Pharmaceutical Calculations
50 calculators in five groups: formulation and manufacturing; solutions, physical pharmacy and stability; analysis and quality control; microbiology, sterility and endotoxins; dosing and pharmacokinetics. Results update as you type, and the governing equation and reference are shown under each one.
References follow the editions in force: USP–NF 2026, BP 2026, Ph. Eur. 12th Edition (12.3, in force since 1 July 2026) and the latest ICH Step 4 guidelines. Last reviewed October 2026. Each reference links to its official page; USP–NF, BP and Ph. Eur. texts need a subscription. All references and pharmacopoeias
Formulation and manufacturing
Solutions, physical pharmacy and stability
Analysis and quality control
Microbiology, sterility and endotoxins
Dosing and pharmacokinetics
% assay: m = LC × SF × 100 ÷ P; µg/mg: m = LC × 1000 ÷ P; IU/mg: m = LC ÷ P, where P is the as-is potency. On a dried, anhydrous or solvent-free basis, P = assay × (100 − W − RS) ÷ 100, with W the water content or LOD and RS the residual solvents (%); leave RS at 0 when LOD is used, since LOD already includes volatile solvents. Take assay and water from the certificate of analysis of the lot in use, and lower the q.s. diluent by the compensation amount so the unit weight stays constant. Example: amoxicillin trihydrate is specified as 900–1050 µg of amoxicillin per mg on the anhydrous basis.
References (current editions):USP–NF 2026, General Notices ↗Ph. Eur. 12.3, General Notices ↗BP 2026 (incl. Ph. Eur. texts) ↗
| Ingredient | mg per unit | % w/w | kg per batch | |
|---|---|---|---|---|
| 80.65% | 50.000 | |||
| 12.90% | 8.000 | |||
| 3.23% | 2.000 | |||
| 2.42% | 1.500 | |||
| 0.81% | 0.500 |
The formula below is an example. Replace the rows with your own.
References (current editions):Remington, 23rd ed. (2020)
High-HLB fraction = (required − low) ÷ (high − low)
References (current editions):Remington, 23rd ed. (2020)Handbook of Pharmaceutical Excipients, 9th ed. (2020)
USP <1174> scale. Carr index ≤ 10 excellent, 11–15 good, 16–20 fair, 21–25 passable, 26–31 poor, 32–37 very poor, ≥ 38 very, very poor; the matching Hausner ratios are 1.00–1.11, 1.12–1.18, 1.19–1.25, 1.26–1.34, 1.35–1.45, 1.46–1.59 and ≥ 1.60. Angle of repose 25–30° excellent up to > 66° very, very poor. Bulk and tapped volumes are measured per USP <616>.
References (current editions):USP–NF 2026 <1174> ↗Ph. Eur. 12.3 2.9.36 ↗BP 2026 (incl. Ph. Eur. texts) ↗
| Size | Body volume (mL) | Maximum fill at this density (mg) |
|---|---|---|
| 000 | 1.37 | 891 |
| 00el | 1.02 | 663 |
| 00 | 0.91 | 592 |
| 0el | 0.78 | 507 |
| 0 | 0.68 | 442 |
| 1 | 0.50 | 325 |
| 2 | 0.37 | 241 |
| 3 | 0.30 | 195 |
| 4 | 0.21 | 137 |
| 5 | 0.13 | 85 |
Nominal body volumes from capsule manufacturers' data; confirm with your supplier. A fill above about 90% of the body volume leaves little margin for density variation.
References (current editions):Remington, 23rd ed. (2020)
Diametral compression of flat-faced round tablets (Fell and Newton): σ = 2F ÷ (π·D·t); for convex tablets use the Pitt equation. 1 kp = 9.807 N. A tensile strength of about 1.7 MPa or more is generally regarded as sufficient for coating and handling, and immediate-release tablets are commonly compressed to a solid fraction of about 0.80–0.90.
References (current editions):USP–NF 2026 <1217> ↗Ph. Eur. 12.3 2.9.8 ↗BP 2026 (incl. Ph. Eur. texts) ↗
Solids applied = core weight × weight gain; solids to spray = applied ÷ efficiency; suspension = solids to spray ÷ solids fraction. Prepare a working excess (often 10–20%) for line priming and losses.
References (current editions):Remington, 23rd ed. (2020)
Base per unit = mould capacity − (drug ÷ displacement value). Displacement value is the grams of drug that displace 1 g of base.
