# Dosage Dosage Calculations Ratio

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```					2.2 Dosage Calculations

Ratio Problems

Eg)     A hospital employs 126 nurses and 27 doctors. What is the ratio of doctors to nurses?

doctors     27   9
=   9 : 42
nurses     126 42

Eg)     To treat water 4 mL of a 2% tincture of iodine was added to 12 L of water. What is the
ratio of iodine tincture to water?

iodine    4mL      4       4     1
=         =     =     1 part tincture : 3000 parts water
water     12 L 12 × 1000 12000 3000

a tincture is an alcoholic extract (e.g. of a herb) or solution of a nonvolatile substance (e.g. of
iodine, mercurochrome.) Solutions of volatile substances were called spirits

A volatile substance is a compound that gives off vapors or fumes at room temperature.
Volatile substances are also commonly known as solvents or inhalants. They include: butane
gas, aerosol sprays, petrol, glue, correction fluids and paint thinners.

Proportion Problems

Eg) A technician at a nuclear power plant is exposed to a radiation field of 300
millirems/hour. Estimate his exposure after 15 minutes.

300 x
=
60 15
300 × 15
x=          = 75millirems
60

The millirem is a unit of absorbed radiation dose.
A person would get this amount of radiation from

•   Three days of living in Atlanta
•   Two days of living in Denver
•   About seven hours in some spots in the Espirito Santo State of Brazil.

10009 22Dosage W09                              1                                   2/16/2009
Eg)   Solve for x
45 mg : 10 mL = x mg : 35 mL

45 x
=
10 35
45 × 35
x=         = 157.5mL
10

Eg)   A copper sulphate solution is diluted with water at a ratio of 2:5 ( Cu2SO4 to water ).
How much of the Cu2SO4 solution needs to be mixed with 500 mL of water?

Cu 2SO 4   2mL   x
=
water    5mL 500
1000
x=       = 200mL
5
200mL of Cu2SO4 solution is required.

Eg)   Has the toxic level of I2 been reached if a 70 kg person ingests 3 g of I2 . Assuming
the toxicity for iodine for humans is 28 mg/kg.

28mg    x
=        x = 70 × 28 = 1960mg
1kg   70
1g
1960mg = 1960mg ×          = 1.96 g
1000mg

The person has taken a toxic dose of I2

Eg)   An IV medication of 450mL is to infuse at the rate of 80 mL/h.. What is the total
infusion time?

80mL 450mL
=
1h       x
450 ×1
x=        = 5, 625h
80

Homework course booklet pg 9 1 - 12

10009 22Dosage W09                      2                                 2/16/2009
Percent Concentration
-   the concentration of a drug can be expressed as a quantity of solute ( a substance
dissolved in a solution ) in a defined volume of solution
grams of solute
percent weight-in-volume
100 mL of solution

grams of solute
percent weight-in-weight
100 g of preparation ( solution )

millilitres of solute
percent volume-in-volume
100 mL of solution

eg)    How many grams of salt should be used to create a 250 mL of a 5% strength saline
solution?
5g       xg
=
100mL 250mL
5 × 250
x=         = 12.5 g
100
12.5 g of salt is dissolved in 250 mL of water to create a 5% saline solution

eg)  How many grams of calcium carbonate ( CaCO3 ) should be used to create a 1 litre,
10% suspension?
10 g        x
=
100mL 1000mL
10 × 1000
x=           = 100 g
100
100 g of CaCO3 is suspended in 1 litre of water to create a 10% chalk suspension

eg)   How many milligrams of potassium chloride ( KCl ) is required to prepare a 0.01%, 500
mL solution
0.01mg      xg
=
100mL 500mL
0.01× 500
x=            = 0.05 g = 50mg
100

50 mg of KCl is dissolved in 500 mL of water to create a 0.01% solution

10009 22Dosage W09                       3                                   2/16/2009
Eg) A formulation contains 0.1% of a drug. How many milligrams of the drug are contained
within 10 mL of the formulation?

0.1g       xg
=
100mL 10mL
0.1× 10
x=          = 0.01g = 10mg
100
0.01 mg of the dug are found in 10 mL of the formulation

eg)   How many litres of a 2% solution can be prepared from 50 g of a drug?

