About the Sleep Cycle Calculator
Alarm clocks don't know where you are in your sleep cycle. If they ring during deep (slow-wave) sleep you wake up groggy even after a long night; if they ring between cycles you can feel fine after less sleep. That mismatch is called sleep inertia.
This calculator works backwards from your wake-up time in 90-minute steps and adds ~15 minutes of falling-asleep time, giving you several bedtimes that should end a cycle right as your alarm rings. It's a simple heuristic — but a genuinely useful one that millions of people search for every week.