Opioid Rotation and Cross-Tolerance Calculator
Opioid Rotation and Cross-Tolerance Calculator
The arithmetic equivalent of one oral opioid in another, then the published reduction for incomplete cross-tolerance applied on top of it — with the measured ratios that show the conversion is not the same in both directions.
Arithmetic equivalent, then the published reduction
7 opioids, 4 published reductionsOral morphine 60 mg a day, changing to oral oxycodone, with the 25 per cent reduction selected
Two steps, and the second one is the one that matters
Step 1 — arithmetic equivalent of the second drug = oral morphine equivalent ÷ potency of the second drug
Step 2 — published practice: reduce that figure by 25 to 50 per cent for incomplete cross-tolerance, and by at least 50 per cent above about 500 mg of oral morphine equivalent a day or in the frail and elderly
Potencies relative to oral morphine (Faculty of Pain Medicine): codeine 0.1, dihydrocodeine 0.1, tramadol 0.1, morphine 1, oxycodone 1.5, tapentadol 0.4, hydromorphone 5
- incomplete cross-tolerance
- tolerance to one opioid carries over only partly to another. A patient comfortable on a large dose of one drug is, in effect, partly opioid-naive to the next one, so the arithmetic equivalent over-estimates what they tolerate. This is the single reason the published reduction exists, and the reason it is applied after the equivalence rather than built into the potency table
- why the reduction is not in the table
- because the potency table answers a different question. It was built from single-dose comparisons of analgesic effect, not from switches in tolerant patients. The reduction is the correction between the two, and every source that publishes the table also publishes the correction separately
- the round trip, and why it is exact
- a potency vector has one number per drug, so dividing by it and multiplying back returns the original by arithmetic necessity. The measured ratios are direction-dependent and cannot be stored that way, so the exactness of the round trip is evidence that the table is a convention rather than a measurement
- morphine and hydromorphone, 5 against 3.7
- the one pair for which both directions were measured in patients. Lawlor and colleagues concluded hydromorphone is about five times as potent when it is the second drug and about 3.7 times when it is the first, and recommended using 5 for morphine-to-hydromorphone and 3.7 for the reverse; Bruera and colleagues found 5.33 and 3.57. Using one figure in both directions is a 35 per cent error, in the unsafe direction half the time
- when rotation is not the answer
- the Faculty of Pain Medicine states that “Opioid rotation is not recommended if a patient has responded to one opioid”, and that a switch is considered where analgesia is adequate but adverse effects are severe. It also says the switch should be supervised by a practitioner with the relevant competence and experience
- the half-lives, which this page cannot compute
- a switch has a middle. Two drugs with different onset and different half-lives overlap or leave a gap, and the published guidance is to consider both so the patient has neither breakthrough pain nor a double exposure during the change. No ratio addresses this
- what the second step is not
- a dose. Every figure on this page is arithmetic applied to a published convention. The page renders no dose, no target and no limit
Worked example
Oral morphine 60 mg a day, changing to oral oxycodone, with the 25 per cent reduction selected
Step 1, oral morphine equivalent: 60 × 1 = 60 mg a day
Step 1, arithmetic equivalent in oxycodone, potency 1.5: 60 ÷ 1.5 = 40.00 mg a day. That is the headline, and it is the figure every source says is too high
Step 2, the published 25 per cent reduction: 40.00 × 0.75 = 30.00
Step 2 at the other end of the published range, 50 per cent: 40.00 × 0.5 = 20.00. The published range alone spans 1.5-fold, before any disagreement about the potency
Convert straight back: 40.00 × 1.5 ÷ 1 = 60.00, exactly the dose entered. The table round-trips because it is a potency vector, not because the two conversions were separately validated
