The sleep cycle lasts around 90 minutes in total, consisting of four stages three NREM and one REM stage. The body’s actual recovery comes during the REM stage but the cycle must be completed to avoid sleep inertia, the heavy groggy feeling.
When the REM cycle is interrupted, you will feel tired and groggy when upon awakening, a feeling that can possibly extend through the day.
If someone slept 8-10 hours and didn’t fully complete any cycles, due to nature or noise, they will still awaken feeling groggy and tired even though they slept most of the night.
Getting complete cycles is more important than just sleeping time by itself. Even if you aren't able to get 7.5 hours, or the recommended amount of sleep for your age, consult the tables on the sleep calculator to see how many complete cycles you can get with the time you have available to sleep.
The perfect amount of time for a well rested nap will be one complete cycle or 90 minutes.
Most of us aren't able to take a 90 minute break in the middle of the workday however, so what are the options?
If you want to fall asleep, set your clock for 20 to 30 minutes. This will allow you to wake up before falling into a deep sleep. While you won't get the rest from REM sleep, you will avoid the sleep inertia.
Another option is to just lay on flat on your back with you eyes closed for as long as possible without falling asleep. Laying in this position has been shown to lower blood pressure, ease tension and reduce stress.
This is often just as good if you just need to get through the work day and will have the added benefit of helping reduce risk of heart attack.
Avoid taking a nap too late in the day, which may upset your circadian rhythm preventing you from falling asleep at your normal schedule.