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An average sleep cycle lasts from 90 to 110 minutes, in a flux from light sleep to deep sleep. Consider the stages:  Stage 1 is the first and shallowest stage of sleep – it lasts anywhere from 5 to 10 minutes. Your eyes are closed, but it's easy to wake you up. You probably won't feel terribly refreshed if you nap for five minutes, but you shouldn't feel too groggy, either. Stage 2 is a slightly deeper stage of shallow sleep. Your heart rate slows, your body temperature drops, and you begin to sleep into deep sleep. This may last 5-10 minutes. Stage 3 is the "deep sleep" stage. If you're awoken during deep sleep, you will feel groggy and disoriented for a few minutes. Set an alarm for about 25 minutes from now: 20 minutes to sleep, and 5 minutes to fall asleep. A short "power nap" ends before your brain sleeps into deep or slow-wave sleep; you will wake feeling rejuvenated, and you shouldn't feel groggy. If you nap for longer than 20 minutes, you may slip into a deeper sleep phase – and if so, you may find yourself groggier if you wake before the end of the full sleep cycle. The 20-minute power nap, sometimes called the stage 2 nap, is good for alertness and motor learning skills – things like typing and playing the piano. Research shows that longer naps help boost memory and enhance creativity. When you nap for 30-60 minutes, you slip into slow-wave sleep, which is the deep phase that comes between REM "dream" sleep. A 30-60 minute nap is good for decision-making skills – e.g. memorizing vocabulary or recalling directions. Be aware that you may wake up groggier, at first, if you are awoken during the deepest part of the sleep cycle. REM (rapid eye movement) sleep is the final phase of the sleep cycle; it is when dreams happen, and it is when your brain restores itself. REM sleep plays a key role in making new connections in the brain and solving creative problems. The purpose of a nap is to rejuvenate your body, so it's important that you give yourself plenty of time. Set an alarm to make sure that you stick to your desired naptime. If you want to get very precise, add several minutes to your "nap time" to allow yourself plenty of time to fall asleep.
Plan your nap to minimize grogginess. Nap for 20 minutes at a time for a quick "power nap". Nap for 30-60 minutes to slip into slow-wave sleep. Nap for 60-90 minutes to reap the benefits of REM sleep. Try not to oversleep.