Homeopathic dilution calculator
The dilution calculator converts a labelled potency into its underlying dilution factor and translates between the scales still in active use. The reader is usually a practitioner verifying a prescription, a student moving between continental and Anglo-American conventions, or a pharmacy hand preparing a dispensing label.
Four scales recur in the canonical literature: the centesimal (CH or C), the decimal (DH, D, or X), the fifty-millesimal — the LM or Q potency — and the Korsakovian (CK or K) single-glass scale Hahnemann's later students adopted. Each has a fixed dilution factor per step and a fixed succussion protocol. Mixing them is the most common notation mistake a calculator exists to catch.
Scales a practitioner-grade calculator must cover
| Scale | Notation | Dilution per step | Where it appears |
|---|---|---|---|
| Centesimal | 6CH, 30C, 200CH | 1:100 | Continental Europe, India, Latin America |
| Decimal | 6X, 12DH | 1:10 | Germany, Anglo pharmacy notation |
| Fifty-millesimal (LM / Q) | LM1, Q3 | 1:50,000 with 100 succussions per step | Sankaran-school and revised-classical practice |
| Korsakovian | 200K, 1MK | 1:100 single-glass | High potencies, U.S. and U.K. pharmacy |
A calculator therefore needs four behaviours: convert between scales where the conversion is meaningful (CH↔X has a clean 2× step ratio; CH↔LM does not); flag the conversions that are not meaningful and explain why; and switch to scientific notation at high potencies.
Dilution arithmetic is descriptive, not therapeutic. The output is a notation conversion and a dilution-factor display; the clinical reading of any given potency belongs with the remedy, not the math.
From 12C (or 24X) upward, the dilution factor is large enough that scientific notation is the only legible display.
Practical use
Most practitioners reach for a conversion twice a week: once to read a prescription written in a scale they don't routinely use, once to verify a label before dispensing. For one-off conversions and for teaching, a stand-alone widget is the right tool; for working cases, potency notation belongs inside the case manager next to the prescription itself, where the Similia workflow surfaces it.
A calculator without scale-mixing guardrails can cause more notation errors than it prevents — the practitioner assumes the conversion is meaningful where it is not (LM↔CH being the canonical trap). The cleaner behaviour is to refuse the meaningless conversion outright with a one-line explanation of why the scales are incommensurable, rather than render a number that looks authoritative.
References
Hahnemann, S. (1842) Organon of the Medical Art, 6th edition, §270 and footnote on the fifty-millesimal scale; Boericke & Tafel translation, 1922.
Deutscher Apotheker Verlag (2020) Homöopathisches Arzneibuch (HAB), monograph on decimal (D) dilutions.
Sankaran, R. (1994) The Substance of Homeopathy, Homeopathic Medical Publishers, Bombay, chapter on LM potencies.
United States Homoeopathic Pharmacopoeia Convention (2023) Homoeopathic Pharmacopoeia of the United States (HPUS), general pharmacy chapter on Korsakovian (K) dilution.
Korsakov, S. N. (1832) on single-glass high-potency dilution, as codified in the modern HPUS.