Airway & Respiratory, JEMS Games, Patient Care, Training

Math Phobic No More

You arrive on scene and exit your ambulance. As you near the home, you discover you must enter through a window to access your patient. You find your patient faces many complications: an obstructed airway, difficult IV access, poor lighting. You are tense but handle each complication, moving from one difficulty to the next.

Soon you discover your patient now needs pharmacological intervention for hypotension. Medical command advises you to administer dopamine to your 158-lb. patient at a rate of 2 mcg/kg/hour. You freeze. Your face pales and your hands tremble. You take out your pad of paper and numbers begin to appear, but they soon seem to swirl. Sweat now appears on your forehead. Your mind is blank. You can’t remember formulas or even addition and subtraction. You call to your partner to assist you. Time ticks away, and the stress is taking its toll.

It’s not a real call, but it could be. This encounter occurred many times during the 2007 JEMS Games competition at the EMS Today Conference and Exposition. In this instance, a JEMS Games judge, inches away, clutches her clipboard and grips her pen and timer tightly. She’s feeling your pain and longs to tell you to take a deep breath and start over, but game rules prohibit this. Instead, she prays that you have recall and your mind clears.

The JEMS Games feature competitive EMS teams from around the world who are judged on their performance of critical prehospital assessment skills and treatment rendered to simulated patients. Unusual scenarios test teams as they react to and manage a number of patient assessment, treatment and transportation challenges. Scoring is based on skill, speed and technical accuracy, which contributes to the stress of performing in front of your peers.

I served as a judge at the third and fourth annual JEMS Games and was fascinated by the different ways we in EMS approach the same things, and the creativity used by teams to progress through the course. I learned several new skills I can apply to my own practice, but I also witnessed the sheer terror of participants as their minds went blank at the pharmacology station. This concerned me and prompted me to prepare a medication calculation review that was thorough, non-threatening and most of all, easy to recall.

You might be thinking right about now, ˙why do I need to do this if I have a chart I can refer to, or access to an automatic syringe or IV pump that will do the calculation for me?Ó Well, references can be lost and machines can fail. Most importantly, however, as a professional, you must know the science and rationale to support your decisions and treatments. Otherwise, you’re just a technician, not capable of critical thinking or decision-making skills.

Using formulas
Let’s first quickly review basic medication math. Hopefully, you’re already comfortable with this, and it’ll serve as a good review. But if you’re not, and have been afraid to tell your partner or training officer that it’s one of your weaknesses, it’ll be an important lesson for you.

Use a formula to find correct units of measure:Using incorrect units of measure is one of the most common dosage calculation errors. Here is an example: Medical Command orders you to give 3 mg of Versed, IV stat. The drug is only available in 5 mg/5 mL vial. How many milliliters should you give? Before you even begin, organize the information:„

>THE ORDER: 3 mg Versed, IV

>ON HAND: 5 mg/5 mL Versed


Complete in the following formula:X = 5 mL (volume in the vial) x 3 mg (the desired dose)
„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„ 5 mg (dose in vial/on hand)

First, multiply the top numbers. (Note: The mg on top cancels out the mg on the bottom. This will leave the unit of mL.)
„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„X = 15 mL (volume in vial x desired dose)
„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„ 5 (dose in vial/on hand)

Then, reduce the fraction. Divide the bottom into the top.

„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„ X = 3 mL„

This formula can be used with orders involving„PO, IM, SQ, or IV or rectal administration.

Let’s try another practice problem. By protocol, you’re to administer 40 mg of Lasix IV before calling medical command. The vial in the ambulance reads 80 mg/10 mL. How many mL do you push?„

>THE ORDER: 40 mg Lasix, IV

>ON HAND: 80 mg/10 mL Lasix


Fill in the formula:„„„„„„„„„X = 10 mL x 40 mg
„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„ 80 mg

Reduce the fraction by dividing the bottom into the top.

„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„ X = 5 mL„

Question strange answers:Be especially careful to recheck suspicious-looking calculations. For example, if a dosage calculation suggests giving 18 tablets or 223 mL (a questionable number) of a solution, assume you’ve made an error and recheck your calculation. If you’re still unsure about your results, have a coworker check your math or contact Medical Command.