2g     50 g
=
100mL xmL
100mL xmL
=
2g     50 g
50 ×100
x=          = 2500mL = 2.5L
2

2.5L of the 2% solution can be prepared from 50 g of the drug
eg)   What is the percentage strength of a urea solution if 90 mL contains 18 g?

xg     18 g
=
100mL 90mL
18 ×100
x=         = 20 g = 20%
90
The 90 mL is a 20% urea solution

eg)   A nurse uses 25 mg of menthol in preparing 250 mL of a mouthwash. What is the
percentage strength of menthol in the solution?
xg     0.025 g
=
100mL 250mL
0.025 × 100
x=             = 0.01g = 0.01%
250
The mouthwash is a 0.01% strength solution of menthol

10009 22Dosage W09                     4                               2/16/2009
Eg) An injection contains 50 mg of pentobarbital in each mL of solution. What is the
strength of the solution?

xg     0.050 g
=
100mL     1mL
0.050 ×100
x=             = 5 g = 5%
1
The injection contains a 5% strength solution
Eg)   How many milliliters of monoacetate should be used to prepare a litre of a 25% lotion?

25mL     xmL
=
100mL 1000mL
25 ×1000
x=          = 250mL
100
250mL of monoacetate will be required to create a litre of a 25% lotion.

Dosage Problems

Eg)   The doctor has ordered 20 mg of Prozac for a patient. The label for the tablets reads
“10 mg Tab”. How many tablets should be given?

10mg 20mg                              20
=            10 x = 1× 20   x=      = 2tab
1tab   x                              10

eg)   60 mg of medication are ordered. Tablets are available which have 30 mg of
medication in each of them. How many tablets are needed to give 60 mg?

30mg 60mg                              60
=            30 x = 1× 60   x=      = 2tab
1tab   x                              30

10009 22Dosage W09                     5                                   2/16/2009
Eg)   A 0.6g dose is ordered. Only 300 mg/tab is available. How many tablets per dose are
needed?
300mg 0.6 g
=
1tab   x
1000mg
0.6 g ×
300mg            1g
=
1tab          x                           1g = 1000 mg
300mg 600mg
=
1tab      x
600mg
x=        = 2tab
300mg

Eg)   You are to prepare a 250 mcg dose. The medication is labeled 0.4 mg/mL. How many
mL will you need?

1000 mcg = 1000 micro grams = 1 mg                  1000 mg = 1 g

0.4mg 250mcg
=                                                  1g
1mL         x
1000mcg                                           10dg = 1g
0.4mg ×
1mg      250mcg                                100cg = 1g
=
1mL              x                                  1000mg = 1g
400mcg 250mcg
=
1mL          x
250mcg                                                1000 μ g = 1000mcg = 1mg
x=          = 0.625mL
400mcg

eg)   A patient is to receive 2 g of a drug. The drug comes 500 mg/5 mL. Each vial contains
10 mL's. How many vials would you need?

- determine the volume required

500mg 2 g                1000mg
=          2g ×        = 2000mg
5mL        x              1g
500mg 2000mg
=
5mL           x
500 x = 5 × 2000
5 × 2000
x=            = 20mL
500

20mL
the number of vials required        = 2 vials
10mL

10009 22Dosage W09                          6                               2/16/2009
eg)   You are to administer 0.75 g of a medication to a patient. The label on the stock
solution is

50 mL

TILCOL

160 mg/mL

How many mL of the stock solution should be used?

160mg 750mg
=
1mL         x
1000mg
0.75 g ×          = 750mg                    160 x = 750
1g
750
x=       = 4.69mL
160

eg)   Order: 25 mg/kg of body wt.

Available: 5 g/20 mL

How many mL's do you give to a 18 kg child?

25mg       x
=
1kg     18kg
25mg       x
=
1kg     18kg
25 ×18                            1g
x=          = 450mg       450mg ×          = 0.45 g
1                            1000mg

5g     0.45 g
=
20mL       x
0.45 × 20
x=           = 1.8mL
5

10009 22Dosage W09                         7                               2/16/2009
eg)   A 11.5 kg infant is to receive 2 mg/kg of a drug. The drug is available in 10 mg/0.5 mL.
How many mL's will be given?

