Transcript Math Calculation Principles

Copyright PRIMED 2015
When performing drug calculations always do
the following:
1. Convert to the same units
2. Consider what dosage is reasonable
3. Calculate
4. When in doubt confirm with another
resource
Fractions: convert to the lowest term & lowest
denominators
Decimals: think of the
decimal point as the
center that separates
whole and fractional
Amounts

The position of the
numbers in relation to
the decimal point
indicates the place value
of the numbers
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For safety always write a zero to the left of
the decimal point if the number has no whole
number
◦ .5 mg should be written as 0.5 mg to avoid the
potential for errors
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To avoid confusion eliminate unnecessary
zeros at the end of a decimal
◦ 0.500 is the same as 0.5
Convert fractions to decimals by dividing the
denominator into the numerator ¼=0.25
 Line up decimals for adding & subtracting
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For many dosage calculations it is necessary to
round off your calculations to the nearest
thousandths (3 places) or the nearest hundredths
(2 places)
Rule:
1. Do not change the numbers in the tenths place
if the number in the hundredths place was 4 or
less ie:0.13= 0.1
2. Increase the number in tenths place by 1 if the
numbers in the hundredths place was 5 or more
ie:0.75= 0.8
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Adding:
1.5 + 0.05= ?
7.8 + 1.12=?
Subtracting: 3.75 – 2.1= ?
5.25 – 3.6=?
Multiplying: 1.5 x 0.5=?
1.72 x 0.9=?
Dividing:
1/ 5
1/4
(1.55)
(8.92)
(1.65)
(1.64)
(0.75)
(1.548; 1.55)
(0.2)
(0.25)
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When performing calculations always convert
to the same units of measurement
Metric is based on the decimal system
The prefix determines the amount of
measurement:
◦
◦
◦
◦
Kilo= 1000 units or one thousand times
Centi= 0.01 units or one hundredth part of
Milli= 0.001 units or one thousand part of
Micro= 0.000001 units or one millionth part of

The prefix determines the type of
measurement:
◦ Milli, kilo, centi

The suffix determines what is being
measured:
◦ Gram = basic unit for weight (solid)
◦ Liter = the basic unit for volume (liquid)
◦ Meter= the basic unit for length

Move the decimal point 3 ways, left or right
depending on the conversion
Kg
G
0.000001
0.001
0.001
1
mg
1
1000
mcg (ug)
1000
100,000
500 mL= L
0.015 g= mg
8 mg= g
10 mg= g
60 mg= g
300 mg= g
0.2 mg= g
0.0025 kg= g
5,000mL= L
250mL= L
2 kg= g
1 g= mg
1mL= L
23 mcg= mg
1.05 kg= g
18 mcg= mg
0.4 mg= mcg
1.5 L= ml
1L= mL
500 mL= L (0.5)
0.015 g= mg (15)
8 mg= g (0.008)
10 mg= g (0.01)
60 mg= g (0.6)
300 mg= g (0.3)
0.2 mg= g (0.0002)
0.0025 kg= g (2.5)
5,000mL= L (5)
250mL= L (0.250)
2 kg= g (2000)
1 g= mg (1000)
1mL= L (1000)
23 mcg= mg (0.023)
1.05 kg= g (1050)
18 mcg= mg (0.018
0.4 mg= mcg (400)
1.5 L= ml (1500)
1L= mL (1000)
Household Unit
SI Unit
1
1
1
1
1
5 milliliters (mL)
15 milliliters (mL)
30 milliliters mL)
250 milliters (mL)
1 Liter (L)
teaspoon (tsp or t)
tablespoon (Tbsp or T)
fluid ounce (oz)
cup (C)
quart (qt)
Drug calculations are completed by 3 methods:
1. Use of a formula
2. Dimensional analysis
3. Ratio and proportion
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Most common method of calculating meds
