Pharmaceutical Calculations

Maria Glaucia Teixeira, PhD, is Associate Professor Emeritus in the School of Pharmacy at the University of Wyoming, where she retired after 23 years on the faculty, following 10 years as Professor at the Federal University of Ceara in Fortaleza, Brazil. She has received numerous recognitions for her teaching, including the Top Prof and Excellence in Teaching awards at Wyoming. She received her PhD in Pharmacology at Paul Sabatier University, Toulouse, France.

Joel L. Zatz, PhD, is Professor Emeritus at Rutgers University, New Jersey.

1 Review of Basic Mathematical Principles 6

1. 1. Significant figures 6

1. 2. Rounding Off 9

1. 3. Fractions 10

1. 4. Exponents and Powers 13

1. 5. Estimation 15

1. 6. Units 17

1. 7. Ratio 19

1. 8. Proportion 20

1. 9. Dimensional Analysis 24

2 Systems of Measurement 39

2. 1. Metrology 39

2. 2. The Metric System 39

2. 3. The English Systems 40

2. 3. 1. The Avoirdupois System 40

2. 3. 2. The Apothecary or Troy System 41

2. 4. Measurement of Weight 41

2. 4. 1. Metric Weight 41

2. 4. 2. English Weight 43

2. 4. 2.1. Avoirdupois Weight 43

2. 4. 2. 2. Apothecary Weight 44

2. 4. 3. Practical Weight Equivalents 44

2. 5. Measurement of Volume 46

2. 5. 1. Metric Volume 46

2. 5. 2. English Volume 47

2. 5. 3. Practical Volume Equivalents 47

2. 6. Measurement of Length 49

2. 7. Intersystem Relationships 52

2. 8. Household Equivalents and Metric Estimation 53

3 Prescriptions and Medication Orders 64

3. 1. Prescribing Authority 64

3. 2. Components 67

3. 4. Common Abbreviations 70

3. 5. Outpatient Prescription Drug Orders 78

3. 5. 1. Prescriptions for Manufactured Drug Products 78

3. 5. 2. Prescriptions for Compounded Drug Products 79

3. 5. 2. 1. Types of Compounded Orders 80

3. 5. 2. 1. 1. Formulation Based on Total Quantity 80

3. 5. 2. 1. 2. Formulation Based on Single Dosage Unit 80

3. 6. Inpatient Medication Orders 82

3. 7. Interpretation 87

3. 8. Calculations to Check "DEA" Numbers 88

3. 9. Reducing and Enlarging Formulas 90

3. 10. Parts Formulas 97

4 Weighing and Measuring in Pharmacy Practice 117

4. 1. Measurement Errors 117

4. 2. Indication of Error 118

4. 2. 1. Absolute Error: Indication of Error Based on Maximum Deviation and Significant Figures 118

4. 2. 2. Relative Error: Indication of Error based on Percentage of Estimated Value 121

4. 3. Tolerance in Prescription compounding and Pharmaceutical Manufacturing 122

4. 4. Weighing and Measuring 123

4. 4. 1 Electronic Balances 123

4. 4. 2. Prescription Balances (Class A, Torsion) 124

4. 4. 2. 1. Sensitivity Requirement (SR) 124

4. 4. 2. 2. Minimum Weighable Quantity (MWQ) or Least Weighable (LWQ) 124

4. 4. 2. 3. Percent Error 125

4. 4. 3. Volumetric Devices for Pharmaceutical 128

4. 4. 3. 1. The Meniscus and Effect of Viscosity 128

4. 4. 3. 2. Graduates 129

4. 4. 3. 3. Pipets (pipettes) 129

4. 4. 3. 4. Syringes 130

4. 4. 3. 5. Droppers 130

4. 5. Aliquot Method and Triturations 134

4. 5. 1. Solid-Solid Aliquot Method 134

4. 5. 2. Solid-Solid Triturations 138

4. 5. 3. Liquid-Liquid Aliquots and Triturations 148

4. 5. 4. Solid-Solid Aliquots 153

4. 5. 5. Serial Dilutions 157

4. 6. Density 161

4. 7. Specific Gravity 163

5 Dosage Calculations 181

5. 1. Calculations Involving Dose, Size, Number of Doses, Amount Dispensed, and Quanity of a Specific Ingredient in a Dose 181

