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Opioid Conversion & MME Practice Problems

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Opioid math converts between opioids and routes using an equianalgesic table anchored to 30 mg of oral morphine, and totals a regimen in morphine milligram equivalents (MME) for safety review. Fentanyl patch selection is a separate range-based lookup.

FormulasProportion from the equianalgesic table (30 mg PO morphine = anchor)Switching to a different opioid: reduce the calculated dose by 25 to 50% for incomplete cross-toleranceMME/day = daily dose × (30 ÷ that drug's equianalgesic dose)  •  MME totals risk; it is not a dose conversion
Worked example

Oxycodone 10 mg three times daily = 30 mg/day. Table: 20 mg oxycodone ≈ 30 mg morphine, so MME = 30 × (30 ÷ 20) = 45 MME/day.

90 MME/day is the common safety-review threshold; watch route differences. The same drug by a different route has a different number.

Streak 0
Correct 0/0
MME
A patient takes hydrocodone (PO) 10 mg, 3 times daily. Using the equianalgesic table below, what is the total daily dose in morphine milligram equivalents (MME/day)?
OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to the nearest whole number.
MME/day

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How to set up an opioid conversion

Opioid conversions are proportions read off an equianalgesic table. Each row of the table gives the dose of a drug, by a particular route, that is roughly as effective as 30 mg of oral morphine. To convert a daily dose from one opioid to another you find the two rows, set up a proportion, and then, if the drug is changing, reduce the result for incomplete cross-tolerance. The table below is the one the practice problems here use.

new daily dose = old daily dose × (new drug's table dose ÷ old drug's table dose)

Exams supply the table. Numbers differ a little between references, so use the one in the question, not the one in your head.

Worked example 1: morphine milligram equivalents

A patient takes hydromorphone 4 mg orally four times daily. What is the MME/day?

daily dose = 4 × 4 = 16 mg/day

MME = 16 × 30 ÷ 7.5 = 64 MME/day

MME is just a conversion to oral morphine, used to total a regimen for safety review rather than to write a new prescription. It uses the oral rows only; a parenteral dose is first converted to its oral equivalent. 90 MME/day is the threshold most guidance flags for review.

Worked example 2: switching drugs, with the cross-tolerance reduction

A patient on morphine 60 mg/day orally is switched to oral oxycodone, reducing by 25% for incomplete cross-tolerance.

raw equivalent = 60 × 20 ÷ 30 = 40 mg/day

reduced = 40 × 0.75 = 30 mg/day of oxycodone

The reduction exists because tolerance built up to one opioid does not fully carry over to another, so the calculated equivalent would be an overdose. It's applied after the conversion, never before. The question says how much to reduce (25 to 50%); when it's your call, reduce more for elderly or frail patients, and use the larger reduction when switching to methadone, which has its own conversion rules and is not on this table.

Worked example 3: same drug, different route

A patient on IV morphine 20 mg/day is moved to oral morphine.

oral = 20 × 30 ÷ 10 = 60 mg/day

Same drug, so no cross-tolerance reduction. Oral morphine is a third as potent as IV because of first-pass metabolism; the table already accounts for that.

Fentanyl patches are a lookup, not a proportion

The transdermal fentanyl label converts from total daily oral morphine to a patch strength using ranges: 60 to 134 mg/day → 25 mcg/hr, 135 to 224 → 50, 225 to 314 → 75, 315 to 404 → 100. Find the range that contains the patient's daily morphine equivalent and read across. Don't interpolate, and don't apply a further 25 to 50% reduction on top; the manufacturer's table is already conservative. A patient on 180 mg/day of oral morphine equivalents gets the 50 mcg/hr patch. Patches are changed every 72 hours and are for opioid-tolerant patients only.

Where students lose the points

10 Opioid Conversion & MME practice problems with worked solutions

Every problem below is worked start to finish. Try it yourself first, then check the steps. For a fresh problem every time, use the practice box above. It generates unlimited variations of these same question types.

Problem 1: Equianalgesic Conversion

A patient is receiving 10 mg/day of morphine (IV). Using the equianalgesic table below, what is the equivalent daily dose of hydrocodone (PO) in mg/day, before any cross-tolerance reduction?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to one decimal place.

Answer 30.0 mg/day

Solution
  1. Pull the two relevant rows, drug AND route: morphine (IV) = 10 mg ≈ hydrocodone (PO) = 30 mg.
  2. Set up the proportion: 10 mg / 30 mg = 10 mg / x.
  3. x = 10 × 30 ÷ 10 = 30 mg/day = 30 mg/day of hydrocodone (PO).
  4. Rounded as the question asks: 30.0 mg/day.

