Dose Calculations
Advanced Care Paramedicine
Module: 6
Session: 4
Systems of Measure
 Three common systems still used
today
 Each deals with units of mass and
volume
 Metric
 Apothecary
 Household
Metric System
 Most commonly used
 Considered the most convenient since
based on units of 10
 Basic units are
 Meter
 Liter
 Gram
Length
Volume
(Weight) Mass
Metric System
Length
Volume
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1 kilometer (km) = 1000 meters
1 hectometer = 100 meters
1 decameter = 10 meters
Meter
1 decimeter = 1/10 meter
1 centimeter (cm)= 1/100 meter
1 millimeter (mm) = 1/1000 meter
1 kiloliter = 1000 liters
1 hectoliter = 100 liters
1 decaliter = 10 liters
Liter (L)
1 deciliter = 1/10 liter
1 centiliter = 1/100 liter
1 milliliter (ml) = 1/1000 liter
Weight
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1 kilogram (kg) = 1000 grams
1 hectogram = 100 grams
1 decagram = 10 grams
Gram
1 decigram = 1/10 gram
1 centigram = 1/100 gram
1 milligram (mg) = 1/1000 gram
1 Gram = 1 ml = 1 cc
1 Kg = 1000 g = 2.2 lbs
1 mcg (μg) = one-millionth
of a gram (0.000001 g)
Apothecary System
 Old system of measurement
 Considered to be less precise and convenient
 Basic units are
 Minim
 Grain
Volume
(Weight) Mass
 Written prescriptions place abbreviations before a
roman numeral (gr V = 5 grains)
 ¼ of a grain would be written as gr ¼ not 0.25 gr
1 Grain (gr) = 60 – 65 mg
1 dram = 60 gr
8 dr = 1 oz
16 oz = 1 lb
Household System
 Approximate system of measurement
 Basic units are
 Weight
 Volume
ounces, pounds
glass, cup, tablespoon, drop,
quart, pint and gallon
1 t = 4 – 5 ml
1 T = 15 – 16 ml
1 pt = 500 ml
1 qt = 1000 ml = 2 pt
1 in = 2.54 cm
Dose calculations
 As a paramedic you will have to calculate
drug doses, infusion rates and strengths of
drugs in the field.
 Remember:
 All units of measure must be converted to the
same unit and system
 The computed dose must be assessed to
determine if it is reasonable
 Use the same method of calculation every time
Concentrations
 Refers to the strength of the drug (how
many of one thing is present in something
else)
 10 mg of drug in 1 ml of solution
 Accomplished by dividing the weight of the
drug by the volume of fluid it is in
Weight =
Volume
10 mg =
1 ml
10 mg/ml
Concentrations
 Some drugs are labeled as a percentage
 Refers to # of grams in 100 ml of solution
 1% Lidocaine
 10% MgSO4
 D 5W
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1 g of Lidocaine in 100 ml
10 g of MgSO4 in 100 ml
5% Dextrose in water
5 g of dextrose in 100 ml of Water
 A 10 ml of 10% MgSO4 has 1 g of drug per 10 ml (or 100
mg/ml)
10% MgSO4
=
10 g MgSO4
100 ml
=
10000 mg
100 ml
= 100 mg/ml
Calculations
 Three common types
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Basic Formula (Most common)
Dimensional analysis
Ratios and proportions
May also see the ‘T’ method
Dimensional Analysis
 Sets up all conversion factors in one
equation and separated by ‘X’
 To solve calculation:
 Set up the equation
 Cancel pairs of units of
numerator/denominator
 Multiply the numerators
 Multiply the denominators
 Divide the numerator by the denominator
Dimensional Analysis
 Example 1:
 You are to administer fentanyl 50 mg IM.
You have 75 mg of the drug in a 1 ml
solution. How many ml will you give?
ml = 1 ml X 50 mg = 50 ml = 2 ml = 0.66 ml
75
3
75 mg
1
Dimensional Analysis
 Example 2:
 You are to administer 5 mg IV of valium.
You have 10 mg of the drug in a 1 ml
solution. How many ml will you give?
ml = 1 ml X 5 mg = 5 ml = 1 ml = 0.5 ml
10
2
10 mg
1
Ratio and Proportions
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Compares two numbers and works like a fraction
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Example:
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Administer morphine 3 mg IV. You have 10 mg in 1 ml of
solution. How many ml will you give?
