1. Med Math
MakiNg Nurses’ Lives
Simple in Numbers
Dr. Cyruz P. Tuppal
RN, RM, RT, MSN, MASPED, DMS, DNSc
drcyruztuppal@gmail.com
drcyruztuppal@yahoo.com

2. Tips for success
Pick one method, that is easiest for
YOU
Study it
Learn it
Practice it
Practice it
Practice it

3. Topics
Apothecary System
Weight and Temperature Conversions
Metric System
Med Math
 Administration Doses
 Weight Based Doses
 Drip Rate Calculations

4. Apothecary System
Phased out and replaced by metric
system
Basic Units: grain (gr), dram (dr), drop
(gtt), ounce, (oz), pint (pt), quart (qt)
Equivalents
1dr = 1 tsp = 60 gtts
3tsp = 1 Tbsp

5. Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds
(lbs)
Fact: Weight in kgs X 2.2 = weight in
pounds

6. Conversion Practice
80 kilogram patient, what is weight in
pounds
kilograms X 2.2 = pounds
80 X 2.2 = 176 lbs.

7. Conversion Practice
100 kilogram patient, what is weight in
pounds
kilograms X 2.2 = pounds
100 X 2.2 = 220 lbs.

8. Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds
(lbs)
Fact: Weight in kgs X 2.2 = weight in
pounds
Fact: Weight in pounds / 2.2 = weight
in kilograms

9. Conversion Practice
245 lb patient, what is weight in
kilograms
lbs / 2.2 = kilograms
245 / 2.2 = 111.36 kgs

10. Conversion Practice
140 lb patient, what is the weight in
kilograms
lbs / 2.2 = kilograms
140 / 2.2 = 63.63 kilograms

11. Conversion Practice
The easy way…
Half of weight in pounds, subtract 10%
Example: 180 lbs . . . . . 90
10% of 90 = 9
81 kilograms

12. Conversion Practice
180 lb patient, what is the weight in
kilograms
lbs / 2.2 = kilograms
180 / 2.2 = 81.82 kilograms

13. KNOW YOUR WEIGHT
CONVERSIONS!!!!!

14. Temperature Conversions
Fahrenheit:
 Water Freezes at 32º F
 Water Boils at 212º F
Celsuis:
 Water Freezes at 0º C
 Water Boils at 100º C

15. Temperature Conversions
Fahrenheit  Celsius
Subtract 32 from the temperature
Multiply by 0.556 or 5/9
98.6 – 32 = 66.6
66.6 X 0.556 = 37.03 = 37º C

16. Practice
Convert 103º F to Celsius
103 – 32 = 71
71 X 0.556 = 39.48º C

17. Temperature Conversions
Celsius  Fahrenheit
Multiply by 1.8
Add 32
37º X 1.8 = 66.6
66.6 + 32 = 96.6º F

18. Practice
Convert 44º C to Fahrenheit
44 X 1.8 = 79.2
79.2 + 32 = 111.2 º F

19. On your own
120 º F  Celsius
76.4 º F  Celsuis
60 º C  Fahrenheit
24 º C  Fahrenheit

20. Metric System
System of 10 (base 10)
No fractions only decimals
EASY!

21. Metric System

22. Metric System
Deca 10 Deci 0.1
Hecto 100 Centi 0.01
Kilo 1000 Mili 0.001

23. Metric System
Gram = g 1 L = 1000 mL
Liter = l 1 mL = 1 cc
Kilogram = kg 1 g = 1000 mg
Milliliter = mL 1 mg = 1000 g
Milligram = mg 1cc = 1 mL
Cubic centimeter = 1 g = 0.001 mg
cc 1 mg = 0.001 g
Microgram = g

24. The math
Adding – keep the decimal points in line
Subtracting – see above
Multiplying – multiply without regard to
decimals then add decimal places
Dividing – make the divisor a whole
number and add zeroes to the dividend

25. Addition
4.3795
+ 5.2389
---------------
9.6184

26. Subtraction
9.6184
- 5.2389
---------------
4.3795

27. Multiplication
34.76
X 4.935
--------------
17154060
Add decimal places = 5
171.54060 = 171.5406

28. Division
.75 / .995
75 / 99.5  move decimal
--------------
0.7537

29. Converting
1g = 1000mg so… g  mg X 1000
1mg = 1000 µg so… mg  g X 1000
1g = ???? g = 1,000,000 g

30. Converting
500mL = 0.5L so… mL  L / 1000
The Bottom Line…
To convert from the base to mili X 1000
To convert from mili to the base / 1000
To convert from mili to X 1000
To convert from base to X 1000000