DxQ
H
D= desired dose or dose prescribed
H= have dose or drug dose available
Q= quantity or form and amount in which
drug comes
1. Doctor orders metformin 500 mg PO OD. The drug container
reads metformin 100 mg tablets. Give_______________
2. Hydrochlorothizide 12.5 mg PO TID ordered; 25 mg tablets
Available. Give___________
3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tablets
Give__________
4. Ibuprofen 600 mg PO BID. Available Ibuprofen 300 mg
tablets. Give_______________
5. Available: Cefazolin 1 g per 10 ml. Dose to be given is
Cefazolin 500mg. Give___________
6. Levothyroxine 50 mcg tablets available. Dose ordered
Levothyroxine 0.05 mg PO OD. Give______________
7. Propanolol 15 mg PO TID. Dose available Propanolol 10 mg.
Give____________
1. Doctor orders metformin 500 mg PO OD. The drug container
reads metformin 100 mg tablets. Give_______________(1 tab)
2. Hydrochlorothizide 12.5 mg PO TID ordered; 25 mg tablets
Available. Give___________(1/2 tab)
3. Digoxin 0.125mg PO TID. Available Digoxin 0.25 mg tablets
Give__________(1/2 tab)
4. Ibuprofen 600 mg PO BID. Available Ibuprofen 300 mg
tablets. Give_______________(2 tabs)
5. Available: Cefazolin 1 g per 10 ml. Dose to be given is
Cefazolin 500mg. Give___________(5 mLs)
6. Levothyroxine 50 mcg tablets available. Dose ordered
Levothyroxine 0.05 mg PO OD. Give______________(1 tab)
7. Propanolol 15 mg PO TID. Dose available Propanololl 10 mg.
Give____________(1.5 tabs)
Useful when meds are ordered in different
units
 For example:
the available dose is 750 mg in 2.5 mL which
you must prepare a 600 mg dose. How many
mL is this?
mL= 2.5 mL x 600 mg = (2.5 x 600)/750= 2mLs
750mg
1 units
cross multiply & cancel
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We use ratios to make comparisons between two
things. When we express ratios in words, we use
the word "to"‐‐we say "the ratio of something to
something else." Ratios can be written in several
different ways: as a fraction, using the word "to", or
with a colon
A proportion is simply a statement that two ratios
are equal. It can be written in two ways: as two
equal fractions a/b = c/d; or using a colon, a:b =
c:d. The following proportion is read as "twenty is to
twenty five as four is to five."
To solve equations using this method it is
necessary to express the numbers as ratios or as
fraction and cross multiply:
5: 10 = 10:20 is the same as 5 = 10
10 20
The 2 outer numbers are called the extremes and
the 2 inner numbers are called the means.
In this method the extremes are multiplied and the
means are multiplied or cross multiplied.
5x20= 100 & 10x10=100
5x20 = 10x10
100 = 100
Find the value of x rounded to 2 places:
0.5 = 250
2
x
0.5 x = 250 x 2
x= 500/0.5
2. 250 = 750
(250 x=750; x= 750/250)
1
x
3. How much salt would you add to 500 mL of
water to make a solution that contains 5 mL of
salt for every 250 mL?
5mL/250mL=xmL/750mL: (5mL /250 x 750mL/1
=15mL)
•Drips rates need to be calculated to
ensure safe delivery of IV fluids
•Many are administered via a pump
•To calculate manually you need to
determine the hourly rate and then
calculate the gtt/min to obtain the
necessary rate
For infusion pump:
Flow Rate (ml/hr) = Total infusion (ml)
Hours of infusion
1000 ml/ 8 hr= 125 ml/hr
Calculating based on drop factor:
X gtt/min = amount of soln (ml) X drop factor
time in min
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Macrodrip: drip factor 10‐20 gtt/ml
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Microdrip: drip factor is 60 gtts/ml
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Drip factor is on IV tube packaging
Calculate the flow rate you will program the IV pump
for the following:
1.
2.
3.
4.
5.
6.
1 L D5W to infuse in 10 hrs_______________ mL/hr
1800 mL NS to infuse in 15 hrs ____________mL/hr
2000mL D5W in 24 hrs ___________________mL/hr
100 mL NS IV piggyback in 30 min______mL/hr
30 mL medication in 15 minutes __________mL/hr
2 L NS IV in 20 hrs ______________mL/hr
Calculate the flow rate you will program the IV pump for the
following:
1.
2.
