Med Math 101: The Basics Everyone Should Know
The Units of Measurement
In the EMS setting, we worry about three metric units of measurement…
Attached to these units of measurement will be one of the following…
Now let’s combine the two…
Metric System Practice Problems
Tip: If you’re going from a smaller unit to a larger unit, move the decimal point to the left.
Tip: If you’re going from a larger unit to a smaller unit, move the decimal point to the right.
1) Grams to Milligrams (move the decimal 3 points to the right)
2) Kilograms to Grams (move the decimal 3 points to the right)
1kg ———- 1,000g ———- 1,000,000mg ———- 1,000,000,000 mcg
Converting Pounds to Kilograms
As a paramedic, you will be required to quickly convert a patient’s weight in pounds to kilograms. As you are well aware by now, this is done for any medication that has weight-based dosing. When the pressure is on, you will need a fast and easy-to-remember way to do your conversions.
Converting Kilograms to Pounds
Occasionally, you may need to convert kilograms to pounds. Here is a quick and easy way to do so:
Medication Concentrations & Bolus Doses
Glossary of Terms
While most of these terms are self-explanatory, let’s define them so there is no confusion.
Medication Concentrations
Fortunately for EMS professionals, most of our medication concentrations are expressed as a unit of weight per volume. Usually, you will see this expressed on a medication as either g/ml, mg/ml or mcg/ml. You can find this number on the medication box or vial.
So let’s put this all together…
Concentration (mg/ml) = Total Drug / Total Volume
Fill in the numbers we see on Furosemide (Lasix)
Furosemide Concentration = 40mg / 10 ml = 4mg/ml
Sometimes concentrations are expressed as a percentage (Dextrose 50%, Lidocaine 2%). There is a very simple way to solve this so don’t make this too complicated! Let’s look at Lidocaine 2%.
2g / 100mL = 2000mg / 100mL = 20mg/mL
(This is the concentration seen on a prehospital Lidocaine vial)
Feel like trying Dextrose 50%? Ok, lets do it.
50g / 100mL = 50000mg / 100mL = 500mg / 1mL = 0.5g/mL
(This is the concentration seen on a D50% box)
Bolus Medications
When you administer a bolus of a medication, you are giving a specific amount all at once. This is different from a drip, where a certain amount of drug is administered slowly over a period of time. Paramedics usually administer medication by bolus instead of drip. Every medication has a solute and a solution, leading to a concentration. It is up to you as a paramedic to determine how much you need to administer to deliver the correct amount of medication to your patient.
Depending on the information you have, you can use one of two equations to calculate how many mL of a drug you will need to administer:
X (mL to be given) = (Total Volume x Desired Dose) / Total Amount of Drug
X (mL to be given) = Desired Dose / Concentration
Volume (mL to be given): X
Total Amount of Drug: 25mg
Total Volume: 5mL
Desired Dose: 15mg
X (mL to be given) = (Total Volume x Desired Dose) / Total Amount of Drug
X (mL to be given) = (5mL x 15mg) / 25mg
X (mL to be given) = 75mL / 25 (mg cancels out)
X (mL to be given) = 3mL
Your patient in cardiac arrest requires 300mg of Amiodarone per 2010 ACLS guidelines. The Amiodarone is supplied in a pre-filled syringe that contains 450mg in 3mL. How many mL will you need to draw up?
Volume (mL to be given): X
Concentration: 450mg / 3mL = 150mg/mL
Desired Dose: 15mg
X (mL to be given) = Desired Dose / Concentration
Fill in known information to equation:
X (mL to be given) = 300mg / (150mg/mL) (mg cancels out)
X (mL to be given) = 2mL
Medication administration: Drip Sets
IV Drip Components:
Note: The abbreviation for drip rate is drips/minute, or gtt/min.
IV Drip Formulas
There are two formulas that can be used when calculating drip rates. One formula is the general formula for calculating drip rates and the other is used for calculating specific amounts of fluid administration over time.
General formula: a certain amount of drug (with a specified concentration) to be given at a desired dose
X = (Desired Dose x Drip Set) / Drug Concentration
X: calculated drip rate, expressed in drips/minute (gtt/min)
Desired Dose: total amount of drug needing to be administered, usually defined as a rate (ex. 450mcg/min)
Drip Set: number of drips required to produce one mL of solution (ex. 60gtt/mL)
Drug Concentration: amount of drug in vial/bag (ex. 400mg/250mL)
Fluid administration formula: administration of a specified volume of solution given over time
X = (Total Volume x Drip Set) / Total Time
X: calculated drip rate, expressed in drips/minute (gtt/min)
Total Volume: total amount of volume needing to be administered (ex. 10 Liters of NS)
Drip Set: number of drips required to produce one mL of solution (ex. 15gtt/mL)
Total Time: total amount of time that fluid needs to be administered over (ex. 8 hours)
You are preparing to administer a nitroglycerin drip for your patient. You need to administer 40mcg/min of Nitroglycerin. If you are using a 60-drop/mL drip set, what should your flow rate be (gtt/min)?