Use of a calculator:A handheld calculator canimprove the accuracy and speed of your calculations, but it can’tguarantee accuracy. You must know how to carefully set up your formulas and double check units of measure and decimal places. Note: Some EMS competitions, such as the JEMS Games, prohibit teams from using calculators at medication stations.

Watch your decimal points carefully:An error in the number of decimal places or zeros in a dosage calculation can cause tenfold or greater dosage error.

Calculating Micrograms
Now the fun begins because we must face the dreaded micrograms! Combine that with many weight-based, critical-care drugs, and this is the perfect set-up for EMS terror. Guessing is not an option, and estimation is out of the question. ˙I think it looks about right,Ó isn’t an acceptable answer, nor is ˙What am I, a pharmacist?Ó Accuracy ensures superior patient care. In addition, it’s often necessary to perform these calculations quickly because the patient is critical.„

[Several helpful drug calculation books on the market are geared to the prehospital professional, and take you deeper into problem solving and different scenarios. These include:Dosage Calculations Made Incredibly Easy by Springhouse,Drug Dosage Calculations for the Emergency Care Provider by Alan A. Mikolaj,Clinical Calculations Made Easy by Gloria P. Craig andEasy 4-Step Method to Drug Calculations by S.D. Foust.

Many of these books have wonderful explanations for solving complex calculations. Some even go into detail on the ˙clock methodÓ or the ˙common rule of four clocksÓ that are often taught in the classroom or used by a provider to calculate these dosages. For providers who like to sequence, work with numbers and find math fun, these are great resources and methods to learn and apply.]

I’ve spent my career in a field in which I’m required to perform emergent drug calculations, but I’ll admit I’ve avoided the microgram whenever possible. I rely on the most exacting but simple methods that someone who’s primarily right-brained can work with. This leads me to present the following basic explanation and formula.

First, however, you must remember a few fundamental facts about micrograms and IV drip calculations:„

>A microgram is a unit of mass equal to one thousandth of a milligram or one millionth of a gram.

>Micrograms are abbreviated asmcg, notug, which could be easily confused with milligrams (mg).

>We’re dealing with tiny amounts of a drug; thus, a misplaced decimal point can make a huge difference and create dramatic and deadly over- or under-dosing.

When you need to calculate a patient’s weight in pounds in order to perform the calculation and follow the physician’s order, several methods may be used. You can use a calculator or do the calculations in your head (if the patient is heavier than 10 lbs.).

Calculator:Take the patient’s weight in pounds and divide that number by 2.2. The result is the patient’s weight in kilograms.

Calculation #1:You have a 220-lb. patient. Find their weight in kilograms.

220 _ 2.2 = 100 kg„

In your head:Take the patient’s weight in pounds and divide it in half. Then subtract 10% from the quotient. Ta-da! That’s your patient’s weight in kilograms.

Calculation #2:You have a 100-lb. patient. Find their weight in kilograms.

100 divided in half = 50„
10% of 50 = 5„
50 Ï 10% (5) = 45 kg„

Calculation #3:You have a 156-lb. patient. Find their weight in kilograms.

156 _ 2 = 78„
10% of 78 = 7.8 (rounded to 8)„
78 Ï 10% (8) = 70 kg„

OK, now for the nitty-gritty part of the formula. After reviewing the material, I had this process down pat in less than five minutes, so it’s not as difficult as it seems.

There are three basic steps:

1.Memorize the formula or have it handy on a card;

2.Know the patient’s weight in kilograms; and

3.Know the concentration of drug in one milliliter (1 mL) of the infusion. You may need to calculate this, which is a piece of cake once you understand the formula.

(Weight in kg) x (dose in mcg/kg/min) x 60 = mL/hr
„„„„„„„„„„„ Drug concentration in 1 mL

Let’s break this formula apart. We’ve already calculated the weight in kg. We multiply that by the dose the physician orders in mcg/kg/min. Then we multiply that times 60, which is aconstant because there are 60 minutes in one hour. This number is then divided by the concentration in 1 mL (that we’ve already calculated). You can see that up to this point, this will be an easy three-step problem:„

1.Calculate the weight in kg;

2.Calculate the concentration in 1 mL of your infusion; and

3.Plug these numbers into the formula to get your answer in mL/hour.