3.
4.
5.
6.
1 L D5W to infuse in 10 hrs_______________ mL/hr (100)
1800 mL NS to infuse in 15 hrs __________mL/hr(120)
2000mL D5W in 24 hrs _________________mL/hr (83.33)
100 mL NS IV piggyback in 30 min_______mL/hr (200)
30 mL medication in 15 min __________mL/hr (120)
2 L NS IV in 20 hrs ______________mL/hr (100)
Calculate the IV flow rate in drops per minute
(gtt/min) using the formula method
V/T x C= R
V= total volume to be infused in mL
T= total time in minutes
C= drop factor gtt/mL
R= rate of flow gtt/min
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Order 3000 mL D5W to run for 24 hrs drop
factor 10 gtt/ml
3000/(24 x 60) x 10=20.8=21 gtts/min
OR
3000/24=125 ;
125/60 x 10=20.8=21 gtts/min
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Order 250 mL RL to infuse in 5 hrs drop
factor 60 gtt/mL
250/(5 x 60) x 60= 50 gtts/min
OR
250/5=50 mLs/hr
50O60 x 60= 50 gtts/min
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Order 100 mL NS medication to infuse
in 40 min dropfactor 20 gtt/mL
100/40 min x 20 = 50 gtts/min
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NS to run at 25 mL/hr drop factor 60
gtt/ mL
25/60 x 60=25 gtts/min
For each drop factor there is a constant as follows:
 10 gtt/mL= 6
 15 gtt/mL= 4
 20 gtt/ml= 3
 60 gtt/ml= 1
Calculate the IV flow rates in drops per minute
(gtt/min) by using the short cut method:
mL/h
= gtt/min
Drop factor
1.
2.
3.
4.
order 1000 mL D5W to infuse in 4 hrs drop
factor 15gtt/mL
2. order 750 mL to infuse in 6 hrs drop
factor 20 gtt/m
3. order 500mL 2/3 + 1/3 to infuse in 3 hrs
drop factor 10 gtt/mL
4. order 2 L NS IV to infuse at 60 mL/hr
drop factor 60 gtt/mL (
1. order 1000 mL D5W to infuse in 4 hrs drop
factor 15gtt/mL (1000/4)/4(constant)= 250/4= 62.5=63
gtts/min
2. order 750 mL to infuse in 6 hrs drop factor
20 gtt/m (750/6)/3= 125/3=41.67=42gtts/min
3. order 500mL 2/3 + 1/3 to infuse in 3 hrs
drop factor 10 gtt/mL (500/3)/5= 166/67/5= 33.3=33
gtts/min
4. order 2 L NS IV to infuse at 60 mL/hr drop
factor 60 gtt/mL (60/1=60 gtts/min
Based on this label you need to know:
 What is the total dosage strength of Ceftriaxone in
this vial?
 For what routes of administration is the medication
indicated?
 How much diluent must be added to the vial to
prepare the medication for IV use?
 What kind of diluent is recommended for IV
reconstitution?
 What is the final concentration of the prepared
solution for IV use?
 1 g IV q12h is ordered. How many milliliters will
you give?
Based on this label you need to know:
 What is the total dosage strength of Ceftriaxone in
this vial? (1g or 1000 mg)
 For what routes of administration is the medication
indicated? (IM or IV)
 How much diluent must be added to the vial to
prepare the medication for IV use? (9.6)
 What kind of diluent is recommended for IV
reconstitution? (sterile water)
 What is the final concentration of the prepared
solution for IV use? (100 mg/mL)
 1 g IV q12h is ordered. How many milliliters will
you give? (10mL)
Pediatrics clients less then 45 kg are given medications
based on either their weight or their Body Surface
Area (BSA)
To calculate by weight you need to multiply the dose
per kilogram by the weight of the child
Ie: If you need to give 10 mg/kg of a med for a child
weighing 10 kg then:
10 mg: 1 kg = x mg: 10 kg
multiply the extremes then the means
10 mg x 10 kg= 100 mg/kg
1kg x= 100 mg/ 1kg= 100 mg
Formula Method
Formula Method
BSA(m2)=
height (cm) x weight (kg)
3600
Multiply the height in cm by
weight in kg then divide by
3600 which =? then press √
Button to arrive at m2
Round m2 to nearest hundreth
height (in) x weight (lbs)
3100
Multiply the height in inches by
weight in lbs then divide by
3100 which =? then press √
Button to arrive at m2
Round m2 to nearest hundreth
BSA(m2)=
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Calculation of pediatric dosages, as with adult dosages,
involves the use of ratio and proportion, the formula
method, or dimensional analysis to determine the amount
of medication to administer.
