In clinic we often hear the question — "What's the difference between a CH and a K potency?" or, more pointedly, "Why are you giving me a K?"
The short answer, the one a patient needs, is this: they are two ways of preparing the same kind of remedy, close enough at the same number that we prescribe them on much the same footing — and at the high potencies, a K (from Korsakov, a Russian homeopath who simplified the way to produce high-potency remedies) is often the only form that exists. That satisfies most. But the question has a longer and more interesting answer.
Homeopathic remedies can be produced using either the Hahnemannian method, which relies on multiple measured vials, or the Korsakovian approach, which utilizes a single vessel with unmeasured residue.
Sometimes this is prompted by a real concern. There is a Table that circulates in homeopathic teaching, especially in France, claiming a fixed correspondence between Korsakovian (K) and centesimal Hahnemannian (CH) potencies: 6K = 4CH, 30K = 5CH, 200K = 7CH, 1,000K = 9CH, 10,000K = 15CH, and so on. Recently it surfaced in a teaching context where it was put to practical use — invoked to justify organ-targeting prescriptions, in a discussion that held low potencies to be best for gentle work on the organs and, more particularly, that CH-prepared low potencies are superior to K-prepared ones. The Table was the bridge between the two claims: it let a high-numbered Korsakovian potency be read as a low centesimal one, and so be dispensed into the organ-prescribing logic that prizes low CH. That makes the Table's correctness a clinical question, not an academic one — a prescription was being licensed by it. It is presented, and used, as if it were a law of the pharmacy.
The irony is immediate, and worth naming before we go further. If, in the same breath, one claims that CH preparations are superior to K preparations and that a K potency can be converted into its CH "equivalent," then the conversion is being used to launder a supposedly inferior K into the status of a superior CH — which quietly concedes that they were not equivalent to begin with. One cannot both rank them and equate them. So it is worth asking plainly whether the Table is true — whether a K and a CH potency are, in fact, equivalent. The short answer is that at the level of the number they are loosely comparable, but the fixed conversion the Table asserts is not merely imprecise; it is incoherent, and it can be shown to be so in two independent ways that happen to contradict each other. That mutual contradiction is the whole of the argument.
The two scales, stated plainly
Both the Hahnemannian and the Korsakovian methods are centesimal — one part of the substance to ninety-nine parts of diluent, 1:100, at each step. That shared premise is the only basis on which anyone claims the two can be compared at all.
Although practitioners often treat numerical values from both systems interchangeably, establishing a fixed mathematical conversion between them is fundamentally flawed and mathematically incoherent.
They differ in how the step is carried out. The Hahnemannian method uses a fresh vial at every dilution (the "multiple flask" method): one measured part is carried into ninety-nine measured parts, and the quantity moved forward is known. The Korsakovian method uses a single vial, emptied and refilled: the quantity carried forward is the film of liquid clinging to the emptied glass, assumed — but never measured — to be about one hundredth of the previous contents.
Hold on to that distinction. The whole question turns on it.
Proof one: by the count of steps
Take the shared premise seriously — both scales are 1:100 per step — and simply count.
A 7CH has undergone seven centesimal steps: a dilution factor of (10²)⁷ = 10¹⁴.
A 200K has undergone two hundred centesimal steps: a dilution factor of (10²)²⁰⁰ = 10⁴⁰⁰.
The difference is one hundred ninety-three centesimal steps — a factor of 10³⁸⁶. On the scales' own shared logic, a 200K is diluted roughly 10³⁸⁶ times further than a 7CH. To call these equivalent is to assert that two hundred and seven are the same number. On this reasoning, a 200K corresponds to a 200CH, not a 7CH. The table is self-refuting the moment you apply the very premise it rests on.
