Apnoea-Hypopnoea Index Calculator (AHI, RDI, REI)
Apnoea-Hypopnoea Index Calculator (AHI, RDI, REI)
The AHI, the RDI and the REI from one set of event counts, and the divergence computed — a home study divides by recording time and reads systematically lower on the very same night.
AHI, RDI and REI from one night
Three denominators, one night38 apnoeas, 63 hypopnoeas, 28 RERAs, 360 min of scored sleep inside 480 min of recording
Three formulas, three denominators
- AHI
- the AASM’s 2025 specification of its own severity quality measure defines it, for a laboratory polysomnogram, as total apnoeas plus hypopnoeas per hour of sleep — and defines the home-study AHI as the same count per hour of MONITORING, a different quantity under one name
- RDI
- the same AASM document: apnoeas plus hypopnoeas plus respiratory effort-related arousals per hour of sleep. It exceeds the AHI by exactly the RERA rate
- REI
- the AASM’s 2017 guideline names the mechanism — the use of recording time rather than sleep time as the denominator — and lists it among the factors that can result in underestimation of the true AHI
- the word RDI means two different things
- and this is the trap. Medicare’s PAP local coverage determination defines RDI as apnoeas plus hypopnoeas per hour of RECORDING, reported in type III, type IV and other home studies, and states separately that RERAs are not in the AHI. So Medicare’s RDI is what the AASM calls the REI. On the worked night below the two readings of the one word are 21.5 and 12.6 per hour
- the AASM’s own two editions disagree
- the 2017 specification of this measure states the severity strata over the RDI; the 2025 specification states them over the AHI or the REI. The three definitions are identical across the two documents; which index the strata are read over is not
- units
- events per hour. Enter both times in minutes
Worked example
38 apnoeas, 63 hypopnoeas, 28 RERAs, 360 min of scored sleep inside 480 min of recording
Events = 38 + 63 = 101; sleep 360 ÷ 60 = 6.0 h; recording 480 ÷ 60 = 8.0 h
AHI = 101 ÷ 6.0 = 16.8 events/h of sleep — the moderate band
RDI = 129 ÷ 6.0 = 21.5 events/h — still moderate, but 4.7 higher, and the whole difference is the 28 RERAs
REI = 101 ÷ 8.0 = 12.6 events/h of recording — the MILD band. The same night, the same events
So the 15-per-hour mark is crossed by the AHI and not by the REI. A laboratory study here reads moderate and reaches Medicare's 15-per-hour PAP tier; a home device on the identical night reads mild and does not. Neither device is at fault: a home device has no EEG and nothing to divide by except everything it recorded
The ratio is exact: REI ÷ AHI = sleep ÷ recording = 360 ÷ 480 = 0.75. At 50% sleep efficiency the REI would be half the AHI
Set the recording time to 360 and the RERAs to 0 and all three read 16.8. That coincidence is the degenerate case, not a check: a calculator using one denominator for all three would agree here and nowhere else
Enter 0 for the total sleep time and the page refuses: a study that scored no sleep has no AHI, and printing one would be division by zero dressed up as a result
The three indices on one night, and what each divides by
| Index | Numerator | Denominator | This night |
|---|---|---|---|
| AHI (laboratory polysomnogram) | apnoeas + hypopnoeas | hours of scored sleep | 16.8/h |
| RDI (AASM) | apnoeas + hypopnoeas + RERAs | hours of scored sleep | 21.5/h |
| REI (home sleep apnoea test) | apnoeas + hypopnoeas | hours of recording | 12.6/h |
| RDI (Medicare PAP policy) | apnoeas + hypopnoeas | hours of recording | 12.6/h |
| AHI, home study (AASM measure 277) | apnoeas + hypopnoeas | hours of monitoring | 12.6/h |
What the hypopnoea rule does to the numerator
| Rule | Desaturation | Arousal counts instead |
|---|---|---|
| AASM 1A (recommended) | 3% or more | yes |
| AASM 1B (alternative, and what Medicare requires) | 4% or more | no |
Why the same night produces three different indices
A polysomnography report prints a number of events per hour, and the reader’s instinct is to compare it with 5, 15 and 30. The trouble is that there is more than one such number, the report may not say which one it is printing, and they do not agree: the AHI divides by hours of scored sleep, the RDI adds respiratory effort-related arousals to the numerator, and the REI divides by hours of recording because a home test has no EEG and cannot tell sleep from quiet wakefulness.
