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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 0.5 ml in a syringe from one bottle may be exceeding the amount of drug needed while drawing up 0.5 ml from a different bottle will be much less drug that is needed. 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:

weight/volume, such as gram/ml or micrograms/Liter

ratio, such as 1:20,000 or 6:300

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.

Examples

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. 

When you have a drug with a strength of 300 grams/300 ml you have  300 grams of solute [active ingredient] that is dissolved into  300 ml of solvent. 

When you have a drug with a strength of 2.5 mg/3 ml you have 2.5 of solute [active ingredient] that is dissolved into 3.0 of solvent. 

When you have a drug that is labeled 6grams/300ml , you know that you have 6 grams of active ingredient dissolved into 300 ml of solvent. 

 

 

Ratio

Another common way to express drug strength is to use ratio of solute to solvent.

A drug with a ratio of 1:2 has 1 part solute to 2 part solution.

Examples

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. 

When you have a drug with a ratio of 25:75, you have 25 units of solute [active ingredient] that is dissolved into 75 units of solvent. 

When you have a drug with a ratio of 1:10,000, you have 1 units of solute [active ingredient] that is dissolved into 10,000 units of solvent. 

When you have a drug with a ratio of 10:100, you have 10 units of solute [active ingredient] that is dissolved into 100 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. 

 

Examples

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. 

When you have a drug with a ratio of 25:75, you have 25 grams of solute [active ingredient] that is dissolved into 75 mL of solvent. 

When you have a drug with a ratio of 1:10,000, you have 1 grams of solute [active ingredient] that is dissolved into 10,000 mL of solvent. 

When you have a drug with a ratio of 12:120, you have 12 grams of solute [active ingredient] that is dissolved into 120 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

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 gram : 2.5 mL	1000 mg: 2.5 mL
1:100	1 gram : 100 ml	1000 mg : 100 mL
2:25	2 gram : 25 ml	2000 mg : 25 ml
6: 300	6 grams: 300 ml	6000 mg: 300 ml
100:100	100 grams: 100 ml	100,000 grams: 100 ml
10:10,000	10 grams : 10,000 ml	10,000 mg: 10,000 ml

 

Reduce the ratio

Imagine you are a red-shirt on the Enterprise and Spock turns to  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 situations. 

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	Grams: mL
10:25	1 : 2.5	1 gram : 2.5 ml
120:180	1:1.5	1 gram : 1.5 ml
2:100	1:50	1 gram: 50 mL
2.5:5.0	1: 2	1 gram: 2 mL
600: 300	1: .5	1 gram: .5 mL
500:100	1:.2	1 gram : .2 mL
.1:10,000	1: 100,000	1 gram : 100,000 ml

Now if we need to figure out solute in mg, we need to reduce by adding this step.

 

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
12.0:18.0	1:1.5	1 gram: 1.5 ml	1000 mg: 1.5 ml
2:1000	1:500	1 gram : 500 mL	1000 mg:500 ml
20.5:500.0	1:24.3	1 gram : 24.3 mL	1000 mg : 24.3 ml
6.00: 3.00	1:.5	1 gram : .5 ml	1000 mg: .5 ml
15:12,000	1:800	1 gram : 800 ml	1000 mg: 800 ml
ratio	Reduce to 1:X	Grams: mL	Mg: mL

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	Reduce Mg: mL
.10:2.5	1 :25	1 gram : 25 ml	1000 mg: 25 ml	100 mg: 2.5 ml or 10 mg: .25 ml or 1mg : .025 ml
12.0:18.0	1:1.5	1 gram :1.5 ml	1000 mg: 1.5ml	100mg: .15 ml
2:1000	1:500	1 gram:500 mL	1000 mg: 500ml	10mg:5 ml
20.5:500.0	1:24.3	1 gram:24.3 ml	1000 mg: 24.3ml	100mg: 2.43mL
6.00: 3.00	1: .5	1 gram : .5 ml	1000 mg : .5ml	2000mg: 1ml
50.0:1000	1:20	1 gram : 20 ml	1000 mg : 20ml	500mg: 10ml or 50 mg/1 ml
15:12,000	1:800	1 gram: 800 ml	1000 mg: 800 ml	10 mg: 8 ml

 

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: 4.149	1 gram: 4.149 mL	1000 mg: 4.149 mL	100mg/ 4.149 mL
16.00: 30.00	1: 1.875	1gram: 1.875 ml	1000mg: 1.875ml	100mg:.1875 ml
150:100	1:.666	1gram: .666 ml	1000mg:.666mL	100mg:.0666 ml
1.5:350	1:233	1gram: 233 ml	1000mg:233 ml	10 mg:.2.33 ml

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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 5 grams/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 or 50,000 mg in 100 mL	.5 gram/1 ml or 500 mg/1 ml
4.5%	4.5 : 100	4.5 grams: 100 ml or 4,500 mg:100 ml	45mg: 1ml
12.5%	12.5: 100	12.5 grams: 100 ml 12,500 mg: 100 ml	125 mg: 1 ml
75%	75:100	75gram: 100 ml	.75grams: 1ml
.5%	.5:100	.5grams:100ml 500 mg:100 ml	5 mg:1 mL

 

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:

discover the question being asked and the units in which the answer must appear

conversion to wt/vol

set up the equation

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:

• you have a multi-dose bottle and need to know how many mL [or Liters] you must draw up.  

• 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. 

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 5 gram/100 ml in order to do the next step. 

But if your doctor has ordered 2.5 mg from a bottle labeled 0.5%, you must first convert the 0.5% to 0.5 grams/100 ml and then to 500 mg/100 ml and 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.