Drug Math Tutorial Part III

This part is going to explain a universal formula for dose administration.

What is it?
The Master Formula is a formula that can be used for all drug calculations. It was developed by my paramedic instructor(well published by him, probably developed long before him) and is currently a standard in many educational facilities.

How do I use it?
You plug the appropriate numbers into the previously defined variables. This means that if you are not administering a weight based medication & dose that you do not need to use that portion of the formula. I will explain in the fallowing.

Why do I need to do math?
Luckily, most drug manufacturers package prehospital medications in single-dose containers(vials, ampules, syringes). Unfortunately, some medications are weight-based, and nearly every pediatric dose requires titration by weight. This means that math still has its place in EMS.

The point of doing the math is to end up with an answer in milliliters or drops per minute (gtts/min). This is because our syringes & bags of fluid are measured in milliliters, and we need to figure out how many ml or gtts/min will equal the dose we want to deliver.

The Master Formula:

DD x Wt x SS
C x T

DD = Desired Dose
Wt = Weight
SS = Solution Set
C = Concentration
T = Time

Solution Sets
Mini drip: 60gtts/ml, means every 60 drops equals 1 ml(1cc)
Macro drip: 10gtts/ml, means every 10 drops equals 1ml(1cc)

You are ordered to administer 20 mg of Cardizem to your a-fib patient.
Your Cardizem comes in a 5 cc vial. On the label of that vial it says 25 mg.
How are you going to deliver this med?

Desired Dose(DD): 20 mg
Concentration(C): 25 mg/5 ml

I bet you can do this one in your head, but I am going to write it out for you(and those people who may need a math refresher). Place your desired dose(DD) over the concentration(C). Since this wasn't a weight-based dose, we don't need the Wt part of the formula. Since this is a bolus and not an infusion, we won't need the SS or T part of the formula. So we need to write this out DD/C.
20 mg
25 mg/5 ml

Now you have to reduce C to 1 ml.
25 mg /5 ml = 5 mg /ml

Now rewrite your formula with the C minimized:
_20 mg_
5 mg/ml

Now, when using this formula, you can cross out any variable, such as mg, that repeats itself. So if you see "mg" behind a number above the line, and you see "mg" behind a number below the line, just cross them both out. If both variables are on the top or on the bottom, you can cross them out as well. So basically anytime you see the same thing twice like kg, ml, mg, or mcg, just cross them out.
20 mg
5 mg/ml

Now rewrite this without crossed out variables:
5 /ml

If it makes it easier, you can circle all the single variables left. In this case ml is the only one. So now that you have reduced your variables, you need to reduce the numbers. In fractions, if the top and bottom number are both divisible by the same number, you can reduce them. Since 20 and 5 are both divisible by 5 you want to divide them both by 5.

20 divided by 5 = 4
5 divided by 5 = 1
1 /ml

Now, a mathematician would tell you to multiply the top and bottom by the remaining variable.

& 1/ml(ml)

= 4ml/1

= 4ml

I am just going to tell you that whenever you see 1/ml on the bottom of your formula. You can just bring the ml to the top.
So your answer will be 4 ml.

After getting your answer, ask yourself, "does this make sense?". Well does it?

25 mg of Cardizem in 5 ml, and you want to give 20 mg. Is 4 ml a reasonable answer? YES!!

Lets try Dopamine.
Your dose for Dopamine starts at 5mcg/kg/min.

This tells us that we will be using the weight (wt) portion of the formula.

First we plug the dose, and weight into the formula. Lets say our patient is 110 lbs. That equals 50 kg, because 1 kg = 2.2 lbs.
5 mcg/kg x 50 kg x SS
C x min.

• Notice that the time portion of the dose replaces Time (T) on the bottom of the formula.

• Now we still need our solution set (SS) and concentration (C).

• We will be using a 60gtts/ml(mini drip) drip set.

• Dopamine comes packaged 400mg in a 250ml premixed bag.
5mcg/kg x 50kg x 60gtts/ml
400mg/250ml x min.

Since our dose is in micrograms we need to convert our concentration from milligrams to micrograms.

• 1mg = 1000mcg
5mcg/kg x 50kg x 60gtts/ml
400,000mcg/250ml x min.

Next we need to get our concentration simplified to per 1ml (1cc). This means that you divide both sides of the concentration by the volume (milliliters).

• 400,000 divide by 250 = 1,600

• 250 divided by 250 = 1, We do not show the numeral 1 when there is a variable fallowing it(1ml = ml).
C = 400,000mcg/250ml = 1,600mcg/ml

• Now we can plug our simplified concentration into the formula.
5mcg/kg x 50kg x 60gtts/ml
1600mcg/ml x min.

• Now it’s time to start simplifying our formula.

• First you can eliminate all variables that you see twice

• Since mcg is on the top and the bottom we cross them out
5mcg/kg x 50kg x 60gtts/ml
1600mcg/ml x min.

• Do the same with kg & ml. If it makes it easier for you, circle the variables left.
5mcg/kg x 50kg x 60gtts/ml
1600mcg/ml x min.

• Now you can rewrite the formula without the crossed out variables.

• This will show you what form your dose should end up in. In this example gtts/min.
5 x 50 x 60gtts
1600 x min.

• Now you can just do the math.

• The easiest way is to cross out the zeroes. Cross 1 zero off the top and 1 off the bottom. Then do it again. You will be left with 16 on the bottom.
5 x 50 x 60gtts
1600 x min. =

5 x 5 x 6gtts
16 x min.

• Since 6 is on the top & 16 is on the bottom and they are both divisible by 2, divide both by 2.
5 x 5 x 3gtts
8 x min.
• This is as far as you can simplify so multiply the top then divide the product by the bottom.

5 x 5 x 3gtts
8 x min.

5x5 = 25


In division we divide the top number by the bottom number.

75 divided by 8 = 9.375. Round to the nearest whole number.

Answer: 9 gtts./ min.

Practice this formula on a few more doses.

mini drip = 60gtts/ml
macro drip = 10gtts/ml
  1. Your dose is 20mcg/kg/min and your concentration is 500mg in a 50cc vial. Your patient is 154 pounds. Use a mini drip.
  2. Your dose is 10mcg/min and you have a 250cc vial with 25 mg. Use a mini drip.
  3. Your dose is 2mcg/min and you put 1mg in a 250cc bag. Use a mini drip.
  4. Your dose is 150mg/10min you have a 100cc bag and a macro drip.
  5. Your dose is 0.25mg/kg for a 132 pound and you have a 5cc vial with 25 mg.


Mat said...

Can you post the answers to the extra questions? It's great doing them... but it might help to do them correctly, lol.

Adam Thompson, EMT-P said...

Absolutely. I will try to have them posted by the end of the day. They will be in a separate post, but I will link to them from this one.

Adam Thompson, EMT-P said...

Answer Key is posted