LMHI 2015

The Pharmacy

C, X, and What the Letters Mean on the Label

Explains the centesimal (C) and decimal (X) dilution scales, their notational conventions, and what a given number on a product label translates to in powers of ten. Practical explainer with no therapeutic content.

The scale, the notation and the sugar that carries it/Piece 3 of 5 in this section
A wooden apothecary case of labelled homeopathic vials, arranged in rows, shot from directly above

Labelled by remedy and by potency; what is inside each vial is sugar.Photo: cottonbro studio / Pexels

Rows of empty glass test tubes in a white rack with a few holding colored liquids

C, X or D, and sometimes K: the letter says which scale, the number says how many steps.Photo: Kaboompics / Pexels

Reading the notation

A homeopathic product label carries a number and a letter: 6X, 30C, 200C. The letter names the dilution scale; the number counts the steps taken along it.

X (sometimes written D) denotes the decimal scale, in which each step dilutes the preparation one part in ten. A single X step produces a ratio of 1 in 10, or 10⁻¹. Two steps give 10⁻², and so on. A preparation labelled 6X has passed through six such steps: the dilution factor is 10⁻⁶ — one part in a million.

A chalkboard with 10 to the power of minus 60 worked out in full in chalk, adult hand holding the chalk at the right edge of frame

Sixty zeros, written out.Photo: Kaboompics / Pexels

C denotes the centesimal scale, introduced by Samuel Hahnemann in the Organon der rationellen Heilkunde (first edition, 1810). Each C step dilutes one part in one hundred. A single C step is 10⁻², so the exponents accumulate twice as fast as on the X scale. A 6C preparation carries a dilution factor of 10⁻¹², not 10⁻⁶. At 12C the factor reaches 10⁻²⁴, approaching the zone where Avogadro's number — 6.022 × 10²³ entities per mole — becomes relevant: statistically, fewer than one molecule of the original solute is likely to remain. By 30C, the factor is 10⁻⁶⁰.

The arithmetic is straightforward. For any preparation:

XX scale: dilution factor = 10⁻ⁿ (e.g. 6X = 10⁻⁶)
CC scale: dilution factor = 10⁻²ⁿ (e.g. 6C = 10⁻¹², 30C = 10⁻⁶⁰)
LM/QLM/Q scale: each step = 1 in 50,000 (5 × 10⁻⁵ per step), introduced in the sixth edition of the Organon (1921)
KorsakovKorsakov method: uses a single vial; assumed dilution factor per step differs from standard multi-vial method
  • X scale: dilution factor = 10⁻ⁿ, where n is the number on the label
  • C scale: dilution factor = 10⁻²ⁿ

So 200C is not simply a larger version of 200X. It represents a dilution factor of 10⁻⁴⁰⁰, against 10⁻²⁰⁰ for 200X — a difference of 10²⁰⁰ between them.

A third scale appears on some labels: LM (or Q), introduced by Hahnemann in the sixth edition of the Organon, published posthumously in 1921. Each LM step dilutes one part in 50,000, giving a factor of 2 × 10⁻⁵ per step. LM preparations are not directly comparable to C or X numbers.

A ranked row of glass dilution flasks on a laboratory bench, an adult researcher's hands adjusting one at the near end

Each flask holds one hundredth of what the flask before it held.Photo: Tombson Klarel / Pexels

The Homeopathic Pharmacopoeia of the United States ↗ specifies manufacturing standards for both the centesimal and decimal scales, and the Korsakov single-vial method — in which the same vessel is emptied and refilled at each step rather than a fresh one used — is recognised alongside the multi-vial centesimal method, though the assumed dilution factor per step differs between them.

The label, in short, encodes two pieces of information: which scale (the letter) and how many iterations of that scale (the number). Converting either to a power of ten requires only the multiplication above — nothing more, and nothing less.

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