Appendix H · Units, Measures, and Physiological Constants

How to use this appendix

Physiology is quantitative, and most of the confusion students report about it is not conceptual but dimensional: they know what osmolality means and cannot convert to it; they know the alveolar gas equation exists and cannot find it; they read a calcium of 9.2 and a calcium of 2.3 in two different sources and do not immediately see that these are the same patient.

This appendix collects the numbers and the arithmetic in one place. Sections H.1 through H.4 are conversion machinery. Section H.5 is the reference table of normal physiological values, and it is the section worth actually learning — anchor values are what let you recognize an abnormal number instantly, which is a large fraction of clinical reasoning and a larger fraction of exam performance. Section H.7 collects every equation used in this book, each stated once in plain English and once in symbols, because an equation you can say in words is an equation you can apply to a case.

Following the convention of the rest of the book, US conventional units are given first and SI in parentheses, since that is what US clinical settings use. Appendix B gives full reference intervals in both.

H.1 SI units and prefixes

Base units

Derived units used in this book

Prefixes

A note on deci-: the deciliter is nearly extinct outside clinical medicine, and it is the single commonest source of factor-of-ten errors on exams. Whenever you see mg/dL, multiply by 10 to get mg/L before doing anything else.

H.2 Conversions

Length

Anchors: red blood cell ≈ 7–8 µm; plasma membrane ≈ 7 nm; alveolar wall 0.2–0.6 µm; sarcomere at rest ≈ 2.0–2.2 µm; adult small intestine ≈ 6 m.

Mass

A useful mental shortcut: kg ≈ lb ÷ 2, minus 10%. For 176 lb: 88 − 8.8 ≈ 79 kg (exact 79.8 kg).

Volume

Pressure

This is the conversion set students actually need, because respiratory physiology uses cm H₂O, cardiovascular physiology uses mm Hg, and SI insists on kPa.

Two facts to carry: 1 mm Hg ≈ 1.36 cm H₂O (mercury is 13.6 times denser than water, and the conversion is that ratio divided by ten because of the centimeter), and 1 kPa ≈ 7.5 mm Hg, so a systolic of 120 mm Hg is 16 kPa.

Anchors: atmospheric pressure at sea level 760 mm Hg; central venous pressure 2–8 mm Hg (about 3–11 cm H₂O); intrapleural pressure at rest −4 mm Hg; a spirometer's maximal inspiratory pressure is quoted in cm H₂O because the pressures are small.

Energy

The capital-C "Calorie" on a food label is a kilocalorie: 1 Calorie = 1 kcal = 1,000 small calories. Fuel values: carbohydrate and protein 4 kcal/g (17 kJ/g), fat 9 kcal/g (37 kJ/g), ethanol 7 kcal/g (29 kJ/g).

Temperature

H.3 Concentration units

This is the section worth reading slowly. Five units describe "how much solute," they are not interchangeable, and the distinctions carry real physiology.

Molarity (M, mol/L) — moles of solute per liter of solution. Convenient because you measure volume, which is why nearly all laboratory values are molar.

Molality (m, mol/kg) — moles of solute per kilogram of solvent. Independent of temperature, because mass does not expand when warmed and volume does. Physical chemists prefer it; physiologists use it for the reason below.

Osmolarity (Osm/L) — moles of osmotically active particles per liter of solution. The distinction from molarity is dissociation: 1 mol of glucose gives 1 osmole, but 1 mol of NaCl gives ≈2 osmoles because it separates into Na⁺ and Cl⁻, and 1 mol of CaCl₂ gives ≈3.

Osmolality (Osm/kg) — the same count of particles, per kilogram of water. In dilute biological fluids the numerical difference from osmolarity is about 1%, so the words are often used loosely — but laboratories measure osmolality, because it is what a freezing-point depression osmometer actually determines and because it is unaffected by the volume displaced by plasma proteins and lipids. That last point matters clinically: in severe hyperlipidemia or hyperproteinemia, plasma sodium concentration per liter of plasma falls while sodium per kilogram of water is normal — pseudohyponatremia — and osmolality reveals the artifact.

Equivalents (Eq, mEq/L) — moles of charge. One equivalent is one mole of a monovalent ion, or half a mole of a divalent ion. Electrolyte balance is a charge-balance problem, not a particle-count problem, so cardiology and nephrology quote mEq/L.

mEq/L = mmol/L × valence. For Na⁺, K⁺, Cl⁻, and HCO₃⁻ (all monovalent) the two numbers are identical, which is why students who only ever handle those four never notice the distinction — until they meet Ca²⁺ or Mg²⁺, where mEq/L is twice mmol/L.

