Sleep does not run out evenly. It comes in rounds, and it is kinder to be woken between them than in the middle of one.
Healthy adults typically take somewhere in the region of ten to twenty minutes. If you know your own honest number, use that instead of the default.
A schematic of the shape a night tends to take — not a recording of yours, and not a prediction. Deep sleep clusters in the early cycles; the dreaming stretches get longer towards morning.
Where the ninety minutes comes from. A sleep cycle runs from light sleep down through deep, slow-wave sleep and back up into REM. In adults it averages roughly ninety minutes, but the honest figure is a range — commonly given as about seventy to a hundred and twenty — and it varies between people and across a single night. Early cycles carry more deep sleep and later ones more REM, so they are not even interchangeable with each other.
Why the end of a cycle is the kind place to wake. The grogginess of being hauled out of slow-wave sleep is a real, named thing: sleep inertia. It is worst when you wake from deep sleep and mildest from the light sleep that ends a cycle. That is the whole idea behind this arithmetic.
What this page cannot do. It has no idea when your cycles actually turn over. It is multiplying a population average by a whole number and adding it to a clock. Treat it as a nudge towards a sensible bedtime, not as a measurement — and if you are reliably exhausted, the answer is a doctor, not a calculator.
Sleep-stage architecture and the ninety-minute average are standard sleep-medicine description; the seven-to-nine-hour figure for adults is the common public health recommendation. Nothing on this page is measured, and nothing you type here leaves your browser.