Mathematics and
Dosage Conversions
Toine Penick, LPN, CST
Mathematics Review
Comparing Fractions
Reducing Fractions
 Divide
both terms by the largest nonzero
whole number that will divide both the
numerator and denominator evenly. Value
remains the same.
6
62 3


10 10  2 5
Enlarging Fractions
 Multiply
both terms by the same nonzero
number. Value remains the same.
1
1 2
2


12 12  2 24
Adding or Subtracting Fractions
 Convert
to equivalent fractions with least
common denominators.
 Add or subtract the numerators; place that
value in the numerator. Use the least
common denominator as the denominator.
 Convert answer to mixed number and/or
reduce to lowest terms.
Multiply and Divide Fractions
 To
multiply fractions, cancel terms, multiply
numerators, and multiply denominators.
 To divide fractions, invert the divisor,
cancel terms, and multiply.
 Convert results to a mixed number and/or
reduce to lowest terms.
Division of Fractions
 changed to ×
1 2 1 7 7
   
4 7 4 2 8
Dividend
Divisor
Inverted
Divisor
Quotient
WHOLE NUMBERS
DECIMAL POINT
ten thousandths
thousandths
hundredths
tenths
ones
tens
hundreds
thousands
ten thousands
Decimals
X X X X X . X X X X
DECIMAL FRACTIONS
Comparing Decimals
 Compare
0.125, 0.05, and 0.2 to find
which decimal fraction is largest.
 Align decimal points and add zeros.
0.125  125 or one hundred twenty -five thousandt hs
1000
0.050  50 or fifty thou sandths
1000
0.200  200 or two hundred thousandt hs
1000
Decimal Values: Decimal Point
and Zeros
 Zeros
added to a decimal fraction before
the decimal point or at the end of the
decimal fraction do not change the value.


.5 = 0.5 = 0.50
0.5 is the preferred notation
 In
a decimal number, zeros added before
or after the decimal point do change the
value.

1.5 1.05 and 1.5 10.5
Decimal Values: Decimal Point
and Zeros
 To
avoid overlooking the decimal point in a
decimal fraction, always place a zero to
the left of the decimal point.


Avoid writing a decimal fraction
this way; it could be mistaken for the
whole number 5.
Preferred method of writing a
Example: 0.5
decimal fraction.
Example: .5
Add and Subtract Decimals
 To
add or subtract decimals, align the
decimal points and add zeros, making all
decimals of equal length. Eliminate
unnecessary zeros in the final answer.
Multiply and Divide Decimals
 To
multiply decimals, place the decimal
point in the product to the left as many
decimal places as there are in the two
decimals multiplied.
0.25  0.2  0.050  0.05
Multiply and Divide Decimals
 To
divide decimals, move the decimal
point in the divisor and dividend the
number of decimal places that will make
the divisor a whole number and align it in
the quotient.
2 0.
1.2 24.0.
Multiply and Divide Decimals

To multiply or divide decimals by a multiplier of
10, move the decimal point to the right (to
multiply) or to the left (to divide) the number of
decimal places as there are zeros in the
multiplier of 10.
5.06 10  5.0.6  50.6
2.1  100 .02.1 0.021
Thousandths
Hundredths
Tenths
Rounding Decimals
0 .1 2 3
1. 7 4 4
5.3 2 5
0.6 6 6
 0.12
 1.74
 5.33
 0.67
Rounded to hundredths
(two places)
Hundredths
Tenths
Rounding Decimals
0 .1 3
5.6 4
0.7 5
1. 6 6
0.9 5
 0.1
 5.6
 0.8
 1.7
 1.0  1
Rounded to tenths
(one place)
Ratios, Percents, Simple
Equations, and RatioProportions
Percent
 To
remember the value of a given percent,
replace the % symbol with “/” for per and
“100” for cent.