2mg        x
=
1kg 11.5kg
x = 2 × 11.5 = 23mg

The infant is to receive 23 mg of the drug

10mg 23mg
=
0.5mL xmL
The dosage
23 × 0.5
x=          = 1.15mL
10

Eg)     The recommended dose for a certain medication for is 5 mg/kg/day in 3 equally
divided doses. If a patient weighs 135 lb then how many milligrams should the patient

Remember             1 kg = 2.2 lb

5mg xmg
=
1kg 135lb
5mg         xmg
=
1kg 135lb × 1kg
2.2lb
5mg      xmg
=
1kg 61.36kg
x = 61.36 × 5 = 306.8mg

the 135 lb patient needs to take 306.6mg of the medication per day

306.6
- one dose would be           = 102.2mg
3

eg)   A patient is prescribed 120mg/kg/day in 4 equally divided doses. How many milligrams
should a 210 lb patient receive per dose?
120mg       xmg
=
1kg     95.45kg
1kg                           x = 120 ( 95.45 ) = 11454.5mg
210lb ×         = 95.45kg
2.2lb
11454.5
one dose           = 2863.6mg
4

10009 22Dosage W09                          8                                   2/16/2009
eg)   The recommended dose is 50 mg/kg/day. The patient weighs 140 lb and she is to
receive the medication every 8 hours. The medication is available as 300 mg / 5 mL.

a) How many mg should the patient receive per dose?

1kg
140lb ×         = 63.64kg
2.2lb

50mg     x                   50 × 63.64
=                 x=               = 3181.82mg
1kg   63.64                      1

3181.82
1 dose =           = 1060.6mg
3

b)     How many mL should she receive per dose?

300mg 1060.6mg
=
5mL           x
300 x = 5 ×1060.6
5 × 1060.6
x=             = 17.68mL
300

c)     How many mL should she take per day?

3 × 17.68 = 53.0mL

Eg)   Given a 20mL vial of a Virtol solution ( 1g Virtol : 4 mL water ).

a) How many grams of Virtol are in this vial?

1g   x               20
=            x=      = 5g
4mL 20ml               4

b) If a patient is to receive 140mg of Virtol, how many mL of the medication are
required?

1g
140mg ×
Virtol     1g    140mg                1000mg 0.140 g
=       =                    =
water 4mL           x                x          x
x = 4 × 0.140 = 0.56mL

Homework course booklet pg 11 1 – 10

10009 22Dosage W09                         9                                  2/16/2009
Calculating Intravenous Flow Rates

-   Intravenous fluids are fluids injected directly into a vein.

A physician orders the type, amount, and flow rate for an IV solution or medication.

The flow rate determines how much of the fluid enters the vein in specific period of time.

It is calculated as drops per minute (gtt/min)

traditional pharmacist's abbreviations for a drop. Originally, gt was the singular (1 gt) and gtt
the plural. The symbol comes from the Latin word gutta for a drop.

The following formula can be used to calculate the flow rate:

Volume(in mL ) × Calibration(drop factor in gtt / m L )
Flow Rate(gtt / min) =
Total time(in minutes )

gtt
mL ×
gtt         mL
=
min       min
V ×C
F=
T

Typical flow rates range 20 to 100 gtt/min

-   it is dangerous to arbitrarily speed up or slow down the flow rate, since this can cause
over or under hydration

Eg)    The physician orders 1000 mL of 5% Dextrose in Water to be infused in 8 hours. The
drop factor of the infusion set is calibrated at 20gtt/mL. What is the flow rate in drops
per minute?

60 min
- convert the infuse time into minutes       8hours ×          = 480 min
1hour

gtt
1000mL × 20
V ×C                 mL = 20000 gtt = 41.7 gtt / min
F=      =
T          480 min      480 min

The IV flow rate is set to 42 gtt/min

10009 22Dosage W09                       10                                       2/16/2009
Eg)   Calculate the infusion time in hours and minutes for an IV of 1000cc of dextrose
infusing at 20 gtt/min. The drop factor is 10 gtt/mL.