References (current editions):Remington, 23rd ed. (2020)
Ph. Eur. 2.9.5: weigh 20 units taken at random. Not more than 2 may deviate from the average mass by more than the percentage in the table, and none by more than twice that. Tablets: 10% up to 80 mg, 7.5% between 80 and 250 mg, 5% at 250 mg or more. Capsules, single-dose granules and powders: 10% below 300 mg, 7.5% at 300 mg or more. Powders for parenteral use: 10% above 40 mg. Suppositories and pessaries: 5%. Separate values with spaces, commas or new lines.
References (current editions):Ph. Eur. 12.3 2.9.5 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <1216> / Ph. Eur. 2.9.7: for tablets of 650 mg or less take whole tablets as near as possible to 6.5 g; above 650 mg take 10 tablets. Dedust, weigh, rotate 100 times (25 rpm, 4 min), dedust and weigh again. A maximum mean loss of not more than 1.0% is acceptable for most products; if the result is doubtful or above the target, repeat the test twice and use the mean of the three. No tablet may be cracked, cleaved or broken.
References (current editions):USP–NF 2026 <1216> ↗Ph. Eur. 12.3 2.9.7 ↗BP 2026 (incl. Ph. Eur. texts) ↗
The dry solids stay constant: M_dry = M × (1 − x₀/100) and the mass at the target is M_dry ÷ (1 − x_t/100), with moisture as LOD on the wet basis (USP <731>, Ph. Eur. 2.2.32). Dry-basis moisture = x ÷ (100 − x) × 100. The result assumes all the loss is water; volatile granulating solvents also count in LOD.
References (current editions):USP–NF 2026 <731> ↗Ph. Eur. 12.3 2.2.32 ↗BP 2026 (incl. Ph. Eur. texts) ↗
Maximum allowable carryover of product A into the next product B. Health-based (EMA guideline on HBEL, 2014; PIC/S): MACO = PDE × MBS ÷ MDD. Traditional criteria, still used as additional checks: 1/1000 of the smallest therapeutic dose (MACO = STD × MBS ÷ (SF × MDD)) and 10 ppm of A in B. The lowest value governs. Swab limit = MACO × swabbed area ÷ shared area; the measured swab result is compared with the limit multiplied by the recovery. Rinse limit assumes the residue is evenly distributed in the final rinse.
References (current editions):EMA, Guideline on setting health-based exposure limits (HBEL), EMA/CHMP/CVMP/SWP/169430/2012 ↗
Agent (g) = (0.9% × V − drug (g) × E) ÷ E of agent
References (current editions):Remington, 23rd ed. (2020)
Blood and tears freeze at −0.52 °C. W (% w/v) = (0.52 − a) ÷ b, where a is the depression produced by the drug and b that of a 1% solution of the tonicity agent. ΔTf of a 1% solution ≈ 0.576 × E (sodium chloride equivalent).
References (current editions):Remington, 23rd ed. (2020)
mOsm/L = (mg/mL ÷ MW) × number of particles × 1000, assuming complete dissociation. Measured osmolality is lower: 0.9% NaCl calculates to 308 mOsm/L but measures about 286 mOsm/kg. Plasma osmolality is about 285–295 mOsm/kg; peripheral intravenous solutions are usually kept below about 900 mOsm/L. The example is Ringer's injection.
References (current editions):USP–NF 2026 <785> ↗Ph. Eur. 12.3 2.2.35 ↗BP 2026 (incl. Ph. Eur. texts) ↗
pH = pKa + log([base] ÷ [acid]); thermodynamic pKa values at 25 °C. Ionic strength I = ½ Σ cᵢzᵢ², counting monovalent counter-ions. Activity effects lower the apparent pKa (phosphate pKa₂ is about 6.8–6.9 at I ≈ 0.1 M), so adjust the final pH with a calibrated pH meter. Glacial acetic acid is a liquid: volume (mL) = mass ÷ 1.049.
References (current editions):Remington, 23rd ed. (2020)
Van Slyke equation for a single acid/base pair: β = 2.303·C·Ka·[H₃O⁺] ÷ (Ka + [H₃O⁺])²; β is greatest at pH = pKa, where β = 0.576·C. The capacity of water itself (significant below pH 3 and above pH 11) and activity effects are ignored.
