Sleep Calculator

While you sleep you go round a cycle of light sleep, deep sleep and dream (REM) sleep, again and again through the night. One cycle takes about 90 minutes on average, though it can be anywhere from about 80 to 110 minutes and changes from night to night. Waking at the end of a cycle, when sleep is lighter, often feels easier than being woken from deep sleep. This calculator lines your alarm up with the end of a whole cycle.

The formula

bedtime = wake-up time − (cycles × cycle length) − time to fall asleep
wake-up time = bedtime + time to fall asleep + (cycles × cycle length)
sleep you get = cycles × cycle length

Worked example

You want to wake up at 07:00. Five cycles of 90 minutes is 5 × 90 = 450 minutes, which is 7 hours 30 minutes. Add 15 minutes to fall asleep and you need 7 hours 45 minutes in bed. 07:00 − 7 h 45 min = 23:15. With six cycles (9 hours of sleep) you would go to bed at 21:45; with four cycles (6 hours), at 00:45.

Going the other way, if you get into bed at 23:00 you will probably be asleep by 23:15. Five cycles later is 23:15 + 7 h 30 min = 06:45.

How much sleep you need by age

Ranges are the US National Sleep Foundation's recommendations (Hirshkowitz et al., Sleep Health, 2015). They are general guidance for healthy people; some people do well with a little more or less. For babies and young children, the cycle idea fits less well because their sleep cycles are shorter, so use the ranges as a rough guide only.

Naps

• Power nap (about 20 minutes of sleep): short enough that you usually wake before deep sleep, so you feel refreshed rather than groggy.
• 60 minutes: reaches deep sleep, so you may feel groggy for a little while after waking.
• One full cycle (about 90 minutes): includes light, deep and dream sleep and ends in lighter sleep.

The nap planner adds your time to fall asleep, so the alarm time is when to set your alarm from the moment you lie down. Late-afternoon or evening naps can make it harder to fall asleep at night.

Shift work

After a night shift, the calculator starts your sleep window when you are home and have wound down, and ends it when you need to get up for your next shift. It fits in as many whole cycles as it can. Example: a shift ending at 07:00, 30 minutes to get home and 30 to wind down means bed at 08:00. Starting again at 19:00 with an hour to get ready means getting up by 18:00. That is a 10-hour gap: (600 − 15) ÷ 90 = 6.5, so 6 whole cycles, and the alarm goes at 08:15 + 9 h = 17:15. If the main sleep is short, it suggests a top-up nap before the shift. A dark, quiet, cool room helps with daytime sleep.

Sleep debt

Sleep debt is the gap between the sleep you need and the sleep you got. With the default week (7, 6.5, 6, 7, 5.5, 8 and 9 hours), you slept 49 hours against a need of 8 × 7 = 56 hours, so the debt is 56 − 49 = 7 hours. Paying it back gently, about an extra hour a night by going to bed a little earlier, is usually easier than one very long lie-in.

This calculator gives general sleep-timing ideas, not medical advice. If you often feel very tired in the day, snore loudly, stop breathing in your sleep or can't sleep for weeks at a time, talk to a doctor. Cycle lengths vary from person to person and night to night, so treat the times as a good starting point.