Desired Dose: 40mcg/minute
Drip Set: 60-drop/mL
Drug Concentration: 200mcg/mL
Calculated drip rate: X
X = (Desired Dose x Drip Set) / Drug Concentration
Fill in known information to equation:
X (calculated drip rate) = (40mcg/minute x 60-drop/mL) / 200mcg/mL
X = 2400 (mcg & mL cancel out) / 200
X = 2400 / 200 = 12 gtt/minute
You are preparing to administer an Epinephrine drip for your patient. You need to administer 2mcg/min of Epinephrine. If you are using a 60-drop/mL drip set, what should your flow rate be (gtt/min)?
Desired Dose: 2mcg/minute
Drip Set: 60-drop/mL
Drug Concentration: 1mg/250mL (1000mcg/250mL = 4mcg/mL)
Calculated drip rate: X
X = (Desired Dose X Drip Set) / Drug Concentration
Fill in known information to equation:
X (calculated drip rate) = (2mcg/minute x 60-drop/mL) / 4mcg/mL
X = 120 (mcg & mL cancel out) / 4
X = 120 / 4 = 30 gtt/minute
You have been ordered to administer 1L of Normal Saline during your 1-hour transfer. If you are using a 15-drop/mL drip set, what should your flow rate be (gtt/min)?
Total Volume (mL to be given): 1000mL
Drip Set: 15-drop/mL
Total Time: 60 minutes
Calculated drip rate: X
X = (Total Volume x Drip Set) / Total Time
Fill in known information to equation:
X (calculated drip rate) = (1000mL x 15 drop/mL) / 60 minutes
X = 15000 drops (mL cancels out) / 60 min
X = 15000 drops / 60 minutes = 250 gtt/minute
Using the Parkland formula, you have calculated that you need to give 10L of Normal Saline to your patient over 8 hours. If you are using a 15-drop/mL drip set, what should your flow rate be (gtt/min)?
Total Volume (mL to be given): 10000mL
Drip Set: 15-drop/mL
Total Time: 8 hours
Calculated drip rate: X
X = (Total Volume x Drip Set) / Total Time
Fill in known information to equation:
X (calculated drip rate) = (10000 mL x 15 drop/mL) / 8 hours
X = 150000 drops (mL cancels out) / 480 minutes
X = 150000 drops / 480 minutes = 312.5 gtt/minute
Dopamine:
Your medical kit only has a 250mL bag of Normal Saline in it. How much Dopamine do you need to inject into the bag to achieve the desired concentration of 1600mcg/mL?
Total Volume (mL of solution to be mixed with): 250mL
Desired dose: 1600mcg/mL
X: amount of Dopamine to be injected (mg)
(1600mcg/1mL) = (X/Total volume)
Fill in known information to equation and cross multiply. Then solve for X: 1600mcg / 1mL = X / 250 mL
X = 1600 x 250 (mL cancels out)
X = 400000mcg = 400mg
You should inject 400mg of Dopamine into the 250mL bag of Normal Saline to achieve the desired concentration of 1600mcg/mL.
There are two ways to calculate a Dopamine drip rate:
1. Use the drip rate formula and performing the mathematical operations to find the exact drip rate.
X = (Desired Dose x Drip Set) / Drug Concentration
2. Use the Dopamine clock to quickly obtain a relatively accurate drip rate.
Calculating a Dopamine Drip… Using the Drip Rate Formula
Desired Dose: 10mcg/kg/minute
Drip Set: 60-drop/mL
Drug Concentration: 400mg/250mL (1600mcg/mL)
Calculated drip rate: X
X = (Desired Dose x Drip Set) / Drug Concentration
Fill in known information to equation:
Desired dose = 10mcg/kg/minute X 100kg = 1000mcg/min
X (calculated drip rate) = (1000mcg/minute X 60-drop/mL) / 1600mcg/mL
X = 60000 (mcg & mL cancel out) / 1600
X = 60000 / 1600 = 37.5 gtt/minute
Calculating a Dopamine Drip… Using the Dopamine Clock
Using the same problem and the same numbers, let’s calculate this dopamine drip using the Dopamine Clock.
In order for the math to work properly, you need to ensure that the concentration of Dopamine you are using is 1600 mcg/mL (or you have adjusted your math to account for a different concentration) and you need to be using a 60-drop/mL drip set.
