The numbers behind the numbers
Every sleep table on this site comes out of two assumptions and a multiplication. These pages say where the assumptions came from and what they are not.
Where the ninety minutes came from
A 1957 laboratory finding, what it actually said, and how it became the number every calculator multiplies.
The fifteen minutes before you are asleep
The second assumption, which is a guess about your evening rather than a finding about anybody.
Counting cycles rather than hours
Why a table of bedtimes lands on odd-looking times, and what changes when the cycle length does.
What a cycle boundary is, arithmetically
What this site means by landing at the end of a cycle, and what it is careful not to mean.
What this site cannot know
The list of things a page of arithmetic has no access to, written out so it is not mistaken for modesty.
Clock time against body time
Why moving between zones is a different sum from counting cycles, and which pages do which.
Why two sleep calculators disagree
Four numbers, any of which a site can choose differently, and only two of which most sites show you.
The sources
Four published sources are cited for what this site says about sleep itself. Everything else is either its own arithmetic, done where you can see it, or a default it chose, like the fifteen minutes to drop off, which is a starting point and not a finding.
- Dement and Kleitman, 1957, "Cyclic variations in EEG during sleep and their relation to eye movements, body motility, and dreaming", in Electroencephalography and Clinical Neurophysiology. The laboratory study the ninety-minute convention descends from. Cited on where the ninety minutes came from.
- "Physiology, Sleep Stages", in the StatPearls medical reference, which gives the cycle as averaging ninety minutes. Cited on the same page.
- Frange, Murray and Coelho, 2023, "The Importance of Sleep for Successful Neurorehabilitation after Stroke", a review in Sleep Science. Its subject is recovery after a stroke, and in passing it gives the average first cycle of the night as about 70 to 100 minutes and the later ones as about 90 to 120. Cited on the same page and on what a cycle boundary is.
- Hirshkowitz and others, 2015, the National Sleep Foundation's duration recommendations in Sleep Health, whose conclusion is that the sleep a person needs varies across the lifespan and from person to person. Cited on what this site cannot know, and the reason the week's tally asks for your own target.
The clock facts come from elsewhere. Sunrise and sunset on the wake-time, shift and route pages are worked from the NOAA solar equations for 2026, to the nearest minute as NOAA's own tables give them; a figure that sits against a clock change says 2026 in the text, because it moves with the date of the change. Time-zone offsets come from the IANA time zone database through JavaScript's own date functions: when the site is built, for the figures written into the travel and world clock pages, and in your browser for the live planner and clocks. Changes too recent for some copies of that database, British Columbia's and Morocco's, the site applies itself; the clock-change page lists them with their sources.
None of these pages is medical writing and none of them is advice. They describe what the arithmetic on this site does, which is a much smaller subject than sleep.