Now the pair where both directions were measured. Oral morphine 60 mg a day to oral hydromorphone: 60 ÷ 5 = 12.00 mg by Lawlor's morphine-to-hydromorphone ratio, and 60 ÷ 3.7 = 16.22 mg by the ratio Lawlor recommends for the opposite direction — a 1.35-fold gap on the same pair
And the other way: oral hydromorphone 12 mg a day to oral morphine is 12 × 3.7 = 44.40 mg by the measured reverse ratio, against 12 × 5 = 60.00 mg by the potency vector. A reader who round-trips 60 to 12 and back expects 60 and the measurement says 44.4
Using the Scottish Palliative Care Guidelines' oxycodone potency of 2 instead of the Faculty of Pain Medicine's 1.5, the same 60 mg of morphine becomes 30.00 mg of oxycodone rather than 40.00 — a 1.33-fold difference that sits underneath everything above
The reduction for incomplete cross-tolerance, by source
| Source | Reduction applied to the calculated equivalent | What else it says |
|---|---|---|
| Faculty of Pain Medicine, Opioids Aware | 25 to 50 per cent in most switches | At least 50 per cent above about 500 mg of oral morphine equivalent a day, in the elderly or frail, or where adverse effects are intolerable |
| Scottish Palliative Care Guidelines | Up to 30 per cent | “Consider reducing the dose by up to 30%” and re-titrate; reduce further if the patient is opioid toxic, frail or elderly |
| Severn Hospice conversion table | 25 to 30 per cent | 50 per cent when converting high doses, to avoid toxicity |
| MSD Manuals equianalgesic table | 50 per cent | 75 to 90 per cent for methadone, and the same reduction still applies on top of the dose-banded methadone ratios |
| Wellington ICU Drug Manual, Appendix 6 | 25 to 50 per cent | Calculate the equianalgesic figure first, then cut it |
| Fine and Portenoy, via Treillet et al. 2018 | 25 to 50 per cent, then a further 15 to 30 per cent either way | Explicitly excepts methadone and transdermal and transmucosal fentanyl from the first step |
The measured ratios, which are not the same in both directions
| Pair and direction | Ratio | Source |
|---|---|---|
| Oral morphine to oral hydromorphone | 5.33 to 1 | Bruera et al. 1996, as reported by Treillet et al. 2018 |
| Oral hydromorphone to oral morphine | 1 to 3.57 | Bruera et al. 1996, same report |
| Oral morphine to oral hydromorphone | 5 to 1 | Lawlor et al. 1997, recommended for this direction |
| Oral hydromorphone to oral morphine | 1 to 3.7 | Lawlor et al. 1997, recommended for this direction |
| Either direction, by a potency table | 5 to 1, both ways | Faculty of Pain Medicine, CDC 2022 and the BNSSG chart all publish a single hydromorphone potency of 5 |
| Either direction, Scottish Palliative Care Guidelines | 5 to 7.5, both ways | Oral morphine divided by 5 to 7.5; the worked example uses 7.5 |
| Either direction, CDC pre-2022 | 4 to 1, both ways | CDC’s pre-2022 conversion file and Maryland’s reproduction of it |
The arithmetic is the easy half
Changing a patient from one opioid to another has two steps, and only the first one is arithmetic. The first step puts the current 24-hour dose onto the oral morphine scale and then divides by the potency of the drug being moved to, which is what the headline figure on this page is. The second step is the reduction for incomplete cross-tolerance, and it is the step that separates a safe switch from a fatal one.
Tolerance is not a general property of a patient; it is specific, to a degree, to the drug that produced it. Somebody comfortable on a large daily dose of one opioid is partly opioid-naive to the next one, so the dose the arithmetic says is equivalent is more than they tolerate. Every source read for this page publishes a reduction to apply on top of the equivalence, and none of them publishes zero: the Faculty of Pain Medicine puts it at 25 to 50 per cent and at least 50 per cent above about 500 mg of oral morphine equivalent a day or in the elderly and frail; the Scottish Palliative Care Guidelines at up to 30 per cent; Severn Hospice at 25 to 30 per cent and 50 per cent for high doses; MSD at 50 per cent, and 75 to 90 per cent for methadone; Wellington ICU at 25 to 50 per cent. Fine and Portenoy’s scheme, as Treillet and colleagues report it, adds a second adjustment of 15 to 30 per cent either way and excepts methadone and fentanyl from the first step altogether. The reduction is applied after the equivalence, never instead of it.