Here is what we know:
Desired Dose: 10mcg/kg/minute
Patient Weight (in Kg): 100 kg
The Dopamine Clock is dosed as mcg/min so we need to get our math to show mcg/min. We can do this by multiplying the mcg/kg/minute dose by the patient’s weight (in Kg):
10mcg/kg/minute x 100kg = 1000mcg/minute (kg cancels out)
Now, locate on the clock approximately where 1000mcg/min would be. Then approximate how many drops/minute are required to achieve this dose.
For example, a dose of 1000mcg/min would require approximately 38 gtt/minute.
Lidocaine:
Lidocaine = 4mg/mL
Your medical kit only has a 1000mL bag of Normal Saline in it. How much Lidocaine do you need to inject in to the bag to achieve the desired concentration of 4mg/mL?
Total Volume (mL of solution to be mixed with): 1000mL
Desired dose: 4mg/mL
X: amount of Lidocaine to be injected (mg)
(4mg/1mL) = (X/Total Volume)
Fill in known information to equation and cross multiply. Then solve for X:
4mg / 1mL = X / 1000mL
X = 4 x 1000 (mL cancels out)
X = 4000mg
You should inject 400omg of Lidocaine into the 1000mL bag of Normal Saline to achieve the desired concentration of 4mg/mL.
There are two ways to calculate a Lidocaine drip rate:
1. Use the drip rate formula and perform the mathematical operations to find the exact drip rate.
X = (Desired Dose x Drip Set) / Drug Concentration
2. Use the Lidocaine clock to quickly obtain a relatively accurate drip rate.
Calculating a Lidocaine Drip… Using the Drip Rate Formula
Your cardiac arrest patient has experienced return of spontaneous circulation. Protocol indicates you should start a Lidocaine drip at 2mg/minute. You have 2000mg of Lidocaine in 500mL of Normal Saline and are using a 60-dropmL drip set. What should your flow rate be (gtt/min)?
Desired Dose: 1.5mg/minute
Drip Set: 60-drop/mL
Drug Concentration: 2000mg/500mL (4mg/mL)
Calculated drip rate: X
X = (Desired Dose x Drip Set) / Drug Concentration
Fill in known information to equation:
X (calculated drip rate) = (1.5mg/minute x 60-drop/mL) / 4mg/mL
X = 90 (mg & mL cancel out) / 4
X = 90 / 4 = 22.5 gtt/minute
Calculating a Lidocaine Drip… Using the Lidocaine Clock
Using the same problem and the same numbers, let’s calculate this Lidocaine drip using the Lidocaine Clock.
In order for the math to work properly, you need to ensure that the concentration of Lidocaine you are using is 4 mg/mL (or you have adjusted your math to account for a different concentration) and you need to be using a 60-drop/mL drip set.
Here is what we know:
Desired Dose: 1.5 mg/minute
Now locate on the clock approximately where 1.5mg/minute would be. Then approximate how many drops/minute are required to achieve this dose.
For example, a dose of 2mg/min would require approximately 23 gtt/minute.
Med Math 101: Practice Problems
Below are a series of practice problems meant to increase your proficiency and test your understanding of what you have just learned.
Metric System
Pounds to Kilograms
Kilograms to Pounds
Medication Concentrations
Bolus Medications
IV Drips (answer in gtt/minute)
Fluid Administration (answer in gtt/minute)
Dopamine Drips (answer in gtt/minute)
Lidocaine Drips (answer in gtt/minute)
Dopamine Clock (answer in gtt/minute – draw line on clock)
2. Administer 12mcg/kg/minute Dopamine (concentration of 1600mcg/mL) using a 60-drop/mL drip set. Your patient weighs 150 kg.
3. Administer 20mcg/kg/minute Dopamine (concentration of 0.8g/500mL) using a 60-drop/mL drip set. Your patient weighs 68 kg.
Lidocaine Clock (answer in gtt/minute – draw line on clock)
2. Administer 1.75mg/minute Lidocaine (concentration of 4mg/mL) using a 60-drop/mL drip set.
3. Administer 4.5mg/minute Lidocaine (concentration of 4mg/mL) using a 60-drop/mL drip set.
Med Math 101: Practice Problems
ANSWERS
Metric System
Pounds to Kilograms
Kilograms to Pounds
Medication Concentrations
Bolus Medications
IV Drips
Fluid Administration
Dopamine Drips
Lidocaine Drips
Dopamine Clock
Lidocaine Clock
2. 75mg/minute (a little less than half of the concentration so a little less than halfway around the clock)
3. 4.5mg/minute (just a little more than the concentration so just a little more than one whole time around the clock)
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