THINK: Percent (%) means “100”.
Convert Ratio to Fraction
 To
express a ratio as a fraction, the
number to the left of the colon becomes
the numerator, and the number to the right
of the colon becomes the denominator.
 The colon in a ratio is equivalent to the
division sign in a fraction.
2:3
2

3
Convert Ratio to Decimal
 To
change a ratio to a decimal, convert the
ratio to a fraction, and divide the
numerator by the denominator.
1
1 : 4   1  4  0.25
4
Convert Percent to Fraction
 To
change a percent to a fraction, drop the
% sign and place the remaining number as
the numerator over the denominator 100.
 Reduce the fraction to lowest terms.
 THINK: per (/) cent (100)
75
3

75% 100  4
Convert Percent to Ratio
 To
change a percent to a ratio, convert the
percent to a fraction in lowest terms.
 Place the numerator to the left of the colon
and the denominator to the right of that
colon.
7
35

 7 : 20
35% 
100 20
Convert Percent to Decimal
 To
change a percent to a decimal, drop the
% sign, and divide by 100.
4%  .0 4.  0.04
Convert Decimal to Percent
 To
change a decimal to percent, multiply
by 100, and add the % sign.
0.5  0.5 0 .  50%
Convert Ratio to Percent
 To
change a ratio to a percent, first convert
the ratio to a fraction.
 Convert the resulting fraction to a decimal
and then to a percent.
1
1 : 2   1 2  0.5  0.5 0 .  50%
2
Ratio-Proportion
5 : 10 :: 10 : 20
5 : 10  10 : 20
5 10

10 20
Proportion Cross-products
 If
two fractions are equivalent, or equal,
their cross-products are also equal.
5 10

10 20
5  20  10 10
100  100
Solving for X in a Proportion
 Dividing
each side of an equation by the
same number produces an equivalent
equation. This operation is referred to as
simplifying the equation.
1 X

4
8
Therefore, 4  X  1  8
4x 8
If 4X  8, then
 , and X  2.
4 4
Percentage of a Quantity
 Percentage
(Part) = Percent × Whole
Quantity
 Example: What is 12% of 48?
X  12%  48  0.12  48  5.76
Systems of
Measurement
Metric Prefixes
1
micro  one millionth or 0.000001 or
of the base unit
1,000,000
milli
1
 one thousandt h or 0.001 or
of the base unit
1000
1
centi  one hundredth or 0.01 or
of the base unit
100
deci
1
 one tenth or 0.1 or of the base unit
10
kilo
 one thousand or 1000 times the base unit
International System (SI) of
Metric Units and Abbreviations
Weight
gram (base unit)—g
milligram—mg
microgram—mcg (µg)
kilogram—kg
Volume
liter (base unit)—L (ℓ)
milliliter—mL (mℓ) or
cubic centimeter—cc
Length
meter (base unit)—m
centimeter—cm
millimeter—mm
Comparing Common Metric
Units
Remembering Order
gram
liter
meter
kilo
hecto
deca
K
H
D
“King
Henry
Died
BASE
from a
deci
centi
milli
D
C
M
Disease Called Mumps”
Rules of Metric Notation
(continues)
 The
unit or abbreviation always follows the
amount.

Example: 5 g NOT g 5.
 Decimals
are used to designate fractional
metric units.

Example: 1.5 mL, NOT 1
1
2
mL.
Rules of Metric Notation
(continued)
 Use
a zero to emphasize the decimal point
for fractional metric units of less than 1.


Example: 0.5 mg, NOT .5 mg
This is a critical rule as it will prevent
confusion and potential dosage error.
Consider for a moment if you overlooked the
decimal point and misinterpreted the
medication order as 5 mg instead of 0.5 mg.
The dosage would be 10 times too much.
Rules of Metric Notation
(continued)
 Omit


unnecessary zeros.
Example: 1.5 g, NOT 1.50 g.
This is another critical rule.
 When
in doubt, double check. Ask the
writer for clarification
Metric Units of Measurement
and Equivalents
Weight
Unit
Abbreviation
Equivalents
gram
g
1 g = 1000 mg
milligram
mg
1 mg = 1000 mcg = 0.001 g
microgram
mcg (or μg)
1 mcg = 0.001 mg = 0.000001 g
kilogram
kg
1 kg = 1000 g
Metric Units of Measurement
and Equivalents
Volume
Unit
Abbreviation
Equivalents
liter
L (or ℓ)
1 L = 1000 mL
milliliter
mL (or mℓ)
1 mL = 0.001 L = 1 cc
cubic
centimeter
cc
1 cc = 1 mL = 0.001 L
Metric Units of Measurement
and Equivalents
Length
Unit
Abbreviation
Equivalents
meter
m
1 m = 100 cm = 1000 mm
centimeter
cm
1 cm = 0.01 m = 10 mm
millimeter
mm
1 mm = 0.001m = 0.1 cm
Apothecary System of
Measurement (continues)
 In


the apothecary system:
The common units for dosage calculations are
grain and ounce.
The quantity is best expressed in lowercase
Roman numerals. Amounts greater than ten
may be expressed in Arabic numbers, except
15 (xv), 20 (xx), and 30 (xxx).
Apothecary System of
Measurement (continued)



