# Medical Mathematics for the EMS Provider

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Medical Mathematics for the EMS Provider

Lesson Topics Reviewing metric system Calculating drug formulas
Calculating infusion formulas Calculating drug infusion formulas Practice samples Return to Main Page

Lesson Objectives Review metric system Define desired dose
Define volume to infuse Define total concentration Discuss formulas as a basis for performing drug calculations Understand basic drug formulas In Medical mathematics for EMS providers we will review the metric system including converting patient’s weight from pounds to kilograms. We will define the terms desired dose, volume to infuse and total concentration. We will discuss formulas as a basis for performing drug calculations and solve practice problems. Finally we will work on understanding the basic drug formulas including I.V. infusion formulas. Return to Main Page

Metric System Three fundamental units Grams—Mass Meters—Distance
Liters—Volume The metric system is comprised of three fundamental units. Grams measures mass or weight and most drugs are measured using some form of grams. Meters measures length or distance and we will not be discussing meters. Finally, Liters measure volumes and most fluids are measured with some form of liter. Return to Main Page

Conversion between Prefixes Mass
kilo (kg) 1000 hecto (hg) 100 deka (Dg) 10 gram (g) 1 Base Unit deci (dg) 1/10 or 0.01 centi (cg) 1/100 or 0.001 milli (mg) 1/1000 or micro (mcg) 1/1,000,000 or The metric system is a decimal system that is based on multiples of 10. Multiples larger than the base unit are expressed in multiples of 10, and those smaller than the base units are expressed in decimal fractions that are sub-multiples of 10. Greek prefixes are used to express these multiples and sub-multiples. For example adding the prefix kilo, which means a thousand, to the unit gram can be used to denote 1000 grams. To change between units it is a simple matter of moving the decimal point. Return to Main Page

Conversion between Prefixes Length or Distance
kilo (km) 1000 hecto (hm) 100 deka (Dm) 10 meter (m) 1 Base Unit deci (dm) 1/10 or 0.01 centi (cm) 1/100 or 0.001 milli (mm) 1/1000 or micro (mcm) 1/1,000,000 or Return to Main Page

Conversion between Prefixes Volume
kilo (kL) 1000 hecto (hL) 100 deka (DL) 10 Liter (L) 1 Base Unit deci (dL) 1/10 or 0.01 centi (cL) 1/100 or 0.001 milli (mL) 1/1000 or micro (mcL) 1/1,000,000 or The Liter is actually a nonmetric unit of volume measure but is an approved and preferred unit of volume in the United States and Europe interchangeably with the metric unit of volume which is the cubic meter. Because it is a nonmetric unit it should always be capitalized. Return to Main Page

Conversions To go from grams to milligrams move the decimal point to the right 3 spaces. Convert 2 grams to milligrams 2 Let’s talk about converting between metric units. If I want to convert grams to milligrams all I have to do is move the decimal point to the right 3 spaces. Return to Main Page

3 Conversions Lets convert milliliters to Liters.
3000 mL equals how many Liters? 3 So now lets convert from milliliters to liters. Since we are going up from milliliters we will have to move the decimal point to the left instead of the right. So we move the decimal point 3 places to the left and 3000 mL equals 3 Liters. Return to Main Page

Conversions Converting pounds to kilograms 2.2 lbs = 1 kg
Divide the weight in pounds by 2.2 176 lbs ÷ 2.2 = 80 kg 124 lbs ÷ 2.2 = 56.4 kg 32 lbs ÷ 2.2 = 14.5 kg In the United States when someone asks you for your weight we will always give it in pounds. However, ask someone in any other country and they will probably give you their weight in kilograms. Because some drug calculations are based on the patient’s weight and because drug calculations are based on the metric system we must be able to convert pounds to kilograms. This can easily be done by dividing the amount of weight in pounds by 2.2. In other words 2.2 pounds equals 1 kilogram. Return to Main Page

