# Durg Calculation

IV and Drug Calculations for Busy Paramedics By Kent R. Spitler, MSEd, RN, NREMT-P EMS Educator Charlotte, North Carolina Introduction Medication calculations can cause frustration for EMS providers. Math and pharmacology can make it difficult to succeed on course exams, in the clinical setting, and in the field. There is a solution to make medication calculations easier. The answer to this problem is simple by showing students how to perform calculations using a simple process.

While there are plenty of good drug and solution textbooks, study guides, and presentations available showing the methods of medication calculations, It seems that it much of it causes mathematical confusion often called “math mental blocks” for many EMS providers. There are only a few drug calculations necessary in the prehospital setting. These calculations include IV drip rates, IV piggyback infusion, IM and Subcutaneous injection. A good review of the metric system is in order here since medicine is based on this measurement system. It is necessary to practice drug calculations on a regular basis to gain a comfort level with the methods.

The best way to achieve this comfort level is to practice medication calculations 30 minutes a day for six months and it will come natural after while. Common abbreviations are used in medication administration for all medical fields. Below is a list of some abbreviations that are found in drug calculations used in the prehospital setting: Gram = Meter = Liter = Gm = Gtts = Hr = IVPB = Mcg = Mass Length Volume Grams Drops Hour Intravenous Piggyback Micrograms 5 cc = 15 cc = 30 cc = 30 cc = 60 mg = 1 Gram = X= x= 1 tsp 1 TBS or 3 tsp 1 ounce 2 TBS 1 Grain 15 Grains Multiply Unknown answer / = Per or Each ? Divide – = Minus gtts/ml = Drops per milliliter gtts/min = Drops per minute Conversion Min = Minute Mg = Milligrams Ml = Milliliters Table 1 Convert grams to milligrams: multiply X 1000 Convert liters to milliliters: multiply X 1000 Convert milligrams to grams: divide by 1000 Convert milliliters to liters: multiply X 1000 Don’t forget where to place the decimal It is assumed that the reader has an understanding of general mathematics. It also assumed that the reader has a general understanding of the metric system as it relates to medicine and drug calculations. IV Drip Rate Calculations IV calculations are easier than they appear.

There are four common drip sets in two categories: minidrip set which includes microdrip or pediatric set, and regular drip set which include macrodrip or adult sets. The various drip sets are as follows: 1 60 gtts/ml 10 gtts/ml 15 gtts/ml 20 gtts/ml minidrip drip set regular drip set regular drip set regular drip set (this set is sometimes used, but it’s not as popular) Next, think about where these numbers came from for use in medicine. Since there are 60 minutes in one hour and 60 seconds in one minute, it appears natural to calculate drip rates based on the clock.

There is one (1) 60 minute period in one hour There are six (6) 10 minute periods in one hour There are four (4) 15 minute periods in one hour There are three (3) 20 minute periods in one hour It makes sense doesn’t it? When calculating IV drip rates all that needs to be done is divide the amount to be infused over one (1) hour by how many time periods the drip set has in one (1) hour based on the clock. 60 gtts/ml set If infusing 60 ml/hr using a 10 gtts/ml set 60 divide 60 by 6 (6 – 10 minute periods) which 50 10 10 gtts/ml set is 10 or 10 gtts/min.

If infusing 60 ml/hr using a 60 gtts/ml set divide 60 by 1 (1 60 minute 45 15 15 gtts/ml set period) which is 60 or 60 If infusing 60 ml/hr gtts/min. using a 15 gtts/ml set divide 60 by 4 (4 – 15 40 minute periods) which 20 20 gtts/ml set is 15 or 15 gtts/min. 30 The calculations are based on the following formula: If infusing 60 ml/hr using a 20 gtts/ml set Amount to be infused X drip set = x gtts/min divide 60 by 3 (3 – 20 Time (in minutes) minute periods) which is 20 or 20 gtts/min. Minidrip (Pediatric or Microdrip) Set – 60 drops per milliliter Figure 1 How do we arrive at the correct answer?

