The formula
time = reference ∓ (cycles × 90 min) ∓ time to fall asleep
Where it comes from
Sleep is not one uniform block: it runs in roughly ninety-minute cycles that move from light sleep to deep sleep and on to REM. Waking in the middle of a cycle, especially in deep sleep, leaves that feeling of having slept badly even after more hours. That is why six hours sometimes beat seven: six are four whole cycles and seven cut the fifth in half.
How to work it out by hand
- Start from the time you want to wake up
- Subtract blocks of ninety minutes, one per cycle
- Subtract how long you take to fall asleep, around fifteen minutes
- Pick the option that leaves you five or six cycles, which is seven and a half to nine hours
What is worth knowing
The ninety minutes are an average with a fair spread: people run between seventy and a hundred and twenty, and within one night the early cycles are shorter than the late ones. That is why the page gives several options rather than one exact time. And there is a limit to what this arithmetic can do: five cycles slept badly, with light, noise or alcohol, are not five cycles slept well. Keeping a regular schedule matters more than hitting the exact minute.