Physicochemical Acid-Base Calculator

Static demo. Has not been validated and results might be inaccurate depending on the clinical context and your laboratory reference ranges. Uses the Stewart acid/base model with Figge-Fencl approximations. Inspired by medischesnippers.nl/stewart.

Strong cations Na⁺ (mmol/L), Ref. 135–145 K⁺ (mmol/L), Ref. 3.5–5.0 iCa²⁺, Ref. 1.15–1.29 mmol/L (4.6–5.3 mg/dL) Mg²⁺ total, Ref. 1.7–2.2 mg/dL (0.70–0.95 mmol/L)

Estimated iMg²⁺: — | — | Calculator estimates ionized Mg²⁺ from total serum Mg with a pH adjustment for SIDa and the Gamblegram.

Strong anions Cl⁻ (mmol/L), Ref. 98–107 Lactate⁻, Ref. 0.5–2.0 mmol/L (4.5–18 mg/dL)

Weak acids Albumin (g/dL), Ref. 3.5–5.0 Phosphate, Ref. 0.8–1.45 mmol/L (2.5–4.5 mg/dL) HCO₃⁻ (mmol/L), Ref. 22–26

Derived from pH and pCO₂ unless the measured BMP HCO₃⁻ override is enabled.

Use measured BMP HCO₃⁻ for Gamblegram (editable)

Fix SIG and make HCO₃⁻ the dependent variable

Blood gas pH, Ref. 7.35–7.45 pCO₂ (mmHg), Ref. 35–45 SBE (mmol/L), Ref. −2 to +2

Additional accounted ions

Add measured ions as fully dissociated strong ions. Each row contributes concentration × charge to SIDa and appears separately in the Gamblegram instead of remaining hidden in SIG.

Common presets:

No additional ions added.

Results

Normal SIG: 0–6 mEq/L.

SIDa Typical 37–43 mEq/L: —
SIDe Typical 35–40 mEq/L: —
SIG Normal 0–6 mEq/L: —
AG With K⁺, typical 12–20 mEq/L: —

Gamblegram

Unknown: —

Values update live. Use the toggle above to show non‑SI units.

Stewart reference values vary by source. This app shows practical ranges that match its normal-default assumptions: SIDa 37–43 mEq/L and SIDe 35–40 mEq/L.

AG here includes K⁺; lab-reported “normal AG” values are often lower when K⁺ is omitted.

Formulas used

\[\begin{aligned} \mathrm{SID_a} &= [\mathrm{Na}^+] + [\mathrm{K}^+] + 2[\mathrm{Ca}^{2+}] + 2[\mathrm{Mg}^{2+}] - [\mathrm{Cl}^-] - [\mathrm{Lactate}^-] \\[8pt] &\qquad + \sum (\text{added cations}) - \sum (\text{added anions}) \\[8pt] \mathrm{SID_e} &= [\mathrm{HCO}_3^-] + \mathrm{Alb}^- + \mathrm{Phos}^- \\[8pt] \mathrm{SIG} &= \mathrm{SID_a} - \mathrm{SID_e} \\[8pt] [\mathrm{HCO}_3^-]_{\text{fixed SIG}} &= \mathrm{SID_a} - \mathrm{SIG}_{target} - \mathrm{Alb}^- - \mathrm{Phos}^- \\[8pt] \mathrm{AG} &= [\mathrm{Na}^+] + [\mathrm{K}^+] - [\mathrm{Cl}^-] - [\mathrm{HCO}_3^-] \\[8pt] [\mathrm{HCO}_3^-] &= 0.03\times pCO_2\times 10^{\,\mathrm{pH}\,-\,6.1} \quad\text{(Henderson--Hasselbalch)}\\[10pt] [\mathrm{iMg}^{2+}]_{est} &= \min\!\left([\mathrm{Mg}]_{total},\;\max\!\left(0,\;0.66[\mathrm{Mg}]_{total}+0.039+0.12(7.40-\mathrm{pH})\right)\right)\\[10pt] \mathrm{Alb}^- &= -\,\frac{[\mathrm{Alb}]_{g/L}}{66.5}\;\sum_i \frac{n_i\,(\pm 1)}{1+10^{\,\pm(pK_{a,i}\,-\,\mathrm{pH})}}\quad\text{(Figge–Fencl v3.0)}\\[10pt] \mathrm{Phos}^- &= [\mathrm{PO_4}]\;\frac{K_1[\mathrm{H}^+]^2 + 2K_1K_2[\mathrm{H}^+] + 3K_1K_2K_3}{[\mathrm{H}^+]^3 + K_1[\mathrm{H}^+]^2 + K_1K_2[\mathrm{H}^+] + K_1K_2K_3}\\[12pt] \textbf{Definitions:}\\[4pt] n_i &\;=\; \text{stoichiometric charge contribution of site }i\; (\pm 1;\text{ e.g. His, Lys, Asp/Glu})\\[6pt] pK_{a,i} &\;=\; \text{site-specific acid dissociation constant for residue }i\\[6pt] K_j &\;=\;10^{-pK_j}\;\text{(so }K_1,K_2,K_3\text{ are phosphate dissociation constants)}\\[6pt] [\mathrm{PO_4}] &\;=\;\text{total inorganic phosphate (mmol/L)}\\[6pt] [\mathrm{Alb}]_{g/L} &\;=\;\text{albumin concentration in g/L (use g/dL × 10)}\\[6pt] [\mathrm{Mg}]_{total} &\;=\;\text{total serum magnesium entered by the user; the calculator estimates ionized Mg from this value for SID}_a\text{ / Gamblegram}\\[6pt] \alpha &\;=\;0.03\;\mathrm{L\cdot mmHg^{-1}}\;\text{(CO}_2\text{ solubility at }37\,^\circ\mathrm{C}\text{)}\\[6pt] \text{Sum over }i &\;\text{runs over albumin titratable residues (His, Lys, Arg, Asp/Glu, Tyr, N/C termini); Site pK values follow Figge-Fencl v3.0 (implemented in }\texttt{js/physiology.js}\text{).}\\[6pt] \end{aligned}\]

References

Figge J, Mydosh T, Fencl V. Serum proteins and acid-base equilibria: a follow-up. J Lab Clin Med. 1992;120(5):713-719. PubMed 1431500
Figge J. Figge-Fencl quantitative physicochemical model of human acid-base physiology (v3.0). 2003–2013. figge-fencl.org (archived)
Stewart PA. Modern quantitative acid-base chemistry. Can J Physiol Pharmacol. 1983;61(12):1444-1461. PubMed 6423247
Kellum JA. Clinical review: reunification of acid-base physiology. Crit Care. 2005;9(5):500-507. PubMed 16277737
Sendroy J Jr, Hastings AB. Studies of the solubility of calcium salts. III. J Biol Chem. 1927;71:797-823. (Phosphoric acid apparent dissociation constants for plasma, 37 °C)
Fencl V, Jabor A, Kazda A, Figge J. Diagnosis of metabolic acid-base disturbances in critically ill patients. Am J Respir Crit Care Med. 2000;162(6):2246-2251. PubMed 11112147