References (current editions):Remington, 23rd ed. (2020)
Parts of high = target − low; parts of low = high − target. Strengths share one unit, and portions come out in the unit of the final quantity.
References (current editions):USP–NF 2026 <1160> ↗
1% w/v = 1 g/100 mL = 10 mg/mL; 1 ppm (w/v) = 1 mg/L = 1 µg/mL; ratio strength 1:1000 = 1 g in 1000 mL = 0.1% w/v. The example is adrenaline 1 mg/mL (MW 183.20).
References (current editions):USP–NF 2026 <1160> ↗
mmol = mg ÷ MW; mEq = mmol × valence
References (current editions):USP–NF 2026 <1160> ↗
The IU factor depends on the chemical form, so pick the form named on the raw material certificate of analysis. For vitamin A, 1 IU equals 0.3 mcg RAE.
References (current editions):USP–NF 2026, vitamin monographs ↗
First order: t = ln(C₀/C) ÷ k, so t90 = 0.105 ÷ k and t½ = 0.693 ÷ k; zero order: t = (C₀ − C) ÷ k. Arrhenius: k₂ = k₁·exp[(Ea/R)(1/T₁ − 1/T₂)], R = 8.314 J/(mol·K); Ea of most drug degradations lies between about 50 and 100 kJ/mol. This is an estimate: shelf life is assigned from real-time data per ICH Q1A(R2) and Q1E.
References (current editions):ICH Q1A(R2) (2003) ↗Remington, 23rd ed. (2020)
USP <1079.2> (Haynes): MKT = (ΔH/R) ÷ −ln[(e^(−ΔH/RT₁) + … + e^(−ΔH/RTₙ)) ÷ n], T in kelvin, R = 8.3144 J/(mol·K). The default ΔH = 83.144 kJ/mol (ΔH/R = 10 000 K) is the conventional value. MKT weighs warm periods more than the arithmetic mean does; USP <659> defines controlled room temperature with an MKT not above 25 °C. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <1079.2> ↗USP–NF 2026 <659> ↗
ICH Q1E: the shelf life is the time at which the one-sided 95% confidence limit of the mean regression line meets the acceptance criterion (lower limit for a decreasing attribute, upper limit for an increasing one); limit = ŷ ∓ t₀.₉₅,ₙ₋₂ · s · √(1/n + (t − t̄)²/Sxx). For one batch at room-temperature storage with statistical analysis and no significant change at the accelerated condition, the proposed shelf life may be extrapolated up to twice the long-term period X but not more than 12 months beyond it; with several batches, test poolability first (p > 0.25). Separate values with spaces, commas or new lines.
References (current editions):ICH Q1E (2003) ↗
C_std = W_std × P ÷ V_std; C_sample = (A_u ÷ A_s) × C_std; content per unit = C_sample × V_u ÷ W_u × average weight. The total dilution volume is the final volume multiplied by every dilution factor (e.g. 100 mL, then 5 → 50 mL gives 1000 mL).
References (current editions):USP–NF 2026 <621> ↗Ph. Eur. 12.3 2.2.46 ↗BP 2026 (incl. Ph. Eur. texts) ↗
RRF = response of the impurity ÷ response of the active at equal concentration; when the RRF is unknown, 1.0 is assumed. Reporting, identification and qualification thresholds are given in ICH Q3A(R2) and Q3B(R2).
References (current editions):ICH Q3A(R2) (2006) ↗ICH Q3B(R2) (2006) ↗
c (g/100 mL) = A ÷ (A¹%₁cm × b); ε = A¹%₁cm × MW ÷ 10. Keep absorbance within the linear range of the instrument (typically 0.2–0.8). The example is paracetamol at 257 nm in 0.1 M NaOH, A(1%, 1 cm) = 715.
References (current editions):USP–NF 2026 <857> ↗Ph. Eur. 12.3 2.2.25 ↗BP 2026 (incl. Ph. Eur. texts) ↗
Assay (%) = net volume × (actual ÷ nominal molarity) × E ÷ sample weight × 100, where E is the monograph statement "each mL of titrant is equivalent to … mg". The example is ascorbic acid with 0.05 M iodine (1 mL ≡ 8.806 mg).
References (current editions):USP–NF 2026 <541> ↗
Volumetric KF (USP <921>, Ph. Eur. 2.5.12): F = water in standard ÷ volume; water % = V × F ÷ sample weight × 100. Sodium tartrate dihydrate contains 15.66% water. LOD (USP <731>) also counts volatile solvents.