Quantities of less than one are expressed as
1
fractions, except 12 . One-half ( 2 ) is expressed
by the symbol ss.
The abbreviation or symbol is clearly written
before the quantity.
If you are unsure about the exact meaning of
any medical notation, do not guess or
assume. Ask the writer for clarification.
Apothecary System of
Measurement
Unit
Abbreviation
grain
gr
quart
qt
pint
pt
ounce or fluidounce
dram
minim
Equivalents
qt i = pt ii
qt i =
32
pt i =
16
Household System of
Measurement
Unit
Abbreviation
drop
teaspoon
gtt
t (or tsp)
tablespoon
T (or tbs)
ounce (fluid)
ounce (weight)
cup
pint
quart
oz (
oz
cup
pt
qt
)
Equivalents
1T=3t
2 T = 1 oz
1 lb = 16 oz
1 cup = 8 oz
1 pt = 2 cups
1 qt = 4 cups = 2 pt
Approximate Equivalents
1 g = gr xv
gr i = 60 mg
1t = 5 mL
1 T = 3 t = 15 mL =
ss
i = 30 mL = 6 t
1 L = qt I = 32 pt ii = 4 cups
pt i = 500 mL =
16 = 2 cups
1 cup = 250 mL =
viii
1kg = 2.2 lb
1 in = 2.5 cm
Conversions: Metric,
Apothecary, and Household
Systems
Conversion Factor Method
 Use
the conversion factor method to
convert from one unit of measurement to
another.




Recall the equivalents.
Identify the conversion factor
MULTIPLY by the conversion factor to convert
to a smaller unit. THINK: Larger to Smaller: (×)
DIVIDE by the conversion factor to convert to a
larger unit. THINK: Smaller to Larger: ()
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3.000 = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3.000 = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3.000 = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 .000 = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
= 3000 mL
.
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000
. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000. = 3000 mL
Metric Conversions with
Conversion Factor Method
 MULTIPLY
to convert from a larger unit to
a smaller unit, or move the decimal point
to the right.




Example: 3 L = ? mL
THINK: Larger to Smaller: (×)
Equivalent: 1 L = 1000 mL
3 L = 3 × 1000 or 3 000.= 3000 mL
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
. = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
= 0.4 g
.
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
= 0.4 g
.
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or 400
= 0.4 g
.
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or .400 = 0.4 g
Metric Conversions with
Conversion Factor Method
 DIVIDE
to convert from a smaller unit to a
larger unit, or move the decimal point to
the left.




Example: 400 mg = ? g
THINK: Smaller to Larger: ()
Equivalent: 1 g = 1000 mg
400 mg = 400  1000 or.400 = 0.4 g
Conversion Slide
 You
can use this diagram when converting
dosages within the metric system.
Move decimal point 3 places to the left for each step.
kg
g
mg
mcg
Move decimal point 3 places to the right for each step.
Approximate Equivalents
1 g = gr xv
gr i = 60 mg or gr i = 65 mg (in select instances)
1 t = 5 mL
1 T = 3 t = 15 mL =
ss
i = 30 mL = 6t
1 L = qt i = 32 = pt ii = 4 cups
pt i = 500 mL = 16 = 2 cups
1 cup = 250 mL = viii
1 kg = 2.2 lb
1 in = 2.5 cm
Conversion Clock
60 mg
gr i
45 mg
gr ¾
gr ¼
gr ss
30 mg
15 mg
Weight and Volume Equivalents
VOLUME EQUIVALENTS
6
t
30
5
mL
Weight and Volume Equivalents
WEIGHT EQUIVALENTS
g
15
gr
1000
60
mg
Short-cut Conversion

Rule
Desired amount
 Equivalent that matches the unknown  Quantity
Matching conversion
D
E  Q
M

Example
Convert : gr
1
4
to mg
Approximat e Equivalent : gr i  60 mg
gr
1
4
gr i
 60 mg  15 mg
Understanding Drug
Labels
Sample Medication Label
Sample Medication Label
Sample Medication Label
Sample Medication Label
Parenteral Dosage of
Drugs
Calculation of Drug Dosage by
Formula Method: Parenteral
(continues)
Order: Cleocin 150 mg IM q.12h
 Available: Cleocin (clindamycin phosphate)
300 mg per 2 mL

Calculation of Drug Dosage by
Formula Method: Parenteral
(continued)
 Step 1. Convert

