DuskDial

Wake at 3:15 pm

Four bedtimes, each one a whole number of sleep cycles before the alarm, with a quarter of an hour allowed for actually falling asleep.

Go to bed at 7:30 am

5 cycles and 7h 30m asleep: the row nearest eight hours.

Get into bedCyclesTime asleep
6:00 am6 cycles9h
7:30 am5 cycles7h 30m
9:00 am4 cycles6h
10:30 am3 cycles4h 30m
Bedtime7:30 am
Wake up3:15 pm
121234567891011

7h 30m asleep

The night nearest eight hours, laid on a clock face.

Reading the table

Six cycles wants 6:00 am and three wants 10:30 am, and between those two ends sits 4 and a half hours of sleep — and the same 4 and a half hours of evening, which is the trade the table is really offering.

Every line here is a bedtime on the same evening. None of them crosses midnight.

A wake time this late in the day reads as a night-shift schedule: the sleep runs through the morning rather than through the night, and the arithmetic does not care which.

Every time on this page comes from two numbers: a cycle of 90 minutes and 15 minutes between getting into bed and being asleep. Neither is a measurement of you. The reference pages say where each one comes from.

A quarter of an hour either way

If the alarm is set to something near but not exactly 3:15 pm, the table for it is a page of its own.

The other direction

Already in bed and deciding when to set the alarm? The sleep-now page runs the same sum forwards from the time where you are.