References (current editions):USP–NF 2026 <921> ↗USP–NF 2026 <731> ↗Ph. Eur. 12.3 2.5.12 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <621>: N = 5.54 (t_R ÷ W_h)²; Rs = 1.18 (t_R2 − t_R1) ÷ (W_h1 + W_h2); T = W₀.₀₅ ÷ 2f. The monograph sets the acceptance criteria; common in-house values are %RSD ≤ 2.0% for five or six injections, T ≤ 2.0 and Rs ≥ 2.0. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <621> ↗Ph. Eur. 12.3 2.2.46 ↗BP 2026 (incl. Ph. Eur. texts) ↗
Least-squares line y = S·x + a. ICH Q2(R2): LOD = 3.3σ ÷ S and LOQ = 10σ ÷ S, here with σ the residual standard deviation of the regression; confirm LOD and LOQ experimentally. Separate values with spaces, commas or new lines.
References (current editions):ICH Q2(R2) (2023) ↗
M = m × purity ÷ ((V − V_blank) × E), where E is the mass (mg) of primary standard that reacts with 1 mL of 1 M titrant: KHP 204.22 (1:1); Na₂CO₃ 52.99 for HCl (2 H⁺ per carbonate) and 105.99 for H₂SO₄; KIO₃ 35.67 and K₂Cr₂O₇ 49.03 for thiosulfate (6 S₂O₃²⁻ each); Na₂C₂O₄ 335.0 for KMnO₄ (5 oxalate : 2 permanganate); Zn 65.38 and CaCO₃ 100.09 for edetate; NaCl 58.44 for AgNO₃. Dry the standard as its monograph directs. Factor f is used in assays as M_actual ÷ M_nominal.
References (current editions):USP–NF 2026 <541> ↗Ph. Eur. 12.3 4.2.2 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <781> / Ph. Eur. 2.2.7: for a solution [α] = 100·α ÷ (l·c), with l in dm and c in g per 100 mL (on the dried or anhydrous basis when the monograph says so); for a neat liquid [α] = α ÷ (l·ρ). Measured at the sodium D line (589.3 nm) and 20 °C (Ph. Eur.) or 25 °C (USP) unless the monograph states otherwise. Dextrorotation is positive.
References (current editions):USP–NF 2026 <781> ↗Ph. Eur. 12.3 2.2.7 ↗BP 2026 (incl. Ph. Eur. texts) ↗
ICH Q3C(R9): concentration limit (ppm) = 1000 × PDE (mg/day) ÷ daily dose (g/day). Option 1 assumes 10 g/day, so the limit is PDE × 100 and applies to every component without further calculation. Option 2 sums the solvent from all components of the daily dose and compares it with the PDE. Class 3 solvents: 50 mg/day (0.5%) without justification. Separate values with spaces, commas or new lines.
References (current editions):ICH Q3C(R9) (2024) ↗USP–NF 2026 <467> ↗
ICH Q3D(R2): permitted concentration (µg/g) = PDE (µg/day) ÷ maximum daily dose (g/day); with Option 1 the dose is taken as 10 g/day. When the expected level is consistently below 30% of the PDE (the control threshold), no additional controls are needed. Class 1 and 2A elements must always be assessed; class 2B and 3 only when intentionally added or, for class 3, for parenteral and inhalation products. PDEs from Table A.2.1, including the 2022 corrections for gold, silver and nickel.
References (current editions):ICH Q3D(R2) (2022) ↗USP–NF 2026 <232> ↗
Limit (ppm) = AI (ng/day) ÷ maximum daily dose (mg/day), since 1 ng/mg = 1 ppm. AIs as published by FDA (Control of Nitrosamine Impurities in Human Drugs) and EMA; for nitrosamine drug-substance-related impurities (NDSRIs) without compound-specific data, the Carcinogenic Potency Categorization Approach (CPCA) assigns 26.5, 100, 400 or 1500 ng/day. When several nitrosamines are present, the sum of each intake divided by its AI should not exceed 1. Check the current agency list for the specific nitrosamine.