Let’s look at the other methods and see if it makes sense. Think about the 60 drop per milliliter set (60 gtts/ml. ) Now think about the answer you want which drops per minute. A protocol or medical control will give you fluid amounts to administer most 2 commonly in ml/hr. You already have the amount and the time to be infused. All you do now is choose the appropriate drip set, using a simple formula you can come up with a quick answer: Amount of Solution (in ml) X drip set (gtts/ml) = x drops/min (gtts/min)

Looking at an example, your medical control states you need to establish an IV on a cardiac patient complaining of chest pressure at a rate of 80 ml/hr using a 500 ml bag of Normal Saline solution. The drip set you choose is a 60 gtts/ml minidrip set. The formula is as follows: Divide 60 into 4800 80 ml (amount) X 60 gtts/ml (drip set) 60 (divided my time in minutes – over 1 hour) = 4800 60 = 80 gtts/min When calculating IV drip rates remember that you can reduce to the lowest common denominator by dividing the same number into both the numerator and the denominator to make your calculations much easier.

All samples shown from now on demonstrate this throughout. Simply remember that the numbers are consistent with the 60 minute clock and you will catch on rather quickly. The sample problems will show you by dividing the same number into the drip set and the time. As you see the answer is 80 or 80 gtts/min. 60 goes into 60 once (1). Divide 60 into 60 on the top and bottom. Let’s look at the problem again and see how simple it really is: 80 ml X 60 1 gtts/ml set 60 1 min The only thing necessary is to do is cancel out the 60 on the top line and the bottom line. This leaves you with 1. 0 X 1 80 = = 80 or 80 gtts/min 1 1 Thinking this way will make it easier for you any time a 60 gtts/ml drip set is used. Just divide the amount of solution per hour by 1 and the number that is left is your answer in drops per minute. All you need to do is plug in the amount to be given over an hour. REGULAR DRIP SET – 10 DROPS PER MILLILITER Taking a look at the 10 gtts/ml regular drip set we need to think, how many 10 minute periods are in one hour? The answer is 6. (see page 2. ) The objective here is that there are larger drops leading to less drops per minute.

In the problem below, 10 goes into 10 once and 10 goes into 60 six times. Using the same formula as we did with the 60 gtts/ml set the problem is as follows: 80 ml (amount) X 10 gtts/ml (drip set) 80 X 10 1 80 X 1 80 = = 6 = 6 = 13. 3 or 13 60 (divided my time in minutes – over 1 hour) 60 6 80 divided by 6 is 13. 3 or 13 gtts/min. Now to it even simpler, every time you use a 10 gtts/min gtts/ml regular drip set just divide the amount by 6 since they’re six 10 minute time periods in one hour. All you need to do is plug in the amount of fluid per hour. 80 6 = 13. 3 or 13 gtts/min 3

The two remaining regular drip sets are the 15 gtts/ml set and the 20 gtts/ml set. Remember, all you need to do is figure out how many time periods the drip set has in one hour (don’t forget the clock. ) The 15 gtts/ml drip set is related to four 15 minute time periods in one hour which means we divide the amount per hour by 4. 15 goes into 15 once and 15 goes into 60 four times resulting as 80/4 leaving us with the answer of 20. Observe the example below: 80 ml (amount) X 15 gtts/ml (drip set) 80 X 15 1 = 60 4= 60 (divided my time in minutes – over 1 hour) 80 X 1 = 4 80 4 = 20 gtts/min

So any time you use a 15 gtts/ml drip set just divide the amount of solution per hour by 4. 80 6 = 20 gtts/min The 20 gtts/ml drip set is calculated the same way except you divide by 3 since there are three 20 minute periods in one hour. 20 goes into 20 once and 20 goes into 60 three times. Observe the example below: 80 ml (amount) X 20 gtts/ml (drip set) 60 (divided my time in minutes – over 1 hour) = The answer is 26. 6 or rounded off to 27 gtts/minute. This means all you need to do is divide the amount of solution per hour by 3 to get the gtts/min.

