Potency converter — centesimal, decimal, LM

Homeopathic preparations are labelled in three notation systems: centesimal, decimal, and LM (also written Q). Each centesimal step is a 1:99 serial dilution with succussion; each decimal step is a 1:9 serial dilution with succussion; each LM step is a 1:50,000 serial dilution with succussion onto medicating globules, as defined in §270 of the Organon, 6th edition.

What the three scales mean

Centesimal, written C (or CH), counts hundredfold dilution steps: 1C is one part starting material in ninety-nine parts diluent, succussed; 30C is that step repeated thirty times. Decimal, written X (or D), counts tenfold dilution steps, so 6X is six tenfold dilutions with succussion at each step. LM, written LM or Q with a Roman or Arabic numeral, counts fifty-thousand-fold dilutions onto medicating globules, with succussion at each step; LM I is the first such step. The LM scale belongs to a repeated low-dose schedule — daily or weekly liquid dosing with succussion before each dose — rather than the single high-potency administration of the centesimal tradition.

Conversion table

Two centesimal steps equal four decimal steps by dilution factor — 1C is arithmetically the same dilution as 2X — but they are not interchangeable in case management. The succussion sequence and the prescribing schedule differ across traditions, and a 30C and a 60X are handled as distinct prescriptions even though the dilution arithmetic matches. The LM scale is not a high-potency continuation of the centesimal scale; it is a parallel notation tied to Hahnemann's late-career revision and to a different posology than the single-dose centesimal practice it grew out of.

When a converter is actually helpful

Notation conversion matters in three recurring situations: reading a historic case write-up that uses a different notation than the local pharmacy stocks, reconciling a case-management note across two software products that default to different scales, and converting a study's reported potency into a comparable notation when reviewing the literature. None of those changes a clinical decision; the notation step is administrative, not prescriptive.

Posology traditions by scale

Classical single-remedy prescribers most commonly work in the centesimal scale, selecting potency by the sensitivity of the patient and the acuity of the presentation — lower centesimals (6C, 12C, 30C) for repeated dosing or sensitive patients, higher centesimals (200C, 1M, 10M) for acute states or constitutional work where the simillimum is clear. The decimal scale is favoured in German-speaking traditions and in organopathic prescribing, where tissue-salt practitioners routinely use 6X. The LM scale, as Hahnemann outlined in the Organon sixth edition, is intended for cases requiring frequent repetition — daily or near-daily dosing in liquid with succussion before each dose — and is particularly applied in chronic case management and for patients who react too strongly to higher centesimals.

Where the converter stops

Conversion is a notation operation. It does not indicate which potency to prescribe; that decision belongs to the materia medica, the repertory analysis, and the practitioner's reading of the individual case. Practitioners who want to work through a case by symptom rather than by potency can search the free repertory at similia.io under the classical hierarchy.

References

Hahnemann, S. (1842) Organon of Medicine, 6th edition, §270, published posthumously 1921.

Schmidt, J. M. (2018) Hahnemann's Q-potencies and the 6th edition of the Organon. Homeopathy, 107(2), 80–87.

Boericke, W. (1927) Pocket Manual of Homœopathic Materia Medica with Repertory, 9th edition — potency notes appended to each remedy entry.

Kent, J. T. (1900) Lectures on Homœopathic Philosophy, lectures XXIX–XXXII on the second and third potencies and the single dose.