Worked conversions

The two conversions to memorize outright, because they appear constantly: glucose mg/dL ÷ 18 = mmol/L, and calcium mg/dL ÷ 4 = mmol/L. A fasting glucose of 126 mg/dL, the diabetes threshold, is 7.0 mmol/L. A calcium of 8.0 mg/dL is 2.0 mmol/L.

H.4 Body surface area, and why doses use it

Mosteller formula (the one used in practice):

BSA in square meters equals the square root of height in centimeters times weight in kilograms, divided by 3,600.

BSA (m²) = √[ height(cm) × weight(kg) / 3600 ]

Du Bois formula (older, still cited): BSA = 0.007184 × height(cm)^0.725 × weight(kg)^0.425

Reference values: adult male ≈ 1.9 m², adult female ≈ 1.6 m², newborn ≈ 0.25 m². A 165 cm, 80 kg adult: √(165 × 80 / 3600) = √3.67 = 1.92 m².

Doses are indexed to BSA rather than body weight because the physiological variables that determine drug handling — cardiac output, glomerular filtration rate, basal metabolic rate, extracellular fluid volume — scale with surface area more closely than with mass. This is a consequence of the general allometric relationship between metabolic rate and body size, and it matters most where the therapeutic window is narrow: chemotherapy, and pediatric dosing, where a child's mass is a small fraction of an adult's but their surface area is a much larger fraction. Cardiac index and GFR are reported per 1.73 m² for the same reason.

H.5 Physiological constants and typical values

Body composition and fluid compartments (70 kg adult male)

Cardiovascular (resting adult)

Pressures around the circulation

The arterioles' large pressure drop is the whole reason they are the resistance vessels, and the low pulmonary pressures are the whole reason the right ventricle is thin-walled.

Renal

Respiratory

The arterial PO₂ of 95 versus alveolar 104 is not a mistake: it is the normal alveolar–arterial gradient, produced by bronchial and thebesian venous drainage entering the systemic circulation after gas exchange.

Metabolic

Membrane potentials and ion concentrations

The resting potential sits near the potassium equilibrium potential and far from the sodium one, which tells you immediately that the resting membrane is far more permeable to K⁺ than to Na⁺ (Chapter 11).

The nine defended variables of Chapter 1

H.6 A note on significant figures and clinical precision

An arterial pH is reported to two decimal places and a serum sodium to none, and the difference is not stylistic. Reported precision should reflect two things: what the instrument can resolve, and what magnitude of change is clinically meaningful.

Blood pH is quoted to 0.01 because the entire survivable range spans roughly 6.8 to 7.8, and a change of 0.03 is real and interpretable. Sodium is quoted to the whole number because assay imprecision is on the order of ±2 mEq/L; writing 139.4 implies a resolution the measurement does not possess. Cardiac output from thermodilution is quoted to one decimal because repeat measurements on an unchanged patient vary by roughly 10%; three decimals would be fiction.

Two rules follow. Do not report a calculated value to more digits than its least precise input. An estimated GFR computed from a creatinine measured to two significant figures should be reported as "about 48 mL/min/1.73 m²," not 47.83. And the clinically meaningful change is the unit that matters: a potassium moving from 4.0 to 4.2 is noise, while 5.4 to 6.1 is an emergency, and it is the size of the step relative to the biological consequence — not the number of digits — that tells you which is which.

H.7 Physiological equations collected

Each is given in words first, then in symbols. If you can state the sentence, you can apply the formula to a case you have never seen.

Cardiac output. The heart's output per minute is the volume it ejects per beat times the number of beats. CO = HR × SV · Typical: 70 × 70 mL = 4,900 mL/min ≈ 5 L/min

Ejection fraction. The fraction of the blood in a filled ventricle that leaves it with the next beat. EF = SV ÷ EDV × 100% · Typical: 70 ÷ 120 = 58%

Mean arterial pressure. Because the heart spends about twice as long in diastole as in systole, the average arterial pressure lies nearer the diastolic value — diastolic plus one third of the gap. MAP = DBP + ⅓(SBP − DBP) · For 120/80: 80 + ⅓(40) = 93 mm Hg And, mechanistically: MAP = CO × TPR — flow times resistance, the cardiovascular form of Ohm's law.

Fick principle. Whatever the tissues consume must equal what the blood delivered minus what it carried away, so oxygen consumption divided by the arteriovenous oxygen difference gives cardiac output. CO = VO₂ ÷ (CaO₂ − CvO₂) · 250 mL/min ÷ (200 − 150 mL/L) = 5 L/min

Net filtration pressure (glomerulus). Filtration is what is left when the outward hydrostatic push is reduced by the opposing hydrostatic pressure in the capsule and the inward pull of plasma proteins. NFP = P_glomerular − (P_Bowman + π_plasma) · 55 − (15 + 30) = 10 mm Hg (In systemic capillaries the same balance, written as Starling's equation, gives net filtration at the arteriolar end and net reabsorption at the venular end — Chapter 19.)