Summary • Drip sets used in medicine are based on the 60 minute clock for timing and calculations. All you need to do is divide the amount to be infused each hour by how many time periods the drip set has in one hour which is based on the clock. The drip sets include the minidrip set, 60 gtts/ml, and three regular drip sets which include the 10 gtts/ml set, 15 gtt/ml set, and the 20 gtts/ml set. There is one (1) 60 minute period in one hour, six (6) 10 minute periods in one hour, four (4) 15 minute periods in one hour, and three (3) 20 minute periods in one hour.

When reducing fractions to allow easier calculations remember to divide the same number into both the numerator and the denominator to arrive at the lowest common denominator. Thinking about the problems presented you must divide the same number into the drops per milliliter and the time (in minutes. ) 60 goes into 60 = 1 60 goes into 60 = 1 10 goes into 10 = 1 10 goes into 60 = 6 15 goes into 15 = 1 15 goes into 60 = 4 20 goes into 20 = 1 20 goes into 60 = 3 4 80 X 20 1 80 X 1 = 60 3 = 3 80 3 = 26. 6 • • • Looking at these examples you notice that there is a pattern the stays the same.

Since there are only four (4) different IV drip sets available, all you have to do is just insert the amount of solution to be delivered over one (1) hour. When setting up each problem remember all you have to do is divide the number of periods each drip set has in the 60 minute clock and divide that number into the amount of solution to delivered in one (1) hour. It’s simple as that! Problems You have an order to start an IV of NS How many drops per minute do you want to set the IV drip rate for the following? 1. 150 ml/hr using a 10 drop per milliliter set. 2. 75 ml/hr using a 60 drop per milliliter set 3. 00 ml/hr using a 15 drop per milliliter set 4. 200 ml/hr using a 20 drop per milliliter set IV Infusion/Piggyback Medications Medication administration in field can become complicated in the field when you need an the drug dose in a hurry. The medications we give are usually limited to IV push medications, SL medications, IM and Subcutaneous medications. It seems like paramedic students struggle with drug calculations, but do not get the opportunity to do many calculations in the clinical setting and the skill is limited in the field. The amount of medication to give is usually the answer we want.

Medication comes in ampules, vials, prefilled syringes, and premixed IV bags. Piggyback infusions are given frequently in the field, but when they are there is no room for error. The goal here is to use a simple method of calculating medication drip rates effectively spending the least amount of time doing so. There are two basic issues that we need to think about for piggyback infusions. The first is calculating drip rates for medication in milligrams (mg), e. g. , lidocaine, Procainamide, and Bretylium, which are common medications used in ACLS and in the field.

The second issue is calculating IV infusion rates in micrograms (mcg). Medication dosing may include the patient’s weight as well which needs to be figured into the problem to assure the patient receives the correct amount of medication. There are several methods used in calculating medication doses for IV infusion. We will start with lidocaine as an example because it is one of the most common IV infusions drug in the field. Let’s start with the following information: Lidocaine Drug ordered: Drug on hand: IV Solution: 2 mg/min IVPB 2 Grams Lidocaine 20% in 5 ml (the 5 ml is irrelevant in our calculations) 500 ml of Normal Saline 5

Drug Concentration in the IV Solution: IV Drip Set: Want to Know: 4 mg/ml (this is achieved by dividing the amount of IV solution into the drug. But first you must convert grams to milligrams to properly calculate the problem 60 drops per milliliter Gtts/min to be administered to the patient Using the “Rule of Fours” Method Some think the “rule of fours” method is easier than other methods, but this is up to the EMS provider which method is best. This method is sometimes called the Lidocaine clock method. The three simple steps used here are: Compare, Prepare, and Observe.