References (current editions):FDA, Control of Nitrosamine Impurities in Human Drugs, Rev. 2 (2024) ↗EMA, Q&A on nitrosamine impurities (EMA/409815/2020, current revision) ↗
| Time (min) | Concentration (mg/mL) | % released |
|---|---|---|
| 10 | 0.251 | 45.2% |
| 15 | 0.392 | 71.1% |
| 20 | 0.481 | 87.9% |
| 30 | 0.532 | 98.0% |
| 45 | 0.548 | 102.0% |
Amount at point n = Cₙ × medium volume + v × Σ C of earlier points; without replacement the medium volume falls by v at each sampling. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <711> ↗Ph. Eur. 12.3 2.9.3 ↗BP 2026 (incl. Ph. Eur. texts) ↗
f2 of 50–100 means similar profiles (f1 0–15). Conditions: at least 12 units per product, identical time points, no more than one point above 85% dissolved for either product, and a coefficient of variation of no more than 20% at early points and 10% at later points. If both products release ≥ 85% within 15 minutes, the profiles are similar without f2. Separate values with spaces, commas or new lines.
References (current editions):FDA, Dissolution Testing of IR Solid Oral Dosage Forms (1997) ↗EMA, Guideline on the Investigation of Bioequivalence, Rev. 1 (2010) ↗
USP <905> / Ph. Eur. 2.9.40, for a target content T ≤ 101.5%: M = X̄ when 98.5 ≤ X̄ ≤ 101.5, otherwise 98.5 or 101.5; k = 2.4 for 10 units and 2.0 for 30. With 30 units, no unit may lie outside 0.75M–1.25M (L2 = 25.0). Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <905> ↗Ph. Eur. 12.3 2.9.40 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <85> and Ph. Eur. 2.6.14 / 5.1.10: endotoxin limit = K/M, with K = 5.0 EU/kg (0.2 EU/kg intrathecal) and M the maximum dose per kg of body mass given within one hour (USP takes 70 kg for an average adult). Radiopharmaceuticals: 175/V EU/mL (14/V intrathecal). MVD = endotoxin limit × concentration of the test solution ÷ λ (concentration = 1 when the limit is per mL); MVC = λ × M ÷ K. The test may be run at any dilution up to the MVD; λ is the labelled gel-clot sensitivity or the lowest concentration of the photometric standard curve.
References (current editions):USP–NF 2026 <85> ↗Ph. Eur. 12.3 2.6.14 ↗Ph. Eur. 12.3 5.1.10 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <85> / Ph. Eur. 2.6.14, photometric methods (kinetic turbidimetric or chromogenic): the log–log regression of reaction time on endotoxin concentration must have |r| ≥ 0.980 over at least three standards; the endotoxin found in the positive product control (PPC), less that in the sample, must be 50–200% of the spike. Results below the lowest standard are reported as less than it. The limit is compared with the result corrected for dilution. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <85> ↗Ph. Eur. 12.3 2.6.14 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <85> / Ph. Eur. 2.6.14, gel-clot method: the end-point is the lowest concentration in a series of decreasing endotoxin concentrations that gives a firm clot. Geometric mean end-point = antilog(Σ log eᵢ ÷ f) for f replicate series (four in the confirmation of λ). The labelled sensitivity is confirmed, and the product shows no interference, when the geometric mean lies between 0.5λ and 2λ. A negative limit test at dilution d shows less than d × λ EU/mL in the undiluted sample. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <85> ↗Ph. Eur. 12.3 2.6.14 ↗BP 2026 (incl. Ph. Eur. texts) ↗
F₀ is the equivalent time in minutes at 121 °C delivered to the product, with z = 10 °C for bacterial spores (Ph. Eur. 5.1.5): lethal rate L = 10^((T − T_ref)/z), F₀ = Δt × ΣL. 121.1 °C (250 °F) is also widely used as reference. The Ph. Eur. 5.1.1 reference cycle for aqueous preparations is at least 15 min at 121 °C. Separate values with spaces, commas or new lines.
References (current editions):Ph. Eur. 12.3 5.1.1 ↗Ph. Eur. 12.3 5.1.5 ↗USP–NF 2026 <1229> ↗BP 2026 (incl. Ph. Eur. texts) ↗
First-order inactivation: D = t ÷ (log N₀ − log N) is the time for a 1-log (90%) reduction. After a lethality F the expected survivors per unit are N = N₀ × 10^(−F/D); a terminally sterilised product must reach a sterility assurance level of 10⁻⁶ or better (Ph. Eur. 5.1.1, USP <1229>). F and D must refer to the same temperature (for F₀, D at 121 °C).