No conversion is necessary.
 Step

2. Think
You want to give less than 2 mL. Actually, you
want to give 150 mg, which is of 21300 mg
and of212 mL, or 1 mL. Calculate to doublecheck your estimate.
Calculation of Drug Dosage by
Formula Method: Parenteral
(continued)
 Step 3. Calculate
1
1
150 mg
D
2
Q 
 2 mL  mL 1mL
H
300 mg
2
2
1
Given intramuscularly every 12 hours.
Select a 3 mL syringe, and measure 1 mL of
Cleocin 300 mg/2 mL.
Calculation by Formula Method:
Parenteral with Conversion
(continues)
Order: Robinul 150 mcg IM
stat
 Supply: Robinul 0.2 mg per
mL

Calculation by Formula Method:
Parenteral with Conversion
(continued)
 Step 1. Convert


Equivalent: 1 mg = 1000 mcg
0.2 mg = 0.200 .= 200 mcg
 Step

2. Think
You want to give less than 1 mL but more than
0.5 mL. Don’t be fooled into thinking 0.2 mg is
less than 150 mcg. You can see that 0.2 mg
is more than 150 mcg; because 0.2 mg = 200
mcg, which is more than 150 mcg.
Calculation by Formula Method:
Parenteral with Conversion
(continued)

Step 3. Calculate
3
150 mcg
D
3
Q
 1mL mL  0.75 mL
H
200 mcg
4
4
Given intramuscularly immediately.
Select a 1 mL syringe, and measure 0.75 mL of
Robinul 0.2 mg/mL. You may have to change
needles, as this is an IM injection.
Guidelines for Syringe Selection
(continues)
 Calculate
dose volumes and prepare
injectable fractional doses in a syringe
using these guidelines:

Standard doses more than 1 mL: Round to
tenths and measure in a 3 mL syringe. The 3
mL syringe is calibrated to 0.1 mL increments.
• Example: 1.53 mL is rounded to 1.5 mL and drawn
up in a 3 mL syringe.
Guidelines for Syringe Selection
(continued)

Small (less than 1 mL), critical care, or
children’s doses: Round to hundredths and
measure in 1 mL syringe. The 1 mL syringe is
calibrated in 0.01 increments.
• Example: 0.257 mL is rounded to 0.26 mL and
drawn up in a 1 mL syringe.

Amounts of 0.5–1 mL calculated in tenths can
be accurately measured in either a 1 mL or 3
mL syringe.
Reconstitution of
Solutions
Parts of Solutions
Reconstitution Drug
Parenteral Solution from a Solid
Solute
Solvent or diluent
4.8 mL sterile water
Solid solute
Zithromax 500 mg
5 mL reconstituted solution
Zithromax 100 mg/mL
Reconstitution Label for
Zithromax
1/10/xx, 0800, reconstituted as
100 mg/mL. Expires 1/17/xx,
0800. Keep refrigerated. G.D.P.
Parenteral Solution Reconstitution
Procedure (continues)
Order: Kefzol 225 mg IM q.6h
Parenteral Solution Reconstitution
Procedure (continued)
Withdraw 1 mL
Kefzol solution for
the ordered dosage
of 225 mg
Inject 2 mL air
into sterile
water diluent
vial
Withdraw
2 mL
sterile
water
Make Kefzol
500 mg in 2.2 mL
reconstituted
Add 2 mL sterile
water to Kefzol solution for Kefzol
225 mg/mL
500 mg powder
and shake well
Multiple-Strength Reconstitution
Drug
Different IM and IV Reconstitution
Instructions
Reconstitution Drug Order
(continues)
 Order:
Solu-Medrol 200 mg IV q.6h
Reconstitution Drug Order
(continued)
 Supply:
500 mg vial of powdered SoluMedrol for IM or IV injection with directions
on the left side of the label that state,
“Reconstitute with 8 mL Bacteriostatic
Water for Injection with Benzyl Alcohol.
When reconstituted as directed each 8 mL
contains: Methylprednisolone sodium
succinate equivalent to 500 mg
methylprednisolone (62.5 mg per mL).”
Reconstitution Dosage
Calculation (continues)
 What


do we know?
First, to fill the order, how much and what type
of diluent must you add? The directions state
to add 8 mL of bacteriostatic water for
injection with benzyl alcohol.
Second, what is the supply dosage of the
reconstituted Solu-Medrol? When adding 8
mL of diluent, the supply dosage is 62.5
mg/mL.
Reconstitution Dosage
Calculation (continued)