Using the information above for our problem we can conclude that there is 4 mg of lidocaine for each milliliter of IV solution (That is by putting 2 grams or 2000 mg of lidocaine into 500 ml of NS and dividing 2000 mg by 500 ml = 4 mg/ml) This means that there is 4 mg = 1 ml which means we will have 4mg for every 60 drops of solution because the drip set is a 60 gtts/ml IV set. The Rule of Fours Method (Lidocaine Clock Method) 4 mg 60 3 mg 45 Gtts/min 15 1 mg 30 2 mg Look at the drug order and compare to the clock in the circle. 2 mg = 30 gtts/min is observed and is the answer to the problem.

There is another method that is popular among people with a chemistry and math education, but anyone can use it. Find out the concentration of medication you have. Remember, the drug order is 2 mg of Lidocaine 20% and a bag of 500 ml Normal Saline. First convert the 2 Gms of Lidocaine into mgs which equals 2000 mg. This needs to be done because the order is in milligrams per minute. 6 We always divide the amount of solution into the amount of drug. Divide 500 ml into 2000 mg Lidocaine 2 Gm = 2000 mg. The answer you get is 4 mg/ml.

The formula is now set up as follows: IV Bag Amount (ml) X dose ordered (mg/min) X drip set (gtts/ml) = Drug on hand (mg) Another method found useful is the following: Drug order (2 mg/min) X IV drip set (60 gtts/ml) = Drug Concentration 4mg/ml X 1 minute Reduce fraction 30 drops per minute 120 4 = 30 gtts/min You can use these methods with any drugs in the field when giving drugs in milligrams, such as. Bretyllium and Procainamide.. IV infusion drugs in Micrograms Now we need to consider drugs given in micrograms. This group of drugs includes dopamine, epinephrine, dobutamine, and Isoproterenol.

When calculating a drug, such as dopamine, using the micrograms can be a little tricky, but remember it’s just a way to measure medicine in smaller amounts (units. ) What this really means is dopamine is potent stuff and we need to keep the math as simple as possible (you know, the KISS method) Dopamine and other complicated Medications can be challenging to calculate, but there is a simple formula method that will make it easier for you. The first formula will include the patient’s weight. Of course, it is assumed you already know how to convert pounds (lbs. to kilograms (kgs. ) But if you are not sure let’s review. All you need to know is that 2. 2 lbs. = 1 kg. And 1 kg. = 2. 2 lbs. This means if you want to convert pounds to kilograms just divide the weight (in lbs. ) by 2. 2. Now to convert kilograms to pounds just multiply the weight (in kgs) X 2. 2. Look at the example below: A 50 year old cardiac patient weighs 150 pounds. You need to convert this patients weight to kilograms because medication based on weight is almost always given in kilograms. 150 divided by 2. 2: it should look like this: Note:

Remember to move the decimal to the right (we don’t want to deal with decimals any more than we have to) When you move the decimal 22. 1500. 150 or 2. 2 150. 2. 2 The answer is: 68. 1 or 68 kgs. (rounded off) to the right you must also move it the same amount of spaces to the right in the for the number you are dividing. We’ll set up a dopamine drip based on the patient’s weight (most IV infusion drugs are based on the patient’s weight. ) This is probably as hard as it’s going to get for EMS providers. Take a look and see if you find this fairly easy: Dopamine 7

Information Drug order – Concentration on hand Drip Set Time Patient’s Weight IV Bag – 7 mcg/kg/min 800 mg (it may come in a premixed IV bag or in 200 mg vials) We know this has to be converted to mcg because that’s the drug order, right? 60 gtts/ml We already know it’s per minute 220 lbs. 500 ml Normal Saline First convert the patients weight from lbs. to kilograms: Divide 220 by 2. 2 = 100 kgs. Second convert the concentration on hand, 800 mg to micrograms. How do we do that? Multiply 800 X 1000 (review your metric conversions if you don’t understand. ) The answer is 800,00 mcg. Remember, to convert mg to mcg just multiply X 1000.