Proof two: by the residual film
Why, then, would anyone write "200K = 7CH"? Only by quietly abandoning the 1:100 premise for the Korsakovian side. The argument runs: the film left clinging to the emptied Korsakovian vial is thicker and messier than a clean hundredth, so each K "step" dilutes less than a true centesimal step; therefore two hundred sloppy K steps might reach only the molecular concentration of a handful of clean CH steps — "about a 7CH, by concentration."
But this rescue destroys the equivalence from the other side, three times over.
It rests on an unmeasured quantity. The residual film is never quantified in practice; a process whose per-step dilution is admittedly not a fixed number cannot be set equal to a process whose per-step dilution is exactly defined. You cannot place an equals sign on a quantity no one has measured.
It speaks only of molecular concentration — which is beside the point in this range. The correspondence is offered, in its own sources, "as a function of molecular concentration alone." But a 7CH (10⁻¹⁴) still contains molecules of the original substance, while a 200K is diluted so far beyond the point where any molecule could remain that it is a purely dynamic potency. One still materially contains the substance; the other cannot. Equating a dilution that still holds the drug with one that physically cannot is a category error, not a conversion.
And it contradicts the first proof outright. Proof one, taking 1:100 at face value, says the 200K is astronomically more dilute than the 7CH. Proof two, invoking the film, says the 200K is about as dilute as the 7CH. Both cannot be true. The table survives only by holding the centesimal premise for CH and dropping it for K — using whichever assumption is convenient in the moment. A relationship that can be stated only by contradicting itself is not a relationship.
The physics of the film: viscosity and what really stays on the glass
The second proof leans on the "thick residual film," so it is worth asking what chemistry actually says about how much liquid remains inside a vessel once it is emptied. There is a real, named phenomenon here, and it deserves to be stated accurately rather than hand-waved.
When liquid drains from a wall or is withdrawn from a vessel, a thin film is dragged onto the glass — the Landau–Levich–Derjaguin film. Its thickness is not arbitrary; it is governed by a competition between viscosity, which thickens the retained film, and surface tension, which resists the dragging, modulated by the speed of withdrawal or draining and then thinned over time by gravity. In the classical result, the film thickness scales with the capillary number — roughly with (viscosity × speed ÷ surface tension) to the two-thirds power. In plain terms: a more viscous liquid, emptied faster, leaves a thicker film; a thinner liquid, drained slowly, leaves less.
This is the crucial point for the Korsakovian question, and it cuts against the conversion table rather than for it. The amount of liquid left clinging to the bottle is real and physically describable — but it is not a fixed fraction, and nothing in the physics pins it to one hundredth. It depends on:
- Viscosity — a water–alcohol homeopathic medium is more viscous than pure water, and its viscosity changes with the alcohol percentage and the temperature. Warm the room or change the dilution medium and the retained film changes.
- Draining speed and technique — a vial tipped quickly by hand retains a different film than one emptied slowly, or by a machine on a fixed cycle. The "step" is not standardized across operators or devices.
- The vessel's geometry and wetting — a tall narrow tube retains a different fraction of its contents than a round flask, and how the liquid wets the glass (whether it sheets off cleanly or beads and clings) changes the result again.
Further, there is subtlety that makes matters worse for the table, not better. What clings to the wall is a film of solution, but what the dilution is supposed to carry forward is the solute. Molecules can adsorb onto the glass surface — be mindful that silica has genuine surface chemistry — so the thin film against the wall may be richer or poorer in the dissolved substance than the bulk liquid was. The retained film's concentration is therefore not guaranteed to equal the bulk's, quite apart from its volume.
So the honest conclusion is not that "no one knows what stays in the bottle." It is sharper than that: the retained quantity is physically determined but operationally uncontrolled. It is materially controlled by viscosity, speed, temperature, and geometry (of the vessel), none of which is held constant in practice; moreover, it cannot reliably be one hundredth of anything. A phenomenon can be perfectly real, and perfectly described by fluid mechanics, and still be useless as a unit of measure. The Korsakovian residue is exactly that: real film, no fixed fraction.