Pediatric dosages are much smaller than those for an
adult. Micrograms are used a great deal. The tuberculin
syringe (1‐mL capacity) is used to administer very small
dosages.
Intramuscular (IM) dosages are usually not more than 1 mL
for small children and older infants; however, this can vary
with the size of the child. The recommended IM dosage for
small infants is not more than 0.5 mL.
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The recommended subcutaneous dosage
for children is not more than 0.5 mL.
Dosages that are less than 1 mL may be
measured in tenths of a milliliter, or with a
tuberculin syringe in hundredths of a
milliliter.
Medications in pediatrics generally are not
rounded off to the nearest tenth but may be
administered with a tuberculin syringe
(measured in hundredths) to ensure accuracy.
All syringes must be labeled.
Step 1: convert pounds to kilograms and ounces to parts of a
pound:
To convert from kilograms to pounds, use the conversion1 kg =
2.2 lb.
To convert from kilograms to pounds multiply by 2.2, and
express your weight to the nearest tenth.
For Ounces convert to partial pounds: 16 oz = 1 lb 4 oz=0.25 lb
You may have to convert grams to kilograms
Medication dosages can be calculated based on mg/kg/day,
mg/lb/day, or sometimes mcg/kg. References often state
the safe amount of the drug in mg/kg/day (24‐hour
period). Once you have determined the child's weight in
kilograms, you are ready to calculate the medication
dosage. Calculating the dosage involves three steps:
1.Calculation of the total daily dosage
2.Division of the daily dosage by the number of dosages to be
administered
3.Use ratio and proportion, the formula method, or
dimensional analysis to calculate the number of tablets or
capsules or the volume to give to administer the ordered
dosage
Order: Dilantin 30 mg PO q8h.
Child weighs 18 kg. Is the dosage safe?
 Recommended dosage: 5 mg/kg/day in 2 or 3 equally divided
dosages. (Notice the information written sideways on the left
of the Dilantin label.)
 Now that we have the dosage information and the child’s
weight, we can calculate the safe total daily dosage for the
child.
Note: The child's weight is in kilograms (18 kg), and the
average dose range is 5 mg/kg/day. No conversion of weight
is required.
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Start by calculating the safe total daily dosage for this child.
Multiply the recommended dosage in milligrams by the child's
weight in kilograms.
The safe dosage for this child (total) is 90 mg/day.
Now determine the amount of each dosage. The dosage is to
be given in three equally divided dosages. Therefore:
90/3 = 30 mg per dose
After calculating the safe dosage for a child, you can assess
whether what the prescriber ordered is a safe dosage. The
order is 30 mg Q8H=
Q8H= 24/8= 3doses,
30 mg x 3= 90 mg= Safe Dose
This Is a quick way to calculate titrations
1.
2.
Look at the units of measures in the order ( this is usually
stated that you will give X units of measure/ min or hr) and
the units of measure on medication in the IV bag ( this will
say X units of measure in X mL of solution). Convert these
so that they are the same. Make sure you have the correct
number of decimal point!!!!
Look at the order or rate you are to infuse the medication. If
the dose is dependent on the patient’s weight, figure out
the number of units of medication the patient will get for
their weight. This may mean converting lbs to kg. This will
now give you the measurement of medication you must
give. It may be /min or it may be/hr
3.
4.
If it is units of measure/min, you must
then multiply this by 60 min. This is now
your rate/hr and is your DD (Desired
dose).
Take your DD from step 3 , divide it by the
converted units of measure from step 1
that is in the IV solution (this is you DH,
dose on hand) and multiply by the volume
(which is the number of mL in the IV bag
supplied.