Note that     1 mL = 1 cubic centimeter = 1 cc

V ×C
F=
T
gtt
1000cc × 10
gtt                  cc
20     =
min            T
20T = 10000
T = 500 min

500
= 8.3333h
60
0.3333 × 60 = 20 min

the infusion time is 8 hours and 20 minutes

Eg)   A bag of 0.9% saline solution is infusing at the rate of 20gtt/min. The infusion set is
calibrated for a drop factor of 15gtt/mL. How many mL of solution will infuse during an
8-hour shift?

V ×C
F=
T
gtt
V × 15
gtt           mL
20     =
min 8 × 60 min
15V = 20 × 8 × 60
20 × 8 × 60
V=                = 640mL
15

Over an 8 hour shift 640mL would be infused

10009 22Dosage W09                      11                              2/16/2009
Eg)   1000 mL of a dextrose solution is to be infused at 60 mL/h stating at 0600. At what
time will this IV be completed?

60mL 1000mL
=
1h          x
60 x = 1000
1000
x=        = 16.6667 h  0.6667 × 60 = 40
60
0600 + 1640 = 2240 (10 : 40 pm)

The IV will start at 0600 and end at 2240

Eg)   At 0700 an IV is infusing at a rate of 25 gtt/min. How much can you expect the patient
to receive during the next 12 hours given a drop factor of 18 gtt/mL?

V ×C
F=
T
gtt
V ×18
gtt         mL
25      =
min 12 × 60 min
18V = 25 ×12 × 60
25 × 12 × 60
V=                = 1000mL
18

The patient will receive 1000 mL

10009 22Dosage W09                       12                            2/16/2009
HOMEWORK

Determining the Rate of Intravenous Medication

a) An IV is to run at 50mL per hour. The drop factor of the infusion set is 15gtt/mL. What is the
flow rate? {13gtt/min}

b) Calculate the flow rate for an IV of 500mL of normal saline to be infused in 8 hours. The
drop factor of the infusion set is 20gtt/mL. {21gtt/min}

c) A physician orders 2L solution to infuse in a 10 hour period. The drop factor of the infusion
set is 20gtt/mL. What is the flow rate? {67gtt/min}

of IV solution. It is to infuse in 1 hour. The drop factor of the infusion set is 60gtt/mL. What is
the flow rate? {50gtt/min}

e) An 1000mL of 5% solution is to infuse at 200mL per hour. What is the infusion time? {5
hours}

f) A medication is prepared in 50mL of an IV solution. It is infusing at 30 drops per minute.
The drop factor of the infusion set is 20gtt/mL. What is the infusion time? {33.3min}

g) The physician orders an IV solution to infuse at the rate of 52gtt/min. The infusion set is
calibrated for a drop factor of 15gtt/mL. How much of the solution will infuse during 2 1/2
hour? {520mL}

h) 900mL mL of a dextrose solution is to be infused at 50 mL/h stating at 1600. At what time
will this IV be completed? {0200}

i) At 1800 an IV is infusing at a rate of 15 gtt/min. How much can you expect the patient to
receive during the next 8 hours and 20 minutes given a drop factor of 12 gtt/mL? {625mL}

10009 22Dosage W09                        13                                 2/16/2009
HOMEWORK FULL SOLUTIONS

a) An IV is to run at 50mL per hour. The drop factor of the infusion set is 15gtt/mL. What is the
flow rate?

gtt
50mL × 15
V ×C               mL = 750 gtt = 12.5 gtt / min
F=        =
T         60 min      60 min

b) Calculate the flow rate for an IV of 500mL of normal saline to be infused in 8 hours. The
drop factor of the infusion set is 20gtt/mL.

gtt
500mL × 20
V ×C                 mL = 10000 gtt = 20.8 gtt / min
F=        =
T        8 × 60 min      480 min

c) A physician orders 2L solution to infuse in a 10 hour period. The drop factor of the infusion
set is 20gtt/mL. What is the flow rate?

gtt
2000mL × 20
V ×C                   mL = 40000 gtt = 66.7 gtt / min
F=      =
T            600 min      600 min

d) An antibiotic is mixed as 50mL of IV solution. It is to infuse in 1 hour. The drop factor of the
infusion set is 60gtt/mL. What is the flow rate?

gtt
50mL × 60
V ×C                 mL = 3000 gtt = 50 gtt / min
F=      =
T           60 min      60 min

e) An 1000mL of 5% solution is to infuse at 200mL per hour. What is the infusion time?