31. Standard Administration
The long formula
dose desired X volume on hand
Volume to administer = ------------------------------------
dose on hand

32. Example
Orders call for 0.5mg Atropine for
symptomatic bradycardia. You have
1mg in 10 mL pre-filled syringe
0.5 mg X 10 mL
------------------ = volume to administer
1.0 mg

33. Example
mg’s cancel out
0.5 X 10mL = 5mL
0.5 mg X 10 mL
------------------ = 5 mL
1.0 mg

34. Another Example
You have 100mg Furosemide in a 10mL
vial. The order is for 40mg
80 mg X 10 mL
------------------ = volume to administer
100 mg

35. Example
mg’s cancel out
80 X 10mL = 800mL/100 = 8
80 mg X 10 mL
------------------ = 8 mL
100 mg

36. Catching on?

37. Try it on your own
Benadryl – 50 mg in 2 mL
Orders are for 12.5 mg
Show your work

38. Benadryl
12.5 mg X 2 mL
------------------ = volume to administer
50 mg
12.5 X 2 = 25 / 50 = 0.5 mL

39. The easy way
Set up an equation
Cross Multiply
Divide
Sound like algebra?

40. The easy way
Order is for 45 mg Benadryl
You have 50 mg in 2 mL
50 45
--- ---
2 X

41. The easy way
50 45
--- ---
2 X
Multiply 45 X 2 = 90
Divide 90 by 50 = 1.8
So… you would administer 1.8 mL = 45 mg

42. Another example
Order is for 3 mg Valium
You have 10 mg in 2 mL
10 3
--- --
2 X

43. Another example
10 3
--- --
2 X
Multiply 3 X 2 = 6
Divide 6 by 10 = 0.6
So… you would administer 0.6 mL = 3 mg

44. Finally, the good stuff
Order is for 145 µg of Fentanyl Citrate
You have 300 mcg in 5 mL
300 145
----- -----
5 X

45. The good stuff
300 145
----- -----
5 X
Multiply 145 X 5 = 725
Divide 735 by 300 = 2.42 = 2.4
So… you would administer 2.4 mL = 145 mg

46. Weight Based Dosage
1. Convert weight to kgs.
2. Calculate the dose to give
3. Calculate the volume to administer

47. Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb
patient in cardiac arrest.
1. Convert the weight to kilograms.
 185 / 2.2 = 84 kgs
Or
 93 – 9.3 = 83.7 = 84 kgs

48. Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb
patient in cardiac arrest.
2. Calculate the dose to give
 84 kgs X 1.5 mg = 126 mg

49. Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb
patient in cardiac arrest.
3. Calculate the volume to administer
 126 mg is the dose we want to give
 10 mL pre-filled syringe containing 100
mg

50. Weight Based Dosage
126 mg X 20 mL
------------------ = volume to administer
200 mg
126 X 20 = 2520 / 200 = 12.6 mL
So, one complete syringe containing 10 mL plus approx. 2.6 mL
from a second syringe

51. Weight Based Dosage
Pediatric
2mg/kg Benadryl for a 25 lb patient
1. Convert weight to kilograms
 25 / 2.2 = 11.36 kgs
Or
 12.5 – 1.2 = 11.3 kgs

52. Weight Based Dosage
Pediatric
2mg/kg Benadryl for a 25 lb patient
2. Calculate the dose to give
 11.3 kgs X 2 mg/kg = 22.6 mg

53. Weight Based Dosage
Pediatric
2mg/kg Benadryl for a 25 lb patient
3. Calculate the volume to administer
22.6 mg X 1 mL
-------------------- = 0.45 mL
50 mg

54. Or the easy way
We know we want 2mg/kg
The child ways 11.3 or roughly 11 kgs
The dose will be 22mg
50 22
--- ---
1 X

55. Or the easy way
50 22
--- ---
1 X
22 X 1 = 22 / 50 = 0.44 mL

56. Drip Rate Calculations
Facts:
 In a 60 drop set, 60 drops = 1 mL
 In a 10 drop set, 10 drops = 1 mL
 In a 15 drop set, 15 drops = 1 mL
 Medications are usually given in 60 gtt sets
 Doesn’t mean you cannot give it in a 10 gtt set
 A 60 drip set is usually called a microdrip
 A 10 drip set is usually called a macrodrip

