingredient is found in 65 ml of a 3.5 mg/ 1ml solution
Pharmacology unit 2.2 page 8