Medic Math


Disclaimer: All non-medical readers browse the archives now. Otherwise I can’t be responsible for the drowsiness this post will induce.

One of my readers is going through paramedic school, and has arrived at that portion of the course that all medic students dread…

Pharmacology.

[cue sinister Psycho music: reep reep reep reep!]

More specifically, dosage calculations. Rookie Bebe, I feel your pain, because I too suck at math.

Well, I don’t actually suck at it. I can understand mathematical concepts, and if I apply myself, can actually make decent grades in math.

What I lack is the academic discipline required to excel at it. I don’t need a math tutor. I need R. Lee Ermey standing behind me, bellowing, “You call that a quadratic equation, maggot? What the fuck is your major malfunction, numbnuts?? I WILL motivate you, Private AD, even if it short dicks every damned math geek in MENSA! Now drop down and graph me a parabola!”

Calculus is the main reason this blog isn’t called A Day In The Life Of An Emergency Physician.

Luckily, you don’t need calculus to do dosage calculations. Hell, if you can do fourth-grade math, you can calculate a dose.

Yes, you read that right. Not to put any undue intimidation on any would-be medic students, but if you can manipulate a fraction and understand the metric system, you can calculate any drug dose you want. If I can do it, I know you can do it. All you need do is remember a few basic rules, and a couple of formulas.

So, without further ado, I present Ambulance Driver’s Tips for Med Calculations:

1. Calculations ain’t the most important thing in the pharmacology section. Seriously folks, it’s just rote memorization. Memorize the formula, plug in the numbers. It is FAR more important to understand, in depth, the pharmacokinetics and pharmacodynamics of every class of drug you may be asked to administer. Do not limit this knowledge to your “drug box” medications. If you know how a drug reaches its site of action, how it works, and how it is metabolized and excreted from the body, you will be far ahead of most of your colleagues. By knowing these things, you will automatically be able to grasp why you’re giving a medication, and more importantly, why not. Don’t be one of those “because it’s in the protocol” medics.

2. Cheat. Use a calculator, write down your most commonly used formulas, use a pocket dosing guide…whatever it takes, and whatever your instructor allows. A smart EMT knows when to use his references.

3. Convert everything to like terms. If, for example, you are asked to provide the answer in milligrams or milliliters, but the theoretical drug is supplied in apothecary measurements, you must convert the apothecary measurement into metric.

This actually only applies to paramedic class. You see, we paramedic instructors just luuuurve to torture students by giving proposed drug concentrations in measurements that haven’t been used in fifty years. It’s just what we do.

Why? Because our instructors did it to us, that’s why. My paramedic instructor took perverse joy in asking us to convert from minims to milliliters. Deal with it. If you need help, try this site.

Now, should you ever encounter a medical control physician in the field, who insists on ordering doses in apothecary measurements, there is but one thing to do. Remember this, because it is very important:

Ask him to hand the phone to a physician who was trained in the latter half of the twentieth century.

You don’t want to be taking orders from a doc who remembers the invention of penicillin and still thinks of paramedics as those guys in white smocks who drive the high-top Cadillac for the funeral home.

4. Memorize the following formulas:

Drug Dosage Formula:

(dose ordered X volume on hand) / concentration = volume to administer

Drug Infusion Formula:

Volume to administer X drip factor = drops per minute

IV Fluid Infusion Formula:

volume to administer X drip factor) / time in minutes = drops per minute

5. Plug in your numbers

6. Reduce to lowest terms. Cancel out any like terms in your numerator and denominator.

7. Solve.

That’s it, folks. It really is that simple. Three fourths of the battle is setting up the terms, in the concentrations ordered in the problem.

Here’s an example problem, straight from the horse’s mouth blog:

Atropine is ordered for your pt 0.7 mg I.M. stat prior to surgery. You have atropine gr 1/120 per ml. Give ____

First, convert the apothecary measurement to metric. 1/120 of a grain equals 0.5 milligrams.

Now plug in the numbers:

[0.7 mg (dose ordered) X 1 ml (volume on hand) ] /0.5 mg (concentration on hand)

Reduce to lowest terms, and cancel like terms. This one can’t be reduced, so the only canceling we can do is remove the milligrams in the numerator and denominator, leaving only milliliters left, which is what we want to know.

Solving the problem leaves us with 1.4 ml to administer to the patient.

Simple, no?

This formula will work with Questions 1, 2 and 3, Rookie Bebe. Question 3 has a number of red herrings:


D5W 500 ml plus KCI 5 mEq at 40 ml per h. KCI is supplied in a 10 ml ampule containing 20 mEq per ml. How many ml of KCI will be added to the 500 ml of D5W?

The only pertinent numbers are KCl 5 mEq (dose ordered), and 20 mEq/ml (concentration and volume. What a gift!). Plug ‘em into the formula.

[5 mEq (dose ordered) X 1 ml (volume on hand)] / 20 mEq (volume on hand) = 0.25 ml

Simple, no?

Questions 4 and 5 can be answered using the IV Fluids Infusion Formula:


The physician orders Dextran 12% 1000 ml within 8 hours for a post -trauma victim. Drop factor is 12 gtt/ml.

_____ml/h. _____ml/min. ______gtt/min

[1000 ml (volume to administer) X 12 gtt/ml (drip factor)] / (8 hours) x 60 minutes

Reduced to lowest terms:

(1000 ml X 12 gtt/ml) / 480 minutes = (1000 X 1) / 40 = 25 X 1 = 25 gtt/min

Now convert 25 gtt/min to ml/min.

25 divided by 12 (gtt/ml) = 2.08, or roughly 2.1

2.1 ml/min X 60 = roughly 126 ml/hr.

Simple, no?

In my experience, medic students tear their hair out doing dosage calculations for two reasons:

1. Math errors.

Solution: Use a calculator. If your instructor won’t let you during class, then take your time and check your work. Then, on the truck, use the freakin’ calculator.

2. They don’t know how to eat an elephant.

Solution: One bite at a time. Don’t look at the elephant. Just grab your fork and dig in. Nibble at little pieces of the problem, until eventually, you look up and the elephant is gone.

And of course, no insanely boring educational blog post would be complete without a little lagniappe, so here it is:

Ambulance Driver’s Superhuman Calculate the Dopamine Dose In Your Head Trick:

For any standard mixture of dopamine (400 mg/250 ml or 800 mg/500 ml), the following will give you an infusion rate equivalent to 5 mcg/kg/minute:

  1. Take the patient’s weight in pounds.
  2. Drop the last digit.
  3. Subtract 2 from the answer.
  4. Plug that number into your infusion pumps as ml/hr.

Johnny weighs 174 pounds and is in severe septic shock. Nurse Heather wants to save his life by administering a dopamine infusion at 5 mcg/kg/minute. Whatever shall Nurse Heather do?

  1. 174 pounds, drop the last digit, you’re left with 17.
  2. 17 minus 2 equals 15.

Nurse Heather programs 15 ml/hr into the infusion pump. Nurse Heather’s colleagues snort derisively, and look up the information on the dosing chart. Presently, said colleagues genuflect before Nurse Heather, crying, “We’re not worthy! However did you figure that in your head?”

Nurse Heather replies, “Ambulance Driver taught me. Here’s the URL to his blog.”