Desired Dose Specific quantity of medication needed
Most doses expressed as weight: Grams Milligrams Micrograms May be standard or based on body weight Return to Main Page

Dosage and Volume on Hand
The amount of drug available in a solution. Concentration is the weight per volume. Return to Main Page

Administration Sets Macro set = 15 or 10 gtt/mL Microdrip = 60 gtt/mL

Calculating Medication Doses
Volume to be administered = Volume on hand x desired dose Dosage on hand Now lets talk about the basic drug formula. You need to be able to figure out how much of a drug you will give based on orders you receive either from protocols or the doctor. The basic drug formula is volume to be administered equals volume on hand times the desired dose divided by total dosage on hand. Return to Main Page

Example 1 (1 of 2) A doctor orders 2 mg of Valium to be administered I.V. to a patient experiencing seizures. You have a 5 mL vial that contains 10 mg of Valium. How many milliliters will you draw into the syringe to push into the I.V.? Return to Main Page

Example 1 (2 of 2) Set up the problem: Order: 2 mg On hand: 10 mg/5 mL
Remember the drug formula is volume to administered equals desired dose times volume on hand divided by dosage on hand. Our desired dose is 2 mg. Our volume on hand is 5 mL and our dosage on hand is 10 mg. Now this is a very simple algebraic problem. We have plugged our numbers into the formula. We can multiply 2 times 5 which equals 10 and then we divide by 10 which equals 1. Notice that the mgs cancel out leaving us with our answer in mLs. Return to Main Page

Example 2 (1 of 2) You are on scene with a pulseless and apneic patient in ventricular fibrillation. The doctor orders 1 mg of epinephrine I.V. The medication comes supplied as 0.1 mg/mL. How many milliliters will you give? Return to Main Page

Example 2 (2 of 2) Set up the problem. Desired dose: 1 mg

Example 3 (1 of 2) Medical control orders 200 mgs of lidocaine I.V. for your patient in ventricular tachycardia. The prefilled syringe reads “50 mg/mL.” How many milliliters will you administer? Return to Main Page

Example 3 (2 of 2) Set up the problem: Desired dose: 200 mg

Example 4 (1 of 2) A doctor orders you to give 5 mg/kg of Bretyllium for your 176 lb patient who is in ventricular tachycardia. Bretyllium comes supplied as 500 mg/5 mL. Return to Main Page

Example 4 (2 of2) Setting up the problem Desired dose: 5 mg/kg
On hand: 500 mg/5 mL 176 lbs ÷ 2.2 = 80 kg 80 x 5 = 400 Now this problem is just a little different from the other problems. We cannot use 5 mg in our formula so we must first do a couple of things. First we must convert the patient’s weight from pounds to kilograms by dividing the patient’s weight by 2.2. Then we must multiply the patient’s weight in kg times 5 to come up with our desired dose. Return to Main Page

Calculating Infusion Rates
Fluid Volume over Time Drops/minute = Volume to be administered x drip factor Time in minutes Return to Main Page

Example 5 (1 of 2) A doctor orders 200 mL of 0.9% Saline to be administered over 1 hour using a microdrip administration set (60 gtt/mL). How many gtt/min will you run the I.V.? Return to Main Page

Example 5 (2 of 2) Set up problem Desired amount: 200 mL
Administration set: microdrip (60 gtt/mL) Time: 1 hour (60 minutes) So we set up the problem the doctor orders 200 mL to be run over 1 hour using a microdrip administration set which equals 60 gtt/mL. So 200 times 60 divided by 60 equals 200 drops per minute. Return to Main Page

Example 6 (1 of 2) A doctor orders you to run 150 mLs of I.V. fluid over 30 minutes using a macrodrip administration set (10 gtt/mL). How many gtt/minute will you run the I.V.? Return to Main Page