You already know the steps to calculate the patient’s weight from pounds to kilograms. Now, how do you determine the concentration of drug as 1 milliliter for the denominator in the formula? Simple.„

1.Take the amount of drug in solution (milligrams or micrograms);

2.Divide by the amount of liquid in the bag (how many milliliters are in the bag?); and

3.If you’re performing a calculation where you’re required to administer micrograms, but your drug is listed on the label in milligrams, convert the milligrams to micrograms by moving the decimal point three spaces to the right.


>200 milligrams of dopamine in 250 mL is equal to 200,000 micrograms in 250 mL.

>400 milligrams of dopamine in 250 mL is equal to 400,000 micrograms in 250 mL.

You can see the easy conversion by moving the decimal point to theright three spaces. (Remember, a microgram is one thousandth of a milligram, which is why you move the point three spaces.)

Now divide your dose in micrograms by the milliliters to get the dose in 1 mL. This will provide you with the denominator used in the formula.

400 mg/250 mL = 400,000 micrograms/250 mL„

400,000 _ 250 mL = 1,600 micrograms/mL„

1,600 mcg in 1 mL„

Now you have everything you need to solve any problem. There may be calculations that aren’t weight-based. In that case, you can eliminate the ˙weight in kilogramsÓ mentioned in the formula.„

Drip Rate
All that’s left at this point is to set your drip rate. If you’re comfortable performing this step, skip this review and go right to the practice problems using this simple formula. If not, spend a minute going over the steps to set your minidrip.

Because you’ll most likely be using minidrip tubing (60 gtt) for accuracy, your mL per hour will be equal to your drops per minute with your minidrip. So if the answer you get after completing the formula is 24 mL per hour, you set your drip rate at 24 drops per minute.

How do you do this, you ask?„

1.Place your watch behind the clear drip chamber so you can see your watch through the chamber;

2.Begin to slowly open the slide clamp to allow the drops to begin to fall; and

3.Regulate the slide until you count 24 drops falling in each minute. (Count the drops as they fall while you observe the second hand on your watch behind the drip chamber for the desired amount of time. Regulate and adjust the flow accordingly until you have the correct number of drops flowing in one minute. This principle can be applied if you use a manual or automated controlling device. Whatever you calculate the desired rate to be, adjust your device accordingly.)

Let’s try a variety of problems to get the hang of this formula and increase your confidence dramatically. Remember, here’s our easy formula. Just fill in your ˙blanks.Ó

(Weight in kg) x (dose in mcg/kg/min) x 60 = mL/hr
„„„„„„„„„„„„„„Drug concentration in 1 mL

Calculation #1:You receive an order for dobutamine to run at 2.5 mcg/kg/minute on a 200-lb. patient. You have a 250 mg vial, a 500 cc bag of IV fluid and a microdrip (60 gtt) drip set. How many drops„per minute will you deliver?„

1.200-lb. patient = 90 kg

2.The order is for micrograms, so first you must calculate the milligrams to micrograms: 250 mg = 250,000 micrograms. (Move decimal three spaces to the right, remember?)

3.Then, 250,000 (micrograms) _ 500 (mL bag) = 500 micrograms per mL. (This will become our denominator Ú sound familiar?)

Just plug the numbers into the formula:

(Weight in kg) x (dose in mcg/kg/min) x 60 = mL/hr
„„„„„„„„„„„ Drug concentration in 1 mL

1.90 kg x 2.5 micrograms/kg/min (ordered dose) x 60 (constant) = 13,500

2.Take the 13,500 and divide it by your 500 micrograms per mL = 27 drops per minute.

3.Set your minidrip for 27 drops per minute.

Your patient does well. Congratulations!

Let’s do another problem, without the walk-through of each step.

Calculation #2:Administer dopamine to run at 6 mcg/kg/min on a 172-lb. patient. You have a 400 mg vial of dopamine, your 250 cc bag and a microdrip (60 gtt) drip set.

78 kg x 6 mcg/kg/min x 60 = 17.5 drops per minute
„„„„„„„„„„„„„„ 1,600 (rounded up to 18)

Did you get it right? I know you did! You remembered to convert pounds to kilograms and to convert the 400 milligrams to 400,000 micrograms. Then, you divided the 400,000 (micrograms) by the 250 (mL bag) = 1,600 micrograms in one mL. (This became your denominator.) Way to go!

Now, try this next one.

Calculation #3:Start a lidocaine drip at 3 mg/min. You have 2 g of lidocaine in your drug box, a 500 mL bag of saline and a microdrip (60 gtt) drip set. Set up your problem with the same formula, but this time, keep in mind:„

1.The drug is not weight-based.

