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Paramedic Math Dosage Calculations

The first and most basic drug dose calculation we are going to look at is the simple dose calculation.

We calculate this when we are told to give the patient X amount of a certain drug (DD)

The first step is to identify the desired dose (DD from the variables) that we have been told to administer

Next we identify how that drug is supplied to us in its vial or ampule (V\C)

Then we use the following formula :

DD/1 x V/C

Basic Dosage calculation formula

 

We remember from the variables page that DD = the desired dose we are supposed to administer, C = the concentration of the drug, and V = the volume that drug is contained in.

Until you get comfortable using the variables and the formulas I suggest writing all the variables down in a block and filling in as many as the “scenario” gives you even if they don’t apply to your particular calculation.

I also suggest that until you can recite these formulas in your sleep you begin each calculation by writing the formula out next to your list of variables.

One of the first tips I can give you is to STAY ORGANIZED – these calculations get more complex as we go and being able to quickly identify what you have figured where will help TREMENDOUSLY when we get to dopamine drips.

Let’s give one a shot shall we:

For this first one I used an image so I could explain what we doing in each step – subsequent ones will just be text so if you get lost refer back to the image for guidance…. Buckle up here we go

You are ordered to administer 75 mg of a medication to a 144 pound patient, the medication is supplied to you in a vial that contains 100 mg of drug in 10 ml.

Begin by identifying the variables in the scenario and plugging them in then work the formula.

So we will be administering 7.5 ml of that medication to get the desired dose of 75 mg.

Let’s try one without the graphic and see if you still follow:

You are ordered to administer 5 mg (DD) of a medication to a 230 pound (WT) patient. That drug is supplied to you in a vial that contains 20 mg (C) of the drug in 10 ml.(V)
  • DD – 5 mg
  • C – 20 mg
  • V – 10 ml
  • gtt – N/A
  • T – N/A
  • WT – 230 pounds (not used in this calculation)

Basic formula : DD/1 X V/C

  • add variables 5 mg /1 X 10 ml / 20 mg
  • eliminate like labels 5 mg /1 X 10 ml / 20 mg
  • reduce =  5 / 1 X 10ml / 20
  • multiply =  5 ml / 2
  • divide  = 2.5 ml

In this case we would administer 2.5 ml to get the desired dose of 5 mg

How’d that one go for you ?

Ready for one last one before we change the kind of administration order we get (and add a step)?

Here you go… no color coding or explanations this time – see if you can follow

You are ordered to administer 7 mg of a medication to a 212 pound patient. The medication is supplied in vials that contain 10 mg or drug in 10 ml
  • DD – 7 mg
  • C – 10 mg
  • V – 10 ml
  • gtt – N/A
  • T – N/A
  • WT – 212 pounds (not used in this calculation)
Basic formula : DD/1 X V/C

  • add variables 7 mg /1 X 10 ml / 10 mg
  • eliminate like labels 7 mg /1 X 10 ml / 10 mg
  • reduce  = 7 / 1 X 10ml / 10
  • multiply =  7 ml / 1
  • divide  = 7 ml

In this case we would administer 7 ml to get the desired dose of 7 mg

 

 

OK so we have the basic formula down… Let’s add some twists to show some of the other ways this particular type of order can come in.

What if your order is for 10 mg/kg (10 mg per kilogram) of a medication ? How does that change the formula?

IT DOESN’T!

What it does do is forces you to calculate what the DD actually is. This will generally be a TWO step process (unless you are given the patients weight in kg)

  • convert patients weight from lb to kg (multiply by 0.453 or divide by 2.2)
  • multiply the ordered dose by the patients weight in kg to get the total dose you must administer

Ready to give it a shot?

 

Administer 1 mg/kg of a medication to a 187 lb patient. The medication comes supplied in a vial containing 5 mg of drug in 100 ml.
  • DD – 1 mg/kg
  • C – 200 mg
  • V – 100 ml
  • gtt – N/A
  • T – N/A
  • WT – 187 pounds
  1. Begin by converting 187 lb to kg 187 X 0.453 = 84.711
  2. round to closest whole number 84.711 = 85
  3. use the patients weight in kg multiplied by the dose per kg to get your DD value
  4. in this case 85 kg X 1 mg = a DD value of 85 mg
Basic formula : DD/1 X V/C

  • add variables 85 mg /1 X 100 ml / 200 mg
  • eliminate like labels 85 mg /1 X 100 ml / 200 mg
  • reduce      =     85 / 1 X 100 ml / 200
  • multiply     =    85 ml / 2
  • divide       =    42.5  ml

In this case we would administer 42.5 ml to get the desired dose of 1 mg/kg

 

 

See the formula doesn’t change – you just have to calculate the actual value of one of the variables before you can work the equation.

One more twist to throw you in dosage calculations before we move on to calculating drip rates…

What if the order this time is for 2 mcg/kg (micrograms per kilogram)?  How does that change the formula?

Again the answer is… you guessed it – IT DOESN’T

It does however force you to convert either the mcg to mg or mg to mcg whichever you personally prefer.

Ready to work one?

Administer 12 mcg/kg of a medication to a 150 lbs patient. The medication is supplied in an ampule that contains 1 mg of the drug in 100 ml.

 

  • DD – 12 mcg/kg
  • C – 1 mg
  • V – 100 ml
  • gtt – N/A
  • T – N/A
  • WT – 150 pounds
  1. Begin by converting 150 lb to kg 150 X 0.453 = 67.95 kg
  2. round to closest whole number 67.95 kg = 68 kg
  3. use the patients weight in kg multiplied by the dose per kg to get your DD value
  4. in this case 68 kg X 12 mcg = a DD value of 816 mcg
Basic formula : DD/1 X V/C

  • add variables 816 mcg /1 X 100 ml / 1 mg
    • we need to convert so we have like terms
    • I am going to convert 1 mg by adding 6 zeros to the right of the value and changing the label from mg to mcg
      • 1 mg = 1000000 mcg
  • eliminate like labels 816 mcg /1 X 100 ml / 1000000 mcg
  • reduce      =      816 / 1 X 100 ml / 1000000
  • multiply    =     816 ml / 10000
  • divide       =     .08 ml (rounded down)

In this case we would administer .08 ml to get the desired dose of 12 mcg/kg

 

That is a pretty unrealistic order, but I wanted you to see the conversion before the actual formula changes later on.

SO what do you think? Ready to tackle the next step – calculating drip rates for volume infusion ?

 

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