The second thing this page is built to show is that the conversion is not symmetrical. Two studies measured the oral morphine and oral hydromorphone ratio in both directions in patients and both found it direction-dependent: about 5.33 or 5 going from morphine to hydromorphone, and about 3.57 or 3.7 coming back. The tables in everyday use store one number per drug, so they cannot express that, and they round-trip exactly. This page prints its own round trip precisely so the exactness is visible and can be read for what it is — an artefact of the method, not a validation of it. A reader who converts 60 mg of morphine to 12 mg of hydromorphone and then converts back expects 60 and the measurement says 44.4.
Underneath both problems sits the disagreement between sources about the potencies themselves, which the oral morphine equivalent page sets out in full: oxycodone is 1.5 in most charts and 2 in some, hydromorphone is 4, 5 or 7.5, tramadol is 0.1 or 0.2. These are population approximations; the published cross-tolerance reduction applies after any equivalence; your own formulary governs. The notes below set all three out in full. Methadone, buprenorphine and the patches are refused here and handled on the methadone page, the buprenorphine page and the fentanyl patch page.
Frequently asked questions
What is incomplete cross-tolerance?
Tolerance to one opioid transfers only partly to another, because the drugs differ in receptor subtype activity, in intrinsic efficacy and in the active metabolites they produce. The practical consequence is that the arithmetic equivalent of a patient’s current dose over-estimates what they tolerate on the new drug, which is why every published source applies a reduction of 25 to 50 per cent after the conversion.
Why does converting back not undo the conversion?
By a potency table it does, exactly — and that is the problem. A potency table holds one number per drug, so dividing and multiplying back is arithmetically forced. The two studies that measured oral morphine against oral hydromorphone in both directions found about 5.33 and 5 one way and about 3.57 and 3.7 the other, a 35 per cent asymmetry that no single-number table can hold. Treillet and colleagues’ summary is blunt: “Both studies found that the po ratio was not bidirectional.”
Which reduction should be used?
That is a decision this page does not make and cannot make. The six sources read for it publish 25 to 50 per cent, up to 30 per cent, 25 to 30 per cent, 50 per cent, 25 to 50 per cent, and 25 to 50 per cent followed by a further 15 to 30 per cent either way — with larger reductions named for high doses, for frail and elderly patients, and far larger ones for methadone. The page prints all of them with what else each source says, and your own formulary or specialist service governs.
Why are methadone, buprenorphine and patches excluded?
Because a single ratio does not describe any of them. Methadone’s potency relative to morphine rises with the dose being converted from — CDC’s own pre-2022 file used four different factors across four dose bands — and it has a long, variable half-life with delayed accumulation. Buprenorphine is a high-affinity partial agonist that can displace a full agonist and precipitate withdrawal, and no source read here publishes a usable ratio for it. A patch is rated in micrograms an hour, which is not a milligram-a-day quantity. All three have their own pages.
Does this page tell me what to change the patient to?
No. It computes an arithmetic equivalence from published potency figures, prints the four published reductions that every source applies on top of it, and shows where the published ratios disagree with each other and with the measured ones. It renders no dose, no target and no limit, and the switch itself is a clinical decision made with the patient in front of you and your own formulary.
Related calculators
References
- Faculty of Pain Medicine of the Royal College of Anaesthetists. Opioids Aware: dose equivalents and changing opioids. Oral potencies, reviewed March 2023 against the BNF: codeine 0.1, dihydrocodeine 0.1, hydromorphone 5, morphine 1, oxycodone 1.5, tapentadol 0.4, tramadol 0.1, methadone “varies” with specialist advice required. Transdermal fentanyl 12, 25, 50, 75 and 100 micrograms an hour against 30, 60, 120, 180 and 240 mg of oral morphine a day. Conversion factors are an approximate guide only “because data are incomplete and individual variation is significant”; in most switches the calculated equivalent is cut by 25 to 50 per cent, and by at least 50 per cent above about 500 mg of oral morphine equivalent a day or in the elderly or frail; and “Opioid rotation is not recommended if a patient has responded to one opioid”.