200mL 1000mL
=
1hour        x
200 x = 1000
x = 5hours

f) A medication is prepared in 50mL of an IV solution. It is infusing at 30 drops per minute.
The drop factor of the infusion set is 20gtt/mL. What is the infusion time?

V ×C
F=
T
gtt
50mL × 20
gtt             mL
30     =
min        T
30T = 50 × 20
50 × 20
T=           = 33.3min
30

10009 22Dosage W09                          14                                     2/16/2009
g) The physician orders an IV solution to infuse at the rate of 52gtt/min. The infusion set is
calibrated for a drop factor of 15gtt/mL. How much of the solution will infuse during 2 1/2
hour?

V ×C
F=
T
gtt
V × 15
gtt          mL
52      =
min 150 min
52 ×150 = 15V
52 ×150
V=           = 520mL
15

h)     900mL mL of a dextrose solution is to be infused at 50 mL/h stating at 1600. At what
time will this IV be completed?

50mL 900mL
=
1h        x
50 x = 900
900
x=       = 18h    0.6667 × 60 = 40
50
1800 − 1600 = 0200

The IV will start at 1600 and end at 0200 the next day

i)     At 1800 an IV is infusing at a rate of 15 gtt/min. How much can you expect the patient
to receive during the next 8 hours and 20 minutes given a drop factor of 12 gtt/mL?

V ×C
F=
T
gtt
V ×12
gtt           mL
15      =
min 8 × 60 + 20 min
12V = 15 × 500
15 × 500
V=            = 625mL
12

The patient will receive 625 mL

10009 22Dosage W09                       15                                2/16/2009
PEDIATRIC DOSAGE CALCULATIONS

Factors affecting medication for infants and children include
• weight,
• height,
• body surface area (BSA) and
• age.

Two commonly accepted methods of determining pediatric dosage are:
• calculating dosage based on body weight
• calculating dosage based on body surface area (BSA)

When calculating dosage based on body weight, it is important to note the exact weight of the
child in the proper units and use the proper reference values as stated in the medication
reference books and/or drug manufacturers’ label.

The BSA method is considered to be more accurate for calculating pediatric dosages since it
relies on both the weight and height of the child. Since it is very difficult to calculate the BSA
of a child, a nomogram is used.

The formula for calculating the correct dosage for a child with BSA is in proportion to the adult
dosage.

BSA(m 2 )
Child. Dose =           × Adult.Dose
1.7 m 2

Using the nomogram, use a straight edge which will span the columns

approximate the Body Surface Area (BSA) for a child that is:

•   35 inches tall and weighs 30 lb.

0.59m 2

•   35 inches tall and weighing 40 lb.

1.04m 2

•   55 pounds and 44 inches tall

1.38m 2

•   75 pounds and 44 inches tall

1.06m 2

10009 22Dosage W09                        16                                2/16/2009
10009 22Dosage W09   17   2/16/2009
1. A patient is 5 ft 3 in tall and weighs 100lb. A drug is to be administered 25mg per square
metre. Calculate the correct dosage for the patient.

height 5 ft 3 in = 60 + 3 = 63 in
surface area = 1.43 m2

25mg        xmg
2
=
1m       1.43m 2
x = 25 × 1.43 = 35.8mg

2. The physician orders CMS 150 mg/m2. The patient weighs 65 pounds and is 32 inches
tall. What is the correct dose for this patient?
surface area = 0.88 m2

mg
0.88m 2 ×150      = 132mg
m2

3. CL is to be administered 4.5mg per square metre per day to a child who weighs 50lb and
is 3ft 6in tall. Calculate the dosage for this patient. CL is supplied in tablets containing 2mg.
How many tablets are needed?
surface area = 0.84 m2

mg
0.84m 2 × 45      = 3.78mg
m2

3.78mg
number of tablets          = 1.89 = 2tab
2mg

10009 22Dosage W09                        18                                2/16/2009
10009 22Dosage W09   19   2/16/2009

```
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