5. 2. Dosage Measured by Drops 189

5. 3. Dosage Based on Body Weight 192

5. 4. Dosage Based on Body Surface Area (BSA) 195

5. 5. Pediatric and Geriatric Dose Calculations 204

5. 6. Chemotherapy Dose Calculations 208

6 Drug concentration expressions 228

6.1 Concentration 228

6.2.3 Percent Weight-in-Volume 231

6.2.4 Default Rules for Percentage Expressions 233

6.2.5 Prescriptions and Formulations with Ingredients Listed as Percentage 235

6.2.6 Using Specific Gravity to Calculate the Exact Amount of Solvent in a Solution 240

6.2.7 Converting % w/w into %w/v Using Specific Gravity 243

6.5 Ratio Strength Expressions 251

6.5.1 Ratio Volume-in-Volume 251

6.5.2 Ratio Weight-in-Volume 252

6.6 Other Pharmaceutical Expressions of Drug Concentration 257

6.6.1 Milligrams per Milliliter (mg/mL) 257

6.6.2 Milligrams Percent (mg%) and Miligrams Per Deciliter (mg/dL) 258

6.6.3 Parts Per Million (ppm) and Parts Per Bdillion (ppb) 259

6.6.4 Millimols, Milliequivalents and Milliosmols Per Unit of Volume 262

7 Dilution and Concentration 286

7.1. Problem Solving Methodologies 286

7.1.1. Concentration Principle 286

7.1.2. Mass Balance Equation 290

7.1.2.1. Dilution of Powders or Solid Mixtures 290

7.1.2.2. Mixing Different Strengths 295

7.1.2.3. Modifying the Drug Concentration Of a Prepared Product (Increasing Drug Concentration) 298

7.1.3. The CQ Equation: Concentration X Quantity 298

7.1.3.1. Expanded CQ Equation 303

7.1.4. Algebraic Calculations Using the Concentration Equation and the CQ Equation 307

7.1.5. Alligation Alternate 315

7.1.5.1. Use of Alligation When Combining More Than Two Products 321

7.1.6. Stock Solutions Diluted By the Patient 328

8 Isotonicity 349

8.1 Principles 349

8.2 Sodium Chloride Equivalent Values 350

8.3 Isotonicity By The Sodium Chloride Equivalent Method 353

8.3.1 Sodium Chloride Equivalent: Method 1 354

8.3.2 Sodium Chloride Equivalent: Method 2 357

8.4 Other Tonicity Agents 358

8.5 Isotonicity When One Ingredient Is Already Isotonic 360

8.6 Isotonic Buffered Solutions 362

8.6.1 Using the White-Vincent Method to Adjust Tonicity 362

8.7 Other Methods 365

8.7 Determination of the Tonicity of a Solution (Hypotonic, Isotonic, or Hypertonic) 368

9 Dosage Calculations of Electrolytes 379

9.1 Molarity and Molality 379

9.1.1 Mols & Millimols 380

9.1.2 mmol/mL, mmol/L 383

9.2 Electrolyte Dissociation, Valence, Equivalent and Equivalent Weight 384

9.3 Milliequivalents, mEq/mL, mEq/L 387

9.3.1 Problem Solving Methods for Milliequivalents 388

9.4 Osmolarity (Osmolar Strength) 394

9.4.1 Milliosmoles and mOsm/L 395

10 Calculations for Injectable Medications and Sterile Fluids 422

10.1. Reconstitution of Dry Powders 422

10.1.1. Reconstituting With Volumes Other Than Those On Manufacturer's Label 424

10.1.2. Considering Powder Volume 427

10.1.3. Powders As Compounding Sources of Drugs 429

10.2. Calculations Related to Units/mL (Unsulin, Heparin) and Other Units of Potency 430

10.2.1. Calculations of Insulin Single Dose and Combinations 431

10.2.2. Calculations of Heparin Doses 435

10.3. Intravenous Admixtures 437

10.4. Extemporaneous IV Fluids 439

10.5. Flow Rates in Intravenous Sets 441

11 Enteral and Parenteral Nutrition 457

11.1. Screening and Assessment of Nutritional Needs 457

11.1.1. Body Mass Index (BMI), Waist Circumference and Associated Disease Risks 458

11.1.2. Assessment of Malnutrition 460

11.2. Enteral Nutrition 460

11.3. Parenteral Nutrition (PN): 2-in-1 and 3-in-1 Formulations 462

11.4. Calculation of Nutritional Requirements 463

11.4.1. Caloric Requirement Equations 464

11.4.2. Fluid Requirement 469

11.4.3. Protein Requirement (Nitrogen) 469

11.4.4. Carbohydrate and Fat Requirements 472

11.4.5. Micronutrient Requirements (Electrolytes, Vitamins, Trace Elements) 473

11.5. Calculations for Compounding Parenteral Nutrition 473

11.5.1. Calculation of Electrolytes 474

11.5.2. Calculation of Carbohydrate and Fat 477

11.5.3. Calculation of Protein 479

11.5.4. Calculation of Other Additives 482

11.6. Calculations Related to the Design of a PN 488

12 Miscellaneous Practical Calculations in Contemporary Compounding 504

12.1. Compounding with Manufactured Dosage Forms 505

12.1.1. Non-Sterile Products 505

12.1.2. Sterile Products 508

12.2. Suppository Calculations 511

12.2.1. Calibration of Molds 511

12.3. Determination of Amount of Base/Powder Occupied By the Drug(s): Solid Dosage Forms 512

12.3.1. Density Factor Method 513

12.3.2. Quantity/Volume of Base Occupied by Drug (or Density Ratio Method) 520

12.3.3. Dosage Replacement Factor Method 521

12. 4. Lozenges and Lollipops 526

12.4.1. Lozenge/Lollipop Mold Calibration 526

12. 5. Selecting a Capsule Size 527

12.5.1. The Rule of Sixes 527

12.5.2. The Rule of Seven 529

12.5.3. Volume Occupied By Active Ingredient In a Capsule 531

12. 6. Primary Emulsion Calculations (4:2:1 ratio) 532

12. 7. A Little Touch of Veterinary Compounding 534

APPENDICES 548

Appendix 1: Systems of Measurement 549

Appendix 2: Atomic weights and symbols of some chemical elements with pharmaceutical importance 552

Appendix 3: Calibration of Medicinal Dropper 556

Appendix 4: Solutions used to compound parenteral nutrition (PN) 558

Appendix 5: Conversions: temperature, time, proof strength 563

Appendix 6: HLB system 568

Appendix 7: Base versus salt or ester forms of drugs 571

Appendix 8: pH, Buffers and Buffer Capacity 574

Appendix 9: Normal Concentration 582

Appendix 10: Biologics for Immunization 584

Literature Consulted 588

Reviews of the prior edition: "a well-structured approach to the topic " (Drug Development and Industrial Pharmacy)

"...a perfectly organized manual that serves as a expert guide " (Electric Review)