Clearance. The volume of plasma completely cleared of a substance per minute equals how much appears in the urine divided by how much is in the plasma. C = (U × V̇) ÷ P, where U is urine concentration, V̇ urine flow rate, P plasma concentration. Inulin clearance = GFR; PAH clearance ≈ renal plasma flow.

Alveolar gas equation. The oxygen available in the alveolus is what you inhaled after humidification, minus what the carbon dioxide displaces. PAO₂ = FiO₂ × (P_atm − P_H₂O) − (PaCO₂ ÷ R) At sea level on room air: 0.21 × (760 − 47) − (40 ÷ 0.8) = 150 − 50 = 100 mm Hg The A–a gradient is then PAO₂ − PaO₂; normally under 15 mm Hg in a young adult, rising roughly as (age ÷ 4) + 4.

Oxygen content of blood. Almost all oxygen rides on hemoglobin; a trivial amount is dissolved. CaO₂ = (1.34 × Hb × SaO₂) + (0.003 × PaO₂) mL O₂ per dL With Hb 15 g/dL and SaO₂ 98%: (1.34 × 15 × 0.98) + (0.003 × 95) = 19.7 + 0.3 = 20 mL/dL. The 0.3 is the entire dissolved fraction, which is why anemia is dangerous at a normal PaO₂.

Oxygen delivery. Delivery is content times flow. DO₂ = CO × CaO₂ × 10 · 5 L/min × 20 mL/dL × 10 = 1,000 mL O₂/min, of which about 250 mL/min is used at rest — a fourfold reserve.

Anion gap. The measured cations minus the measured anions; the difference is made up by unmeasured anions, chiefly albumin. AG = Na⁺ − (Cl⁻ + HCO₃⁻) · Normal 8–12 mEq/L. Correct for hypoalbuminemia by adding 2.5 mEq/L for every 1 g/dL the albumin falls below 4.0.

Henderson–Hasselbalch. Blood pH is set by the ratio of bicarbonate (the metabolic term, controlled by the kidney) to dissolved carbon dioxide (the respiratory term, controlled by the lung). pH = 6.1 + log₁₀([HCO₃⁻] ÷ (0.03 × PaCO₂)) At 24 mEq/L and 40 mm Hg: 6.1 + log(24 ÷ 1.2) = 6.1 + log 20 = 6.1 + 1.3 = 7.40. The famous ratio is 20:1.

Expected compensation. A compensating system moves in the same direction as the primary disturbance and never fully corrects the pH.

Compensation outside these bounds means a second, independent disorder is present. The acute-versus-chronic difference exists because the acute response is pure chemical buffering while the chronic response is renal bicarbonate handling, which takes three to five days.

Corrected calcium. Laboratories report total calcium, but only the free fraction is active; a low albumin lowers the total without lowering the free. Corrected Ca = measured Ca + 0.8 × (4.0 − albumin in g/dL) Calcium 7.6 mg/dL with albumin 2.0: 7.6 + 0.8(2.0) = 9.2 mg/dL — normal, and no treatment indicated.

Calculated plasma osmolality. Sodium and its accompanying anions, plus glucose and urea. Osm = 2[Na⁺] + (glucose ÷ 18) + (BUN ÷ 2.8) · 2(140) + (90/18) + (14/2.8) = 290 mOsm/kg. A measured value more than 10 mOsm/kg above the calculated one — an osmolar gap — indicates an unmeasured osmotically active solute.

Estimated GFR. Modern practice uses the CKD-EPI creatinine equation, which is not hand-calculable; the historical bedside estimate is Cockcroft–Gault: CrCl (mL/min) = [(140 − age) × weight in kg] ÷ (72 × serum creatinine), multiplied by 0.85 for females. Both estimate the same thing: how much plasma the kidneys clear per minute, normalized in reporting to 1.73 m² of body surface area.

Body mass index. Mass divided by height squared — a measure of mass for stature, not of adiposity. BMI = weight(kg) ÷ height(m)² or BMI = 703 × weight(lb) ÷ height(in)² For 176 lb at 5'5" (65 in): 703 × 176 ÷ 4,225 = 29.3. Categories: under 18.5 underweight; 18.5–24.9 normal; 25.0–29.9 overweight; 30.0 and above obese. BMI does not distinguish muscle from fat and misclassifies muscular individuals, which is why waist circumference and body composition measures are used alongside it.

See also: Appendix B · Normal Laboratory Reference Values for full reference intervals, Appendix F · Hormone Reference Table for endocrine values, and Chapter 31 (Fluid, Electrolyte, and Acid-Base Balance) for the physiology behind the acid-base equations.