57. Microdrips
60 gtts = 1 mL
If your dose was 1 mL / hr what would
your drip rate be?
1 gtt / minute
Why?
60 gtts = 1 mL (our dose)
1 drop / min = 60 gtts/hr = 1 mL = 60 gtts

58. Easy huh?

59. Let’s try another
Using a 60 drop set, the dose is 30
mL/hr
60 gtts = 1 mL
30 mL = 1800 gtts
1800 gtts/60 min = 30 gtts/min

60. And another
Using a 60 drop set, the dose is 45
mL/hr
60 gtts = 1 mL
45 mL = 2700 gtts
2700 gtts / 60 min = 45 gtts / hr

61. Dose not in mL/hr
or
mL/min?

62. No sweat…

63. Understanding Concentration
of drug in fluid
A liter bag of fluid = 1000 cc or 1000
mL
If you add 800 mg of a drug to 1000
mL of fluid, what would ur ratio of drug
to fluid be?
800 mg X mg
---------- --------
1000 mL 1 mL

64. Drug in fluid
800 mg X mg
---------- --------
1000 mL 1 mL
800 X 1 = 800 / 1000 = 0.8 mg/mL

65. Drug in fluid
400 mg X mg
---------- --------
250 mL 1 mL
400 X 1 = 400 / 250 = 1.6 mg / mL
Convert mg  mcg  Dopamine
1.6 X 1000 = 1600 mcg / mL

66. You do it
You add 1 gram of Lidocaine to 250 mL
NS
The answer should be in mg/mL
Survey Says….
1 gm = 1000 mg
1000 mg in 250 mL = 4mg/mL

67. Not mL/hr but mg/min
Lidocaine 2mg/min
Mixed 1gm/250ml
1000mg = 1gm
1000mg/250ml = 4mg/ml
Drip rate = 30gtts/min

68. Why?
4mg/ml
The dose is 2mg/min
Using a microdrip (60) 60gtts=1ml
4mg/min = 60
2mg/min = 30
1mg/min = 15

69. The Math
Drug order (mg/min) X IV Drip rate (gtts/ml)
-------------------------------------------
Drug concentration (mg/ml) X 1min
2mg/min X 60 gtts/ml
--------------------------
4mg/ml X 1min

70. 2mg/min X 60 gtts/ml
--------------------------
4mg/ml X 1min
2 X 60 120
-------- = --- 30 gtts
4X1 4

71. Putting it ALL together

72. Dopamine
Weight Based
Over time (mcg/kg/min)

73. Weight based over time
Order is for 7mcg/kg/min
Drug on hand is 800 mg
Drip Set is 60gtts/ml
Pt weight is 220 lbs
IV solution 500mL NS

74. 1. Convert Weight from lbs to kgs
2. Convert measurements (mgs  µg)
3. Determine µg/mL
4. Formula

75. Step 1: Convert Weight
220 lbs  kgs
220 / 2.2 = 100 kgs

76. Step 2: Convert
Measurements
800 mg  µg
Mg  µg = X 1000
800,000 µg

77. Step 3: Determine µg/mL
800,000 µg / 500 mL
1600 µ / mL

78. Step 4: Formula
Drug order (µg/kg) X weight (kgs) X drip
rate
---------------------------------------------------
Concentration on hand (µg/ml) X time
(min)

79. Step 4: Formula
7 µg/kg X 100 kgs X 60 gtts/mL
---------------------------------------
1600 µg/mL X 1 min
7 X 100 = 700 X 60 = 4200
4200 / 1600 = 26.25 = 26 gtts/min

80. Another
Order is for 5 µg/kg/min
Drug on hand is 800 mg = 800,000 µg
60 Drop set
Pt weighs 175 lbs
IV solution 500 mL NS

81. Step 1: Convert Weight
175 lbs / 2.2 = 79.5 ~ 79 kgs
87.5 – 8.7 = 78.8 ~ 79 kgs

82. Step 2: Convert
Measurements
800 mg  µg
800,000 µg

83. Step 3: Determine µg/mL
800,000 mcg / 500 mL
1600 mcg / mL

84. Step 4: Formula
Drug order X weight X drip rate
---------------------------------------
Conc on hand X time
5 mcg/kg X 79 kgs X 60
-----------------------------
1600 mcg/mL X 1 min

85. Step 4: Formula
5 X 79 X 60 = 23700
23700 / 1600 = 14.81 ~ 15 gtts/min

86. An easy check to your work
For 5 µg / kg / min
Take weight in pounds (175)
Drop the last digit (17)
Subtract 1 (16)  in the ballpark, not
completely accurate