Equations and Calculators
Published April 30, 2026 by Diana D
A reference of common clinical pharmacokinetic and metabolic equations for use in acute and ambulatory care settings. Formulas are organized by clinical category. Normal reference ranges are noted where applicable.
⚠️ These equations are clinical tools. Always interpret results in the context of the full clinical picture. Treat the patient as a whole, not the number.
Metabolic
| Equation |
Formula |
Notes |
| Anion Gap nl 8–12 |
Na − (Cl + HCO₃) |
Elevated AG suggests organic acidosis (MUDPILES). Correct for albumin: AG + 2.5×(4 − Albumin) |
| Calculated Osmoles |
(2×Na) + (Glu/18) + (BUN/2.8) + (EtOH/4.6) |
— |
| Osmolal Gap nl <10 |
Measured Osm − Calculated Osm |
Elevated gap suggests toxic alcohols (methanol, ethylene glycol, isopropanol) |
| Corrected Na hyperglycemia |
Measured Na + 2.4 × (Glu − 100) ÷ 100 |
Some guidelines use 1.6 mEq/L per 100 mg/dL; 2.4 preferred at higher glucose levels |
| Corrected Ca hypoalbuminemia |
Ca + 0.8 × (4 − Albumin) |
Only for total calcium; use ionized Ca when available in critically ill |
Renal Function
| Equation |
Formula |
Notes |
| CrCl (Cockcroft-Gault) |
[(140 − age) × Wt (kg)] ÷ [SCr × 72] × 0.85♀ |
Use ABW in obesity if ABW < IBW; use IBW or adjusted BW otherwise. Standard for drug dosing |
| FENa Pre-renal <1% |
(UNa × PCr) ÷ (PNa × UCr) × 100 |
Intrinsic renal >2%; unreliable if diuretics given. Use FEUrea instead: <35% = pre-renal |
| Total Body Water (TBW) |
Wt (kg) × 0.6 |
Use 0.5 for female/elderly; 0.6 for infants. Used in sodium correction formulas |
Sodium Disorders
| Equation |
Formula |
Notes |
| Δ[Na]/L infusate Hyponatremia |
([Na]inf − [Na]serum) ÷ (TBW + 1) |
Adrogue-Madias equation. Max correction: ≤10–12 mEq/L per 24h to prevent osmotic demyelination |
| Rate of Infusion Hyponatremia |
1000 × TBW × (desired Na − serum Na) ÷ ([Na]inf × time (h)) |
Result in mL/h. Reassess frequently — TBW and Na are dynamic |
| Free Water Deficit Hypernatremia |
TBW × [(Serum Na ÷ 140) − 1] |
Replace deficit slowly: max 10 mEq/L/24h correction to avoid cerebral edema |
| Δ[Na]/L infusate Hypernatremia |
([Na]inf + [K]inf − [Na]serum) ÷ (TBW + 1) |
Accounts for potassium content of infusate (e.g., LR, NS with KCl). Negative value = lowers Na |
| Total Infusion Volume Hypernatremia |
(Desired Na − Serum Na) ÷ Δ[Na]/L infusate |
Result in liters. Rate = total (mL) ÷ 24h |
Pharmacokinetics
| Parameter |
Formula |
Notes |
| Volume of Distribution (Vd) |
Total drug in body ÷ Plasma concentration (Cp) |
Units: L or L/kg. High Vd = extensive tissue distribution |
| Half-life (t½) |
0.693 × Vd ÷ CL |
Steady state reached in ~4–5 half-lives |
| Loading Dose |
Vd × Target Cp ÷ F |
F = bioavailability (1.0 for IV). Used to rapidly achieve therapeutic levels |
| Maintenance Dose |
CL × Target Css × τ ÷ F |
τ = dosing interval; Css = target steady-state concentration |
| Clearance (CL) |
Dose × F ÷ AUC |
CL = CLrenal + CLhepatic. Units: L/h or mL/min |
| Elimination Rate Constant (Ke) |
ln(C₁/C₂) ÷ Δt |
C₁ and C₂ are concentrations at times t₁ and t₂; Ke = 0.693 ÷ t½ |
Hepatic/Nutrition
| Equation |
Formula |
Notes |
| Child-Pugh Score |
Bili + INR + Albumin + Ascites + Encephalopathy |
Class A = 5–6 pts, B = 7–9, C = 10–15. Guides drug dosing in hepatic impairment |
| Harris-Benedict (Male) |
66 + (13.7×W) + (5×H) − (6.8×age) |
W in kg, H in cm. Multiply by activity/stress factor (1.2–2.0) for total energy needs |
| Harris-Benedict (Female) |
655 + (9.6×W) + (1.8×H) − (4.7×age) |
Same units and stress factor as male equation |
Pediatric
| Equation |
Formula |
Notes |
| Fluid Maintenance 4-2-1 Rule |
4 mL/kg/h (1st 10 kg) + 2 mL/kg/h (2nd 10 kg) + 1 mL/kg/h (remainder) |
Daily equivalent: 100/50/20 mL/kg/day. Adjust for clinical status and insensible losses |
| BSA — Mosteller |
√[ Ht (cm) × Wt (kg) ÷ 3600 ] |
Result in m². Used for chemotherapy and weight-sensitive dosing in pediatrics and oncology |
| IBW (Children) |
(Age × 2) + 8 |
Approximation for ages 1–12 years in kg. Not applicable to infants or adolescents |
Clinical Calculators
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References: Lexicomp Online; Dipiro's Pharmacotherapy, 12th ed.; Winter's Basic Clinical Pharmacokinetics, 6th ed. Accessed April 2026.
This resource is intended for educational and reference purposes only. It is not a substitute for clinical judgment. Institutional policies, protocols, and locally approved guidelines take precedence over the information presented here. Clinicians should always consult their own institution’s policies and applicable references before making therapeutic decisions.