From the bench: a centesimal remedy is storable and divisible
There is a practical illustration of this difference worth recounting. At a production pharmacy I visited, I was shown how a centesimal remedy is prepared for dispensing: the bulk stock is held a couple of steps below the final potency — a large jar of the remedy at 198CH — and the last centesimal steps, from 198 up to 200, are carried out on demand to make the medicating liquid that then impregnates the pellets. (I observed the step structure, not the number of succussions per step, which varies from one manufacturer to another and which I make no claim about here.)
What the workflow shows is quietly decisive. A centesimal remedy can be stored in bulk and then divided and carried up into its dispensing potency, because each step is a measured operation performed on a known quantity — a part taken from the jar, diluted into ninety-nine parts, succussed, at whatever scale the bench requires. This is precisely the property the single-vial Korsakovian film cannot have. There is no bulk "198K" sitting in a jar to be parceled out and finished, because a Korsakovian step is not a measured quantity divided from a known volume; it is an unweighted film left on the wall of one vessel. And a scale that cannot be divided cannot be stored, re-dispensed, or verified against itself — which is why the Korsakovian potency must be taken on the machine's word, where the centesimal can be checked against the measured volumes that made it.
The clincher: they are not the same kind of quantity
There is a decisive, practical tell. Because the Hahnemannian method carries a measured quantity at each step, its material is quantified and divisible: from a given centesimal dilution you can parcel out and propagate further calibrated preparations, precisely because you know how much you are moving. The Korsakovian method carries an unmeasured film: there is no defined amount to divide. This is why you cannot develop multiple calibrated vials from a Korsakovian step the way you can from a measured 200CH — there is nothing quantified there to divide.
And that settles it. A CH potency is a measured quantity; a K potency is an unmeasured one, a residue governed by viscosity and draining that no one weighs. Two things that are not even the same kind of quantity cannot stand in a fixed numerical equivalence. An equals sign requires two measured values; the Korsakovian side never had one.
So "200K = 7CH" is not wrong by a margin a better table could fix. It is incoherent at the root: it can be asserted only by using two contradictory definitions of a "step" at the same time.
A word on LM/Q — outside the comparison entirely
It is worth saying plainly that the fifty-millesimal potencies (LM, or Q) do not belong in this discussion at all, and no one should try to slot them into a CH–K table. They are not calibrated on the same basis: the ratio is not 1:100 but roughly 1:50,000 at each step, and the entire LM scale begins only after the substance has first been triturated up to a 3CH, from which the dissolved grain starts the fifty-millesimal ladder. A different dilution ratio, a different starting point, a different granule-medicating procedure — the LM potencies are a separate construction, and comparing their numbers to CH or K numbers is a confusion of scales from the outset.
Why high potencies are necessarily Korsakovian
There is a practical reason this question is not merely academic, and it is one every prescriber who works high is already inside. Very high potencies are necessarily Korsakovian. A 10M means ten thousand centesimal steps; a 50M — written 500MK in some houses — fifty thousand; a CM, a hundred thousand; an MM potency is a million. By the true Hahnemannian method, with a fresh vial at every step, these are physically impossible to make: no one fills ten thousand separate flasks, let alone a million. So, the high potencies exist at all only because the Korsakovian single-vial method — and the continuous-flow machines built on the same principle — can carry one vessel through those steps automatically. When a prescriber writes a 1M, a 10M, a 500MK, or a one-million, they are prescribing a Korsakovian preparation, whether or not the label announces it.
This divides the range rather than pitting the two scales against each other across it. The centesimal method is calibrated but practical only at the lower potencies; the Korsakovian method is uncalibrated but is the only road to the heights. You can have the measured precision of separate vials, or you can have the reach of the single vial run ten thousand times — but not both, because the very step-by-step measurement that makes the centesimal scale divisible and exact is what makes it impossibly laborious at great height. The two methods trade precision for reach, and they divide the ladder between them at the point where hand-measured dilution gives out.
