The document provides an overview of various medical math concepts and formulas for calculating dosages and drip rates. Key topics covered include: - Converting between measurement systems like metric, apothecary, and Fahrenheit/Celsius - Calculating dosages using concentration and volume formulas - Determining drip rates using concentration, dosage, and number of drops per minute - Weight-based dosage calculations using patient weight in kg and mg/kg formulas Practice problems are provided for many of these concepts to help users learn and apply the various medical math formulas.

1. Med Math

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 32 º F Water Boils at 212º F Celsuis: Water Freezes at 0 º 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 = 37 º C

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

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

18. Practice Convert 44 º 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 Hecto 100 Kilo 1000 Deci 0.1 Centi 0.01 Mili 0.001

23. Metric System Gram = g Liter = l Kilogram = kg Milliliter = mL Milligram = mg Cubic centimeter = cc Microgram =  g 1 L = 1000 mL 1 mL = 1 cc 1 g = 1000 mg 1 mg = 1000  g 1cc = 1 mL 1  g = 0.001 mg 1 mg = 0.001 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 µ g 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 Convert weight to kgs. Calculate the dose to give 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 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 -------- = --- 4 X 1 4 30 gtts

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. Convert Weight from lbs to kgs Convert measurements (mgs  µg) Determine µg/mL 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