That last substitution is the one with clinical consequences, and it has a direction. Recording time is never shorter than the sleep inside it, so the REI is never larger than the AHI and is smaller by exactly the sleep efficiency: a patient who slept 75% of the recording gets an REI that is 75% of their AHI. The AASM’s 2017 guideline names that denominator among the factors that can result in underestimation of the true AHI, and recommends polysomnography rather than a repeat home test after a single negative home study. An index is only as meaningful as its denominator: the same event count over a shorter sleep time is a larger index, and nothing about the patient changed.
Then there is the acronym itself. Medicare’s positive airway pressure coverage determination uses RDI to mean apnoeas plus hypopnoeas per hour of recording — the AASM’s REI — and states separately that RERAs do not enter the AHI. The AASM’s RDI does include them, over sleep time. One word, two quantities, differing by nearly nine events per hour on the worked night. Reading the denominator rather than the acronym is the only defence.
Finally the numerator moves too. The AASM’s recommended rule 1A credits a 3% desaturation or an arousal; its alternative rule 1B requires 4% and gives no arousal credit, and Medicare’s own coverage documents require 4%. The same night scored both ways gives two different numbers. Both rules are in circulation, so the report should say which was used. Every number on a sleep study is scoring-rule-dependent and night-to-night variable: the same recording scored under two rules, or the same patient studied on two nights, gives different figures. A coverage or regulatory threshold is jurisdiction-specific and is quoted here as what that named authority publishes, not as a clinical standard and not as advice. A severity band is not a diagnosis. The diagnostic criteria and the severity strata are two different published things, and conflating them is the commonest error on this page’s subject. This page does the arithmetic and names the body that publishes the threshold. It renders no diagnosis and no clinical decision.
Frequently asked questions
What is the difference between AHI, RDI and REI?
They differ in numerator and denominator. The AHI is apnoeas plus hypopnoeas per hour of scored sleep. The AASM’s RDI adds respiratory effort-related arousals to that numerator over the same denominator, so it is always at least as large. The REI keeps the AHI’s numerator and divides by recording time, so it is always at most as large. On the worked night they are 16.8, 21.5 and 12.6 per hour.
Why is the REI lower than the AHI on the same night?
Because a home device cannot score sleep. With no EEG it cannot tell a sleeping hour from an hour lying awake, so it divides by the whole recording — and recording time is never shorter than the sleep inside it. The REI is therefore never larger than the AHI and is smaller in exact proportion to the sleep efficiency. The AASM’s 2017 guideline lists this denominator among the reasons home testing can underestimate the true AHI.
Does the hypopnoea rule change the AHI?
Yes, and it can change the band. Rule 1A credits a 30% flow reduction for at least 10 seconds if there is a 3% desaturation OR an arousal; rule 1B requires 4% and credits no arousal, so every arousal-only event vanishes. The AASM recommends 3%, Medicare requires 4%, and version 3 of the manual made the 4% rule optional. A report that does not say which rule was applied leaves the index incomparable.
Which index does Medicare use for CPAP coverage?
Its positive airway pressure local coverage determination accepts either an AHI, which it defines as events per hour of sleep, or an RDI, which it defines as events per hour of recording. Its tiers are 15 or more events per hour with at least 30 events, or 5 to 14 with at least 10 events plus a documented symptom or comorbidity. Those are coverage rules in one jurisdiction, quoted as what that authority publishes.
Can I trust an AHI from a two-hour recording?
Treat it with caution. Medicare’s CPAP national coverage determination requires that where the index rests on under two hours of continuous recorded sleep, the recorded event count must be at least what two hours at the qualifying rate would have required — which is why its tiers carry event floors of 30 and 10. Twelve events in one recorded hour reads as 12 per hour; the same 12 over two hours read as 6.
Related calculators
References
- American Academy of Sleep Medicine. Sleep Apnea Severity (MIPS clinical quality measure 277, 2025 specification). Darien, IL: AASM; 2025.
- American Academy of Sleep Medicine. Sleep Apnea Severity (quality measure 277, 2017 specification). Darien, IL: AASM; 2017.
- Kapur VK, Auckley DH, Chowdhuri S, et al. Clinical practice guideline for diagnostic testing for adult obstructive sleep apnea: an American Academy of Sleep Medicine clinical practice guideline. J Clin Sleep Med. 2017;13(3):479–504.
- American Academy of Sleep Medicine. AASM clarifies hypopnea scoring criteria. Darien, IL: AASM.
- Centers for Medicare & Medicaid Services. Local Coverage Determination L33718: Positive Airway Pressure (PAP) Devices for the Treatment of Obstructive Sleep Apnea.
- Centers for Medicare & Medicaid Services. National Coverage Determination 240.4: Continuous Positive Airway Pressure (CPAP) Therapy for Obstructive Sleep Apnea, version 3.
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/