Means
10 mg : 1 ml :: 3 mg : x ml
Extremes
 Therefore
10x = 3
x = 3/10
x = 0.3 ml
Basic Formula
Dose = Want (D) X Volume (V)
Have (H)
 D = “desired dose” = Want
 H = “concentration of the drug” = Have
 V = “volume the drug is supplied in” = Volume
Calculation #1
 The adult patient with nausea has no allergy to
Dimenhydrinate. The appropriate dose is 20 mg.
How many milliliters will be administered?
 D = 20 mg
 How is Gravol supplied?
 50 mg in a 5 ml vial
 H = 50 mg
 V = 5 ml
Calculation #1
Dose = D X V
H
= 20 mg X 5 ml
50 mg
= 100 ml
50
= 2 ml
 What is a side
effect of Gravol?
 Burning within the
vein
 How can it be
diminished?
 Dilute with saline
prior to
administration
Calculation #2
 An average size adult patient is actively
seizing. The appropriate dose for diazepam
is 2.5 mg to 5.0 mg IVP.
 How is valium supplied?
 10 mg in 2 ml
 Calculate the administration for the smallest
dose
Calculation #2
Dose = D X V
H
= 2.5 mgX 2 ml
10 mg
= 5 ml
10
= 0.5 ml
Calculation #3
 With the same patient, calculate the
administration for the largest dose (5.0
mg)
Calculation #3
Dose = D X V
H
= 5 mg X 2 ml
10 mg
= 10 ml
10
= 1.0 ml
 Why can valium
not be diluted with
saline?
 Is oil based
 What would
happen if it was
diluted in saline?
 Seizure Salad
Dressing
Calculation #4
 A 28 y/o male has a fracture to the left
tib/fib. His pain is 10/10. The appropriate
dose for morphine sulfate is 2.5 – 5 mg.
 How is morphine supplied?
 10 mg in 1.0 ml
 Calculate the administration for the smallest
dose
Calculation #4
Dose = D X V
H
= 2.5 mgX 1 ml
10 mg
= 2.5 ml
10
= 0.25 ml
Calculation #5
 With the same patient, calculate the
administration for the largest dose (5.0
mg)
Calculation #5
Dose = D X V
H
= 5 mg X 1 ml
10 mg
= 5 ml
10
= 0.5 ml
 How can an ACP
administer morphine
more accurately and
safely?
 Dilute 10 mg in 9 ml of
saline in a 10 cc
syringe
 What is the
concentration of the
drug now?
 1 mg/ml
Calculation #5
Dose = D X V
H
= 5 mg X 1 ml
10 mg
= 5 ml
10
= 0.5 ml
 What are 3
potential side
effects of
morphine?
 Nausea,
hypotension,
respiratory
depression
 How can we treat
these effects?
Calculation #6
 A 70 y/o female is in extremis due to dyspnea
preceded by two weeks of general malaise. She is
lethargic, warm to the touch, diaphoretic, and has
an Sa O2 of 80% on 100% O2. You decide to
intubate. The appropriate dose for Versed is 2.0 –
5.0 mg.
 How is Versed supplied?
 10 mg in 2 ml
 Calculate the administration for the 2.0 mg dose
Calculation #6
Dose = D X V
H
= 2.0 mgX 2 ml
10 mg
= 4.0 ml
10
= 0.4 ml
Calculation #7
 With the same patient, calculate the
administration for the largest dose (5.0
mg)
Calculation #7
Dose = D X V
H
= 5 mg X 2 ml
10 mg
= 10 ml
10
= 1 ml
Calculation #8
 A 70 y/o male is c/o dyspnea. He has a PHx of
CHF and on exam has rales in all lungs fields.
 He is on Furosemide 40 mg PO but has not had
any in two days since his prescription ran out and
has not been refilled.
 What is the most appropriate method of determining
how much lasix the patient should receive?
 Contact OLMC
 How is Lasix supplied?
 40 mg in 4 ml
 Calculate the administration for the 40 mg dose
Calculation #8
Dose = D X V
H
= 40 mg X 4 ml
40 mg
160 ml
=
40
= 4 ml
Calculation #9
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You are called for a 24 y/o female, third trimester, who
presents with grand mal seizures. Her husband states she
has been bedridden with HTN X 3 weeks and denies any
other PHx, medications or drug use.