In practice the calculated dose is reduced by 25 to 50% for incomplete cross-tolerance, exam questions specify whether they want the raw conversion or the reduced dose. Meperidine bonus fact: normeperidine accumulation (seizure risk) makes it inappropriate for chronic pain, which exams like to test.

Problem 2: Fentanyl Patch

A patient's opioid regimen totals 135 mg/day of oral morphine equivalents. Using the conversion table below, which fentanyl patch strength (mcg/hr) is appropriate? This table comes from the product labeling and already builds in the conservative conversion factor, so no further cross-tolerance reduction is applied.

Oral morphine (mg/day)Fentanyl patch (mcg/hr)
60 to 13425
135 to 22450
225 to 31475
315 to 404100
Round your answer to the nearest whole number.

Answer 50 mcg/hr

Solution
  1. Find the range containing 135 mg/day → 135 to 224 mg/day.
  2. That row corresponds to the 50 mcg/hr patch.
  3. Rounded as the question asks: 50 mcg/hr.

Patch selection is a table LOOKUP rather than a proportion, so never interpolate between rows. The Duragesic table is deliberately conservative, so you do NOT subtract a further 25 to 50% on top of it. Patches are changed every 72 hours and are for opioid-tolerant patients only, and exams test both of those facts.

Problem 3: MME

A patient takes oxycodone (PO) 30 mg, 2 times daily. Using the equianalgesic table below, what is the total daily dose in morphine milligram equivalents (MME/day)?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to the nearest whole number.

Answer 90 MME/day

Solution
  1. Find the right cell, drug AND route: 20 mg oxycodone (PO) ≈ 30 mg morphine (PO).
  2. Daily dose: 30 mg/dose × 2 doses/day = 60 mg/day.
  3. Proportion: 20 mg / 30 mg = 60 mg / x → x = 60 mg/day × 30 mg ÷ 20 mg = 90 MME/day.
  4. Rounded as the question asks: 90 MME/day.

MME is just an equianalgesic conversion with 30 mg oral morphine as the anchor. 90 MME/day is the common review threshold in opioid safety guidance. MME factors are defined for ORAL opioids; a parenteral dose must first be converted to its oral equivalent, which is why the CDC table has no IV column.

Problem 4: Equianalgesic Conversion

A patient is receiving 15 mg/day of morphine (IV). Using the equianalgesic table below, what is the equivalent daily dose of meperidine (IV) in mg/day, before any cross-tolerance reduction?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to one decimal place.

Answer 112.5 mg/day

Solution
  1. Pull the two relevant rows, drug AND route: morphine (IV) = 10 mg ≈ meperidine (IV) = 75 mg.
  2. Set up the proportion: 10 mg / 75 mg = 15 mg / x.
  3. x = 15 × 75 ÷ 10 = 112.5 mg/day = 112.5 mg/day of meperidine (IV).
  4. Rounded as the question asks: 112.5 mg/day.

In practice the calculated dose is reduced by 25 to 50% for incomplete cross-tolerance, exam questions specify whether they want the raw conversion or the reduced dose. Meperidine bonus fact: normeperidine accumulation (seizure risk) makes it inappropriate for chronic pain, which exams like to test.

Problem 5: Fentanyl Patch

A patient's opioid regimen totals 70 mg/day of oral morphine equivalents. Using the conversion table below, which fentanyl patch strength (mcg/hr) is appropriate? This table comes from the product labeling and already builds in the conservative conversion factor, so no further cross-tolerance reduction is applied.

Oral morphine (mg/day)Fentanyl patch (mcg/hr)
60 to 13425
135 to 22450
225 to 31475
315 to 404100
Round your answer to the nearest whole number.

Answer 25 mcg/hr

Solution
  1. Find the range containing 70 mg/day → 60 to 134 mg/day.
  2. That row corresponds to the 25 mcg/hr patch.
  3. Rounded as the question asks: 25 mcg/hr.

Patch selection is a table LOOKUP rather than a proportion, so never interpolate between rows. The Duragesic table is deliberately conservative, so you do NOT subtract a further 25 to 50% on top of it. Patches are changed every 72 hours and are for opioid-tolerant patients only, and exams test both of those facts.

Problem 6: MME

A patient takes meperidine (PO) 50 mg, 3 times daily. Using the equianalgesic table below, what is the total daily dose in morphine milligram equivalents (MME/day)?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to the nearest whole number.

Answer 15 MME/day

Solution
  1. Find the right cell, drug AND route: 300 mg meperidine (PO) ≈ 30 mg morphine (PO).
  2. Daily dose: 50 mg/dose × 3 doses/day = 150 mg/day.
  3. Proportion: 300 mg / 30 mg = 150 mg / x → x = 150 mg/day × 30 mg ÷ 300 mg = 15 MME/day.
  4. Rounded as the question asks: 15 MME/day.