Example 6 (2 of 2) Set up the problem Desired amount: 150 mL
Administration set: macrodrip (10 gtt/mL) Time: 30 minutes So we set up the problem by multiplying 150 mL times the drip factor which is 10 and then divide by 30 minutes giving us 50 drops per minute. Return to Main Page

Calculating Infusion Rates
Medicated Infusions Drops/minute = Volume on hand x drip factor x desired dose Dosage on hand Sometimes we must give certain medications by infusion only. If this is the case there is a variation on the drug formula and we must take into account how we will run the infusion to infuse the proper amount of drug. Return to Main Page

Example 7 (1 of 2) A doctor orders 2 mg per minute of lidocaine to be administered to a patient who was experiencing a dysrhythmia. You have an I.V. that contains 1 gram of lidocaine in 250 mLs. Your administration set is a microdrip set (60 gtt/mL). At how many drops per minute will you adjust your administration set? Return to Main Page

Example 7 (2 of 2) Set up the problem Desired dose: 2 mg/min
On hand: 1 gram in 250 mL Administration set: microdrip (60 gtt/mL) To set up the problem we determine that the doctor orders 2 mg per minute, we have 1 gram in 250 mL and a 60 drop administration set. (Time does not play a factor in this equation). But we have one small problem. In our equation we have mgs on top and grams on the bottom and we need these to equal each other. So how do we convert grams to milligrams? We move the decimal point 3 places to the right so that 1 gram equals 1000 mg. Return to Main Page

Sample Problem 1 A radio order is received from medical control to administer 10 mg of Valium IV push to your patient experiencing seizures; 5 mg/mL is printed on the vial of Valium. How many milliliters will you administer? Return to Main Page

Sample Problem 2 Your patient is exhibiting paroxysmal supraventricular tachycardia (PSVT). Vagal maneuvers are ineffective and medical control orders 6 mg of adenosine rapid IV push. The vial reads 3 mg/mL. How many milliliters will you administer? Return to Main Page

Sample Problem 3 A patient’s ventricular fibrillation is refractory to lidocaine and defibrillation attempts. Medical control orders 400 mg of Bretyllium over 1 minute IV. The prefilled syringe reads 50 mg/mL, 10 mL total volume. How many milliliters will you administer? Return to Main Page

Sample Problem 4 Your 150 lb patient is experiencing multifocal PVCs and complains of chest pain. Your standing orders state to administer 1 mg/kg of lidocaine. The vial reads 100 mg/5 mL. How many milliliters will you administer? Return to Main Page

Sample Problem 5 The doctor orders 400 mg/min of dopamine to be administered IV. You have a vial that contains 200 mg of dopamine in 10 mL (200 mg/10 mL). Your ambulance has 250 mL bags of D5W, and you choose a microdrip administration set (60 gtt/mL). At how many drops per minute will you adjust your administration set to drip? Return to Main Page

Sample Problem 6 You are ordered to administer an Isuprel drip at 4 mg/min. You are ordered to place 1 mg into a 250 mL bag of D5W. At what rate will you set your microdrip (60 gtt/mL) administration set? Return to Main Page

Sample Problem 7 The doctor orders you to start an IV of normal saline to run at 100 mL/hr. You have a microdrip administration set. What is the drip rate? Return to Main Page

Sample Problem 8 Your standing order is to start an IV of normal saline to run at 90 mL/hr. Now you have a macrodrip administration set of 10 gtt/mL. What is the drip rate? Return to Main Page

Sample Problem 9 The order on the patient’s chart in a busy emergency center reads 1500 mL Plasmanate IV over 10 hours. You choose a 15 gtt/mL administration set. What is the drip rate? Return to Main Page

Sample Problem 10 While doing internship hours at the emergency center, you are asked to start an IV of D5W to run at 200 mL/hr. You have a macrodrip set (15 gtt/mL). What is the drip rate? Return to Main Page

This concludes our lesson on medical mathematics for the EMS Provider.