Morphine → Methadone Conversion

Dr. Paul W Tervit - 2026

Comparison calculator implementing the mathematical methods described by Baumrucker, Jbara and Rogers (2016)

Clinical safety: Methadone conversion is non-linear and clinically hazardous. The paper explicitly states that the BJR method should not be used clinically until validated in controlled studies. Actual switching requires specialist judgement, assessment of comorbidity and interactions, ECG/QTc considerations, monitoring, and a locally approved protocol.

Input

Oral morphine equivalent dose

Enter total oral morphine equivalents in mg per 24 hours.

The source paper does not provide a complete computable Morley–Makin algorithm. It describes 10:1 conversion at lower doses and a higher-dose every-3-hour PRN regimen; therefore it is shown only as a contextual method, not calculated here.

Calculated total daily methadone

Plonk

—

M ÷ 15 + 15

Linear; paper considers it most useful around 300–600 mg OME/day and potentially excessive at high doses.

Ayonrinde

—

Piecewise ratio

Changing morphine:methadone ratio, with discontinuities at dose-band boundaries.

BJR

—

√(2.3 × M) + 15

Smooth square-root function proposed by the authors; unvalidated.

BJR modified

—

BJR to 1500 mg; Ayonrinde above

The paper proposes using Ayonrinde when OME is exceptionally high (>1500 mg/day).

Spread between calculated methods

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Visual comparison

The vertical marker is the entered OME dose. The saw-tooth appearance of Ayonrinde reflects abrupt ratio changes at 100/101, 300/301, 600/601, 800/801 and 1000/1001 mg.

Methods in the paper

Plonk linear

Methadone = morphine ÷ 15 + 15

The 15 mg intercept implies 15 mg/day even at zero morphine exposure. The paper argues that linear growth will eventually produce overly large doses.

Ayonrinde piecewise ratios

OME mg/day	Morphine:methadone
<100	3:1
101–300	5:1
301–600	10:1
601–800	12:1
801–1000	15:1
>1000	20:1

The article's printed table leaves the exact value 100 mg unstated. This app assigns 100 mg to the 3:1 band, consistent with the authors' example that 300 mg gives 60 mg and 301 mg gives 30.1 mg.

BJR square-root curve

Methadone = √(2.3 × morphine) + 15

Designed empirically to rise rapidly at low OME and more gradually at high OME, while retaining a 15 mg/day intercept.

Modified BJR hybrid

BJR at ≤1500 mg; Ayonrinde at >1500 mg

The BJR and 20:1 Ayonrinde curves intersect mathematically at about 1458 mg OME/day. The paper nevertheless describes 1500 mg/day as the practical switching threshold.

Interpretive limitations

Issue	Implication
Rapid communication, not a clinical validation study	The proposed BJR constant (2.3) was selected empirically from curve behaviour rather than derived from prospective patient outcomes.
No clinical outcome dataset	No estimates of analgesic success, toxicity, respiratory depression, withdrawal, or mortality are provided.
Starting-dose intercept	Plonk and BJR return 15 mg/day when morphine is zero. This is a mathematical feature, not evidence that opioid-naïve patients should receive that dose.
Ayonrinde discontinuities	A 1 mg increase across a boundary can sharply reduce the calculated methadone dose; e.g. 300 mg OME → 60 mg, whereas 301 mg → 30.1 mg.
Extreme-dose uncertainty	At 7000 mg OME/day: Plonk 481 mg, Ayonrinde 350 mg, BJR 142 mg, and modified BJR 350 mg—showing major model divergence.
Patient factors omitted	The equations do not incorporate age, frailty, organ function, QTc, interacting drugs, prior opioid duration, pain mechanism, or inter-individual methadone half-life.