MME is just an equianalgesic conversion with 30 mg oral morphine as the anchor. 90 MME/day is the common review threshold in opioid safety guidance. MME factors are defined for ORAL opioids; a parenteral dose must first be converted to its oral equivalent, which is why the CDC table has no IV column.

Problem 7: Equianalgesic Conversion

A patient is receiving 450 mg/day of meperidine (PO). Using the equianalgesic table below, what is the equivalent daily dose of morphine (IV) in mg/day, before any cross-tolerance reduction?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to one decimal place.

Answer 15.0 mg/day

Solution
  1. Pull the two relevant rows, drug AND route: meperidine (PO) = 300 mg ≈ morphine (IV) = 10 mg.
  2. Set up the proportion: 300 mg / 10 mg = 450 mg / x.
  3. x = 450 × 10 ÷ 300 = 15 mg/day = 15 mg/day of morphine (IV).
  4. Rounded as the question asks: 15.0 mg/day.

In practice the calculated dose is reduced by 25 to 50% for incomplete cross-tolerance, exam questions specify whether they want the raw conversion or the reduced dose. Meperidine bonus fact: normeperidine accumulation (seizure risk) makes it inappropriate for chronic pain, which exams like to test.

Problem 8: Fentanyl Patch

A patient's opioid regimen totals 165 mg/day of oral morphine equivalents. Using the conversion table below, which fentanyl patch strength (mcg/hr) is appropriate? This table comes from the product labeling and already builds in the conservative conversion factor, so no further cross-tolerance reduction is applied.

Oral morphine (mg/day)Fentanyl patch (mcg/hr)
60 to 13425
135 to 22450
225 to 31475
315 to 404100
Round your answer to the nearest whole number.

Answer 50 mcg/hr

Solution
  1. Find the range containing 165 mg/day → 135 to 224 mg/day.
  2. That row corresponds to the 50 mcg/hr patch.
  3. Rounded as the question asks: 50 mcg/hr.

Patch selection is a table LOOKUP rather than a proportion, so never interpolate between rows. The Duragesic table is deliberately conservative, so you do NOT subtract a further 25 to 50% on top of it. Patches are changed every 72 hours and are for opioid-tolerant patients only, and exams test both of those facts.

Problem 9: MME

A patient takes hydromorphone (PO) 2 mg, 4 times daily. Using the equianalgesic table below, what is the total daily dose in morphine milligram equivalents (MME/day)?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to the nearest whole number.

Answer 32 MME/day

Solution
  1. Find the right cell, drug AND route: 7.5 mg hydromorphone (PO) ≈ 30 mg morphine (PO).
  2. Daily dose: 2 mg/dose × 4 doses/day = 8 mg/day.
  3. Proportion: 7.5 mg / 30 mg = 8 mg / x → x = 8 mg/day × 30 mg ÷ 7.5 mg = 32 MME/day.
  4. Rounded as the question asks: 32 MME/day.

MME is just an equianalgesic conversion with 30 mg oral morphine as the anchor. 90 MME/day is the common review threshold in opioid safety guidance. MME factors are defined for ORAL opioids; a parenteral dose must first be converted to its oral equivalent, which is why the CDC table has no IV column.

Problem 10: Equianalgesic Conversion

A patient is receiving 187.5 mg/day of meperidine (IV). Using the equianalgesic table below, what is the equivalent daily dose of fentanyl (IV) in mcg/day, before any cross-tolerance reduction?

OpioidPO (mg)IV (mg)
morphine3010
hydromorphone7.51.5
oxycodone20,
hydrocodone30,
codeine200,
meperidine30075
fentanyl, 0.1 (= 100 mcg)
Round your answer to the nearest whole number.

Answer 250 mcg/day

Solution
  1. Pull the two relevant rows, drug AND route: meperidine (IV) = 75 mg ≈ fentanyl (IV) = 0.1 mg.
  2. Set up the proportion: 75 mg / 0.1 mg = 187.5 mg / x.
  3. x = 187.5 × 0.1 ÷ 75 = 0.25 mg/day = 250 mcg/day of fentanyl (IV).
  4. Rounded as the question asks: 250 mcg/day.

In practice the calculated dose is reduced by 25 to 50% for incomplete cross-tolerance, exam questions specify whether they want the raw conversion or the reduced dose. Meperidine bonus fact: normeperidine accumulation (seizure risk) makes it inappropriate for chronic pain, which exams like to test.

Sources and how far they go

Where a convention on this page comes from a published standard, the standard is named. Where it comes from a textbook or from ordinary practice instead, the entry says so. That difference matters when a preceptor or an exam disagrees with you.

Citations are to the source of the method. They are not a review of this page, and none of these bodies has reviewed or endorsed it.

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