- Treillet E, Laurent S, Hadjiat Y. Practical management of opioid rotation and equianalgesia. J Pain Res. 2018;11:2587–2601. The source of this batch’s non-reciprocity figures, reported from two studies it reviews: “Both studies found that the po ratio was not bidirectional”, with Bruera and colleagues finding oral morphine to oral hydromorphone at 5.33:1 and oral hydromorphone to oral morphine at 1:3.57, and Lawlor and colleagues concluding hydromorphone is about five times as potent when it is the second drug and about 3.7 times when it is the first. Also: “The most reliable method for ratio calculation is based on the evaluation of pain after a single injection of an opioid” and “In general, this ratio is calculated in a postsurgical setting, where patients are usually opioid-naïve”; and Fine and Portenoy’s reduction of 25 to 50 per cent then a further 15 to 30 per cent either way, excepting methadone and fentanyl. Bruera 1996 and Lawlor 1997 are cited through this reproduction because PubMed Central was not reachable from the sandbox this page was written in.
- NHS Scotland. Scottish Palliative Care Guidelines: opioid/opiate conversion tables — switching between opioid medicines (Right Decision Service). Divisors on the 24-hour oral morphine dose: 2 subcutaneous morphine, 3 subcutaneous diamorphine, 2 oral oxycodone, 4 subcutaneous oxycodone, 5 to 7.5 oral hydromorphone, 10 subcutaneous hydromorphone, 30 subcutaneous alfentanil; codeine, dihydrocodeine and tramadol divided by 10. A seven-day buprenorphine patch at 5 micrograms an hour is matched to 12 mg of oral morphine a day. On switching: “Consider reducing the dose by up to 30%” and re-titrate, reducing further if the patient is opioid toxic, frail or elderly. Its oxycodone divisor of 2 is the figure that disagrees with the Faculty of Pain Medicine’s 1.5.
- MSD Manuals Professional Version. Equianalgesic Doses of Opioid Analgesics. Parenteral against oral: morphine 10 to 30 mg, codeine 130 to 200, hydromorphone 1.5 to 7.5, methadone 10 to 20, oxycodone 15 to 20, oxymorphone 1 to 15. Its footnotes state that the equivalences come from single-dose studies and clinical experience and are approximations; that on changing opioid the equianalgesic dose is cut by 50 per cent, and by 75 to 90 per cent for methadone; and that the morphine-to-methadone ratio is non-linear, rising from about 2:1 below 30 mg of oral morphine equivalent a day to about 20:1 at 1000 mg a day and above. Its oral oxymorphone figure of 15 mg against 30 mg of morphine implies a potency of 2, where CDC publishes 3.
- Severn Hospice. Opioid Conversion Table, version 07.19. Oral potencies of 0.1 for codeine and dihydrocodeine but 0.15 for tramadol, and oral oxycodone reached by dividing oral morphine by 2 — two figures that disagree with the Faculty of Pain Medicine’s 0.1 and 1.5 for the same drugs. Transdermal fentanyl “approx. 100 to 150 times more potent than oral morphine” with the table built at 100:1; buprenorphine 5 micrograms an hour matched to 12 mg of oral morphine a day. Puts the switching reduction at 25 to 30 per cent, and at 50 per cent when converting high doses, to avoid toxicity.
- Wellington ICU Drug Manual, Appendix 6: opioid equivalence. Publishes the 24-hour oral morphine to oral methadone ratio in three bands — 4:1 below 90 mg of morphine, 8:1 from 91 to 300 mg, 12:1 from 301 to 600 mg — with oral to intramuscular or intravenous methadone at 2:1, and the instruction to calculate the equianalgesic dose and then cut it by 25 to 50 per cent. Its fentanyl rows match 25 micrograms an hour to 50 mg of oral or 16 mg of intravenous morphine over 24 hours. The appendix’s main table is published as an image rather than as text and was therefore not readable; only the figures quoted here were read as text.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/