Anyway we don’t want to messing with decimals when we don’t have to. 800 mg X 1000 = 800,000 mcg Third, all you have to know now is how many mcg are in each ml of the IV bag we are using (500 ml. ) Divide the solution into the drug to find out: 1600 mcg/ml This is you concentration on hand 500 ml 800,000 mcg Fourth, set up the formula (this is probably the easiest way to do it without using a drug chart): Mcg/kg X weight (kg) X drip set = Gtts/min Concentration on hand X time With the numbers now: 7 mcg/kg X 100 kgs X 60 gtts/ml 1600 mcg/ml X 1 min = 7 X 100 = 700 1600 X 1 = 1600 700 X 60 = 4200 oncentration on hand 4200 1600 = 26 gtts/min actually the answer is 26. 2 but we rounded it off It may not seem easy at first, but remember all you have to do is plug in the right numbers and the simple math. That’s all! Practice – Practice – Practice IVP, IM, SQ Parenteral Medication Calculation The key to finding the answer for the right dose is organizing the right information. Doing well in drug calculations is practice-practice-practice. Earlier, we mentioned to practice 30 minutes each day for six months and you will remember how to do it. When calculating parenteral medication doses there are only three things to remember, drug order, concentration on hand, and the amount you want to give. Using Lasix, for example: Drug order: Concentration on hand: Volume of solution Amount you want to give: 40 mg 100 mg 10 ml X is the answer you want in ml. Two methods easy to use (you decide which one) for calculating drug doses are ratio and proportion (also known as cross multiplication) method and the formula method. Both methods require setting up the problem and the rest is fairly easy.

Want you want to do is keep it simple (you know , the KISS method) so let’s look at the ratio and proportion method first. What needs to be done is put the same form of measurement on the top lines and the bottom lines. Drug ordered (mg) Amount to give (ml) = Concentration on hand (mg) Volume of solution (ml As you can see we put the mg on the top and the ml on the bottom. It is better to do it this way to keep things straight. Once you set up the formula it necessary to cross multiply to arrive at the correct answer.

Using our example, Lasix, we will set up the problem now with the information provided above: Drug ordered Concentration on hand 40 mg X ml This the answer we want = 100 mg 10 ml Volume of solution X = amount to give in ml Next, cross multiply the numbers as shown below: 40 mg X ml Now it will look like this: = 100 mg 10 ml 40 x 10 = 400 100 x X = 100 X 400 = 100 X Since X is the answer we want, which is the amount of drug to give, X needs to be by itself. The way to do this is move the number with the X underneath the number on the other side.

This is how it looks: 400 = 100X 400 X 100 100 = To arrive at the correct answer, all we need to do is divide 400 by 100 which equals 4. This means X = 4 or 4 ml. The only left to do is draw up the drug into a syringe and give the Lasix to the patient. Tips: 9 • • • • • Set the ratio and proportion the same each time. Put like measurements on the same line mg = mg ml ml Use X as the symbol for the answer you want Always move the number with X underneath the other side leaving X by itself Divide leaving you the answer which is the amount to give in ml

The formula method takes a different approach which some practitioners like. It is set up like this: Volume to be given = (X ml) We will use Lasix again: Drug order: Concentration on hand: Volume of solution Amount you want to give: Volume of Solution Volume of solution X Drug order Concentration on hand 40 mg 100 mg 10 ml X is the answer you want in ml. Drug Order Volume to be given = 10 ml X 40 mg X ml 100 mg Concentration on hand As you can see, we need to multiply 10 X 40 and divide the answer by 100. It will look like this: 10 ml X 40 mg = 100 mg 400 = 4 100

X ml is the amount we want to give so just replace x with 4 and we have our answer of 4 ml. Both the ratio and proportion method and the formula method can be used with tablets, IV push, IM, and SQ medication administration. Now isn’t that simple? If you are having trouble it is a good idea to read back through the material and work through the practice problems. Remember, practice-practicepractice! © Kent Spitler 2000 It is the intention of the author to share this information with EMS educators and providers alike. It may be distributed for educational purposes only at no cost. 10