The protocol for seizures with eclampsia states 1 g of
magnesium sulfate
How is MgSO4 supplied?
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5 g in 10 ml
Calculate the administration dose
Calculation #9
Dose = D X V
H
= 1 g X 10 ml
5g
= 10 ml
5
= 2 ml
Calculation #10
 The pt is a 49 y/o female who presents with
dyspnea, tachycardia and pallor.
 She is normotensive, has Sa O2 of 98% on RA and
a regular, narrow complex tachycardia on the
monitor with a rate of 178.
 Protocol states that Adenosine is the appropriate
medication with a starting dose of 6.0 mg.
 How is Adenosine supplied?
 6 mg in 5 ml
 Calculate the administration dose
Calculation #10
Dose = D X V
H
= 6 mg X 5 ml
6 mg
= 30 ml
6
= 5 ml
Calculation #11
 Your pt is a 55 y/o male c/o weakness. O/E
the pt is pale, diaphoretic and has a slow
regular pulse at 40 with a BP of 90/60. The
ECG shows a sinus bradycardia with no
ectopics.
 Atropine is indicated. The dose is 0.5 mg
 How is Atropine supplied?
 1 mg in 10 ml
 Calculate the administration dose
Calculation #11
Dose = D X V
H
= 0.5 mg X 10 ml
1.0 mg
= 5 ml
1
= 5 ml
Calculation #12
 You are called to the home of an 18 y/o female who
has been stung by a bee. She has a known allergy.
She was unable to self administer her epi pen due
to device malfunction.
 Your standing orders are for 0.3 mg SQ of 1:1,000
solution.
 How is Epinephrine 1:1,000 supplied?
 1 mg in 1 ml
 Calculate the administration dose
Calculation #12
Dose = D X V
H
= 0.3 mg X 1 ml
1.0 mg
= 0.3 ml
1
= 0.3 ml
Weight Specific Dosing
 Some medications require a Dose based on
the patients weight. (Typically in kilograms)
 May be a bolus or an infusion
 1.5 mg/kg of Lidocaine bolus in an arrest
protocol
 5 μg/kg/min of Dopamine
 To calculate the dose multiply the dose in
units (g, mg, μg) by the pt’s weight in kg.
Calculation #13
 The pt is a 60 y/o female who presents
unresponsive falling a fall down a flight of stairs.
She has snoring respirations, purposeful
movements of her arms, and an obvious deformity
to her left parietal region. You decide to sedate and
intubate the pt. Following the administration of
Versed, prior to intubating you are to administer
Lidocaine. She weighs approximately 110 lbs.
 How is Lidocaine supplied?
 100 mg in 5 ml
 Calculate the administration dose
Calculation #13
 First convert the weight of this patient
Weight = 110 lb = 50 kg
2.2 kg/lb
 Then calculate the desired dose
Desired Dose = 50 kg X 1.5 mg/kg = 75 mg
Calculation #13
Dose = D X V
H
= 75 mg X 5 ml
100 mg
= 375 ml
100
= 3.75 ml
Calculation #14
 The pt is a 40 y/o, 220 lb male. He is 1
week post operative bowel surgery, released
from hospital 3/7 ago, responsive but
lethargic
 His Sa O2 is 95% on RA, HR 124 Reg and
Weak, BP 70/40.
 Your interventions are 100% O2 and a 1 L
bolus of NaCl and has not shown a
hemodynamic change. The protocol states
5 μg/kg/min infusion of dopamine.
Calculation #14
 What do we need to know?
 How is dopamine supplied?

800 mg in 500 ml of D5W
 Weight of pt in kg
220 lb
100 kg
=
=
2.2 kg/lb
 How much dopamine is to be delivered per minute
Weight
Desired Dose = 100 kg X 5 μg/kg/min =
500 μg/min
 Concentration of dopamine per gtt
800 mg
= 1. 6 mg/ml = 1600 μg/ml
500 ml
 How many gtts per minute (will do this next module)
Concentration =
Practical Session
 Using the ‘D’ Kit. Identify all the
medications found within it and
document the following:
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Name
Concentration
Indications
Contraindications
Dosing parameters
Appropriate calculation of dose
To continue…
 We will continue calculations next
month during the IV session of the
program.