Among the companies seeking to remedy the problem is Southwest Airlines, which allows pilots to choose between morning and evening flight schedules. The United States Navy recently traded an 18-hour submarine shift schedule for a 24-hour one that more closely matches sailors’ biological rhythms. And at some pharmaceutical, software and financial companies, managers expect employees to come to the office for only a few hours in the middle of the day — or to work off site entirely.

“I think circadian rhythms will be a huge issue for human resources in the future,” said Camilla Kring, a Danish consultant who has helped employees at AbbVie, Roche, Medtronic and other companies learn to respect their natural sleep cycles. “It really makes sense to think about when people have the most energy and when they’re peaking mentally.”

Worker fatigue has played a role in many workplace accidents, most famously the Challenger space shuttle explosion and the Exxon Valdez oil spill, but no doubt countless more on the commute to and from work. The National Highway Traffic Safety Administration estimates that drowsy drivers cause 16.5 percent of fatal crashes.

A survey released last year by the National Safety Council found that 97 percent of workers have at least one risk factor for fatigue, with 27 percent reporting having unintentionally fallen asleep on the job in the previous month and 16 percent that they had experienced at least one safety incident because of fatigue.

“We have a 24/7 society, so we knew fatigue was definitely affecting part of our work force,” said Emily Whitcomb, senior program manager of the council’s fatigue initiative. “But we did not anticipate that fatigue was going to be affecting almost 100 percent of our work force.”

Sleep deprivation may even lead to ethical breaches at work. In a 2014 experiment, Christopher Barnes of the University of Washington and colleagues asked 142 people with extreme chronotypes to show up at their laboratory either at 7 a.m. or at midnight for a dice-rolling game that offered a $500 prize. Reporting was on the honor system. Morning people lied 18 percent more when they did the task at midnight than when they did it in the morning, whereas night owls lied 16 percent more when doing the task at 7 a.m.

Dr. Roenneberg has collected data from 300,000 people and found that chronotypes plot as a bell-shaped curve, with a few individuals at each extreme and most falling somewhere in the middle. According to Dr. Roenneberg’s research, the most frequent chronotype — held by about 13 percent of the population — sleeps from around midnight to 8 a.m. Thirty-one percent of people have an earlier natural bedtime, and 56 percent have a later one. That means for at least 69 percent of the population, getting to the office by 8 or 9 a.m. requires waking up before their body is ready.