2.The drug ordered is in milligrams, not micrograms. Therefore, convert the grams in the denominator to the ordered strength (milligrams).

Did you get it? You remembered to convert your 2 g to 2,000 mg and then divided that by the 500 mL of solution to get 4 mg per mL, right? Good job!„

3 mg/min (ordered) x 60 (given) = 45 drops per min.
„„„„„„„„„„„„„„„„„„„„„„„„„„4 (mg/mL)


Diltiazem (infusion)
Lidocaine (infusion)
Procainamide (infusion)

Epinephrine (infusion)


Additional calculations
Try the following problems on your own. If the drug described in the problem isn’t one you administer in your system, try the problem anyway. It’s good practice and you’ll amaze yourself.

Calculation #4:You have an order to begin a Nipride drip to run at 3 mcg/kg/min. Your patient weighs 276 lbs. and you have a 50 mg vial of Nipride, a 250 mL bag of solution and a microdrip (60 gtt) drip set. At how many drops per minute will you set your minidrip?

Answer: 113 drops per minute

Calculation #5: Begin a dopamine drip at 4 mcg/kg/min. In your drug box is a 5 mL vial of 200 mg of dopamine, a 250 mL bag of normal saline and a microdrip (60 gtt) drip set. How many drops per minute will you give to your 132-lb. patient?

(Note: Don’t let the size of the vial throw you off. The 5 mL was put into the problem as a distraction. You’ll do the right thing if you ignore that and keep to the formula you know.)

Answer: 18 drops per minute

Calculation #6:You are asked to give Nitroprusside 0.7 mcg/kg/min. You have in your drug box Nipride 50 mg/500 mL NS. Your patient weighs 145 lbs. Calculate the drops per minute to give the patient.

Answer: 28 drops per minute

Calculation #7:You’re ordered to give dopamine 2.5 mcg/kg/min to your 182-lb. patient. Your dopamine comes as 400 mg/500 mL D5W.

Answer: 15.5 drops per minute

(Round up to 16 drops per minute)

Calculation #8:Now, use the same problem, but have your dopamine come as 400 mg/250 mL D5W.

Answer: 7.7 drops per minute (round up to 8 per minute)

Calculation #9:You are ordered to mix 2 g of lidocaine in 250 mL NSS to run at 2 mg/minute. What is your flow rate?

Answer: 15 drops per minute

Calculation #10: You’re ordered to give a 200-lb. patient dobutamine at 10 mcg/kg/min. The drug comes in a concentration of 250 mg/250 mL of NSS. How many drops per minute should the patient receive?

Answer: 55 drops per minute

Calculation #11:Medical command orders 100 mg of phenylephrine in 250 mL of NSS. You’re directed to begin at 30 mcg/min. What is your flow rate in drops per minute?

Answer: 4.5 drops per minute

(Round off to 5 drops per min)

You’ve succeeded in mastering this easy formula for calculating what used to be difficult drug orders. Be confident, knowing you can provide expert care in a timely professional and manner, and that no medical orders will perplex you. Additionally, you’ll have the certainty of knowing you can go up against the best of the best in any EMS competition orƒmore importantlyƒany real-life situation.

1. Mikolaj AA.Drug Dosage Calculations for the Emergency Care Provider,„ Upper Saddle River,„N.J.: Prentice Hall Brady; 2003.„

2. Springhouse.Dosage Calculations Made Incredibly Easy,„Philadelphia: Lippincott, Williams & Wilkins; 2004.„

3. Foust SD.Easy 4-Step Method to Drug Calculations: Everything You Need to Know to Calculate Liquid Drug Dosages in the Field,„Upper Saddle River,„N.J.: Pearson Prentice Hall; 2004.„

Joyce Foresman-Capuzzi, RN, BSN, CEN, CPN, CTRN, EMT-P, has been a paramedic and an ED nurse for 23 years and has a background in pediatric nursing. She currently serves as Business Development Representative for the„Temple„Health System Transport Team,„Temple„University Health System in„Philadelphia,„Pa. In addition, she’s a staff nurse for the„Taylor Hospital ED in„Ridley Park,„Penn., and an adjunct faculty member for the„Delaware„County (Penn.) Community College paramedic and nursing programs