Clinically we treat the combined ladder as continuous, namely a patient may go from a 200CH to a 1M to a 10M, crossing without ceremony from centesimal into necessarily-Korsakovian territory, and prescribed as a single ascending course it serves. That is the approximation at work, and it is a good one: the direction is right, a 10M is higher and deeper-acting than a 1M than a 200CH. But notice what the approximation is and is not. It is a qualitative ladder — higher means deeper — which is all a prescriber needs. It is not a quantitative equivalence, and the moment one tries to make it one — to write that this many K steps equals that many CH steps — the whole construction fails, for every reason set out above. We already rely, every day, on the honest version: one continuous ladder of rising depth, its lower reaches centesimal and its heights Korsakovian, used as an approximation and never as a conversion.
So where did the Table come from? Follow the reimbursement
If the equivalence is incoherent, why does it persist, and why is it so distinctly French? The most revealing clue is that the very French pharmacy sources that publish the conversion table also state, on the same page, the fact that explains it: Hahnemannian CH dilutions were reimbursed by the French social security system because they were recognized by the French Pharmacopoeia, whereas Korsakovian dilutions were not reimbursed, because they were not part of the Pharmacopeia.
That single asymmetry supplies the motive the physics cannot. France reimbursed homeopathy for decades — at 65% from the mid-1980s, stepped down over the years to 15%, and finally to nothing on 1 January 2021, when the Haute Autorité de Santé's unfavorable opinion ended coverage altogether. During the long reimbursed era, a prescriber who wanted a Korsakovian potency (or could only procure a K potency) faced a patient who would pay for it out of pocket — and pay more, since non-reimbursed medicines also carried a higher value-added tax. A centesimal, by contrast, was recoverable. A Table that "converts" a Korsakovian potency into its centesimal "equivalent" is precisely the bridge that administrative situation would call for: it lets an un-reimbursable K be written, and claimed, as a reimbursable CH.
I offer this as the best explanation of the evidence rather than as a documented statement of intent — I have not found a source declaring "the Table was built to obtain reimbursement." But the facts it rests on are explicit and come from the Table's own sources: CH reimbursed and pharmacopoeia-recognized, K neither. And the explanation accounts for what a physical theory cannot: why the Table is dressed in false precision (a reimbursement claim needs a definite figure to write on the form), why it appears essentially only in France and, secondarily, Italy (only there did the reimbursement split exist), why its own authors hedge it as "for orientation only" while publishing it anyway (operationally useful though physically untrue), and why it is absent elsewhere. In Russia the two methods are treated as parallel, not convertible. In Brazil — a great homeopathic culture with an official Pharmacopoeia and homeopathy recognized as a medical specialty — pharmacy examinations explicitly teach that a CH dynamization is not equivalent to a Korsakovian one, flagging the belief as a trap, and noting that heavy Korsakovian use is a European habit little practiced there. A genuine law of dilution would appear in every language. A reimbursement convention appears only where the reimbursement existed — and, now that French coverage has ended, the administrative reason for the Table has quietly expired with it.
So — are they equivalent?
At the level of the number, loosely: a 30K and a 30CH are both thirtieth centesimal dynamizations, and prescribing a Korsakovian potency on much the same footing as its same-numbered centesimal is reasonable clinical practice. What the demonstration forbids is the fixed cross-scale conversion — the belief that a 200K can be written equal to a 7CH. It cannot. That claim is not a weaker or stronger statement of a real relationship; it is the assertion of a relationship that, examined, dissolves into contradiction — and whose persistence is better explained by a reimbursement form than by the physics of a bottle.
A French translation of this article, for my French-speaking colleagues in homeopathy is posted here!
An audio illustration of this article is available here.
This article is for general educational interest and is not a substitute for individualized homeopathic consultation. The reasoning concerns the preparation and calibration of potencies, not the clinical choice of remedy, which rests on the individual case.