Third, what is the resulting total volume of this
reconstituted solution? The total volume is 8
mL. You know this because 62.5 mg/mL × 8
mL = 500 mg.
Finally, how many full doses of Solu-Medrol
are available in this vial? The vial contains
500 mg and the order is for 200 mg. There
are two full doses in the vial. A reconstitution
label is needed.
Reconstitution Dosage
Calculation (continued)
 This
means that you have available a vial
of 500 mg of Solu-Medrol to which you will
add 8 mL of diluent. The final yield of the
solution is 62.5 mg per mL, which is your
supply dosage. Calculate one dose.

Step 1. Convert
• No conversion is necessary
• Order: Solu-Medrol 200 mg IV q.6h
• Supply: 62.5 mg/mL
Reconstitution Dosage
Calculation (continued)

Step 2. Think
• You want to give more than 1 mL. In fact, you
want to give more than three times 1 mL.

Step 3. Calculate
200 mg
D
Q 
 1mL  3.2 mL
H
62.5 mg
given intravenously every 6 hours
1/30/xx, 0800, reconstituted
as 62.5 mg/mL. Expires
2/01/xx, 0800, store at room
temperature 68-77°F. G.D.P.
Solution Strength (continues)
 When
a fraction expresses the strength of
a solution made from a liquid concentrate:



The numerator of the fraction is the number of
parts of solute.
The denominator of the fraction is the total
number of parts of total solution.
The difference between the denominator (final
solution) and the numerator (parts of solute) is
the number of parts of solvent.
Solution Strength (continued)
 Example:



1
3
strength nutritional formula
1 part concentrate
3 parts of total solution
3 – 1 = 2 parts solvent (water)
Calculating Solutions
 To

prepare solutions:
D (Desired solution strength) × Q (Quantity of
desired solution) = X (Amount of solute)
Or you can apply ratio-proportion to find the
amount of solute:
Ratio for desired solution strength 

Amount of solute
Quantity of desired solution
Quantity of desired solution – Amount of liquid
solute = Amount of solvent
Solution Calculation (continues)
 Example:
Suppose a physician orders a
2
patient’s wound irrigated with 3 strength
hydrogen peroxide and normal saline
solution q.4h while awake. You will need
60 mL per irrigation and will do 3 irrigations
during your 12 hour shift. You will need to
prepare 60 mL × 3 irrigations = 180 mL
total solution. How much stock hydrogen
peroxide and normal saline will you need?
Solution Calculation (continued)
 Step

No conversion is necessary.
 Step

1. Convert
2. Think
2
3
You want to make strength, which means 2
parts solute (concentrated hydrogen peroxide)
to 3 total parts solution. The amount of
solvent is 3 – 2 = 1 part saline. Because you
need 180 mL of solution, you estimate that
you will need 32 of it as solute (120 mL) and 31
of it as solvent (60 mL).
Solution Calculation (continued)

Step 3. Calculate
2
D  Q   180 mL  120 mL of solute
3
Or, use ratio-proportion, if you prefer.
2
X mL (solute)

3 180 mL (solution)
3 X  360
3X 360

3
3
X  120 mL of solute (hydrogen peroxide)
Using Ratio-Proportion
to Calculate Dosages
Three Steps to Dosage Calculation:
Ratio-Proportion Method
 Step

Convert all units to the same system, and all
units to the same size.
 Step

1. Convert
2. Think
Estimate the reasonable amount.
 Step
3. Calculate
Dosage on hand
Dosage desired

Amount on hand X Amount desired
Calculation of Drug Dosage by
Ratio-Proportion
clindamycin 0.6 g IV q.12h
 Supply: Cleocin phosphate (clindamycin)
300 mg/2 mL
 Order:
Calculation of Drug Dosage by
Ratio-Proportion
 Step

1. Convert
Equivalent: 1 g = 1000 mg
1g
0.6 g

1000 mg X mg
X  0.6X  1000  600 mg
0.6 g  600 mg
 Step

2. Think
You want to give more than 2 mL. In fact, you
want two times 2 mL or 4 mL.
Calculation of Drug Dosage by
Ratio-Proportion
 Step
3. Calculate
Dosage on hand
Dosage desired

Amount on hand X Amount desired
300 mg 600 mg

2 mL
X mL
300 X  1200
300X 1200

300
300
1200
X
 4 mL given intravenou sly every 12 hours
300