References (current editions):Ph. Eur. 12.3 5.1.1 ↗USP–NF 2026 <1229> ↗ISO 11138-1:2017 ↗BP 2026 (incl. Ph. Eur. texts) ↗
USP <61> / Ph. Eur. 2.6.12 plate count: cfu per g or mL = mean colonies × dilution factor ÷ volume plated. Use plates with not more than 250 colonies for TAMC and 50 for TYMC (9-cm plates). USP <1111> / Ph. Eur. 5.1.4: an acceptance criterion of 10¹ cfu allows up to 20, 10² up to 200, 10³ up to 2000, and so on. Separate values with spaces, commas or new lines.
References (current editions):USP–NF 2026 <61> ↗USP–NF 2026 <1111> ↗Ph. Eur. 12.3 2.6.12 ↗Ph. Eur. 12.3 5.1.4 ↗BP 2026 (incl. Ph. Eur. texts) ↗
Mosteller: BSA = √(height cm × weight kg ÷ 3600). DuBois: 0.007184 × W^0.425 × H^0.725. Haycock (also used in children): 0.024265 × W^0.5378 × H^0.3964. BMI = weight ÷ height² (WHO: <18.5 underweight, 18.5–24.9 normal, 25–29.9 overweight, ≥30 obese). Devine ideal body weight: 50 kg (men) or 45.5 kg (women) + 2.3 kg per inch above 5 feet (152.4 cm); adjusted weight = IBW + 0.4 × (actual − IBW) when actual weight exceeds 120% of IBW. For education and checking; dosing decisions belong to the treating clinician.
References (current editions):Mosteller, NEJM 1987 ↗DuBois & DuBois, 1916 ↗Haycock, J Pediatr 1978 ↗WHO BMI classification ↗
Cockcroft–Gault (1976): CrCl (mL/min) = (140 − age) × weight ÷ (72 × SCr mg/dL), × 0.85 for women; most drug labels base renal dose adjustment on it. CKD-EPI 2021 (race-free): eGFR = 142 × min(SCr/κ, 1)^α × max(SCr/κ, 1)^−1.200 × 0.9938^age × 1.012 (women), κ = 0.7/0.9 and α = −0.241/−0.302 for women/men. KDIGO stages: G1 ≥ 90, G2 60–89, G3a 45–59, G3b 30–44, G4 15–29, G5 < 15. 1 mg/dL creatinine = 88.4 µmol/L. For education and checking; dosing decisions belong to the treating clinician.
References (current editions):Cockcroft & Gault, Nephron 1976 ↗Inker et al., NEJM 2021 (CKD-EPI 2021) ↗KDIGO CKD guideline (2024) ↗
Concentration = drug in the bag ÷ volume; mL/h = dose per hour ÷ concentration; for weight-based orders, mg/h = µg/kg/min × kg × 60 ÷ 1000. Drops/min = mL/h × drop factor ÷ 60 (macro sets 10–20 drops/mL, micro sets 60). Use an infusion pump for high-alert drugs. For education and checking; dosing decisions belong to the treating clinician.
References (current editions):USP–NF 2026 <1160> ↗
One-compartment model with first-order elimination; both samples in the elimination phase. k = ln(C₁/C₂) ÷ (t₂ − t₁), t½ = 0.693 ÷ k, CL = k × Vd. Accumulation R = 1 ÷ (1 − e^(−kτ)); C_ss,avg = F × dose ÷ (CL × τ); about 3.3 half-lives give 90% of steady state. Loading dose = C_target × Vd ÷ F; maintenance dose = C_target × CL × τ ÷ F. For education and checking; dosing decisions belong to the treating clinician.
References (current editions):Rowland & Tozer, Clinical Pharmacokinetics and Pharmacodynamics, 5th ed. (2019)
FDA guidance (2005), Estimating the Maximum Safe Starting Dose in Initial Clinical Trials for Therapeutics in Adult Healthy Volunteers: HED (mg/kg) = animal NOAEL × (animal Km ÷ human Km), with human Km = 37 (60 kg adult). The maximum recommended starting dose (MRSD) is the HED from the most appropriate species divided by a safety factor, by default 10. Body-surface-area scaling does not apply to every product (e.g. proteins given intravascularly). For education and checking; dosing decisions belong to the treating clinician.
References (current editions):FDA, Estimating the Maximum Safe Starting Dose in Initial Clinical Trials (2005) ↗