With a $1.1 million RM 039, a pilot can calculate fuel burn, flight times and ground speed. The titanium-encased assembly of gears and springs can convert gallons to liters and pounds to kilograms, and even measure altitude.

It also tells the time.

With nearly 1,000 parts, the engineering marvel marks a high point in one of chronography’s most demanding domains: aviator watches. The timepiece, less than a centimeter thick and officially called the Tourbillon RM 039 Aviation E6-B Flyback, handles almost all the calculations done by hand for decades using an aviator’s slide rule.

“It is the perfect instrument for facing the challenges that confront pilots during flights,” says a brochure from producer Richard Mille SA.

Just don’t expect to see a pilot wearing one.

“The market isn’t specifically pilots,” says company spokeswoman Caroline Samson.

Price isn’t the issue. A private jet isn’t cheap, either. The thing is, few aviators need an aviator watch.

“In all my years, I’ve never, ever seen anyone use a watch to do a calculation,” says retired British pilot Nigel Champness, who flew in the Royal Air Force and commercially for 47 years. “The closest I came to a pilot’s watch was a steam-driven RAF one.”

To the mysterious wonders of flight, add this: Just as the need aviators have for watches took a nose dive, the ambition of aviator watches soared.

Ever since jeweler Louis Cartier in 1904 helped his aviator friend Alberto Santos-Dumont by creating one of the first men’s wristwatches of any kind, pilots have worn chronographs. Today, though, stratospherically expensive aviator wristwatches are usually on the arms of armchair pilots and in the dreams of aspiring aviators.

“When I was in high school and learning to fly, all I wanted was a pilot watch—and the sunglasses to go with it,” recalls Toby Bright, a private pilot who went on to a career in aviation and now owns three small planes.

For professional aviators, a watch now is “less for aviation and more for making sure you’re on the right time zone to get dinner when you land,” says watch collector and critic Max Reddick.

Computers now fly jetliners with minimal pilot input. Private aviators rely on simple apps and satellite navigation for more information than any watch can offer.

That doesn’t stop watchmakers from flying in the face of history and seeking a lift from aviation’s air of high-tech machismo. Bell & Ross of France makes square watches that resemble vintage cockpit dials. IWC Schaffhausen, of Switzerland, offers watches with names redolent of aviation lore, including Top Gun, Spitfire and Antoine de Saint Exupery, the French pilot who wrote “The Little Prince.”

British aviation watchmaker Bremont this year joined Boeing Co. to make watches with materials from Boeing’s planes. Bremont also released a limited-edition model, each of which displays a tiny swatch of muslin from the Wright Brothers’ first 1903 plane. A white gold version fetches roughly $48,000.

Bremont also offers a line of watches with Britain’s Martin-Baker, the world’s largest producer of ejection seats. The watches underwent the same shock-testing the seats get.

“You don’t really need to have a watch that ejected,” says Bremont spokeswoman Natalie Keigher. “But people like having a story on their wrist.”

Once, watches were as vital to flying as goggles. Early cockpits carried only a few, unreliable indicators. With a watch and mechanical airspeed gauge, pilots could estimate distance flown. A watch could also back up a failed fuel gauge because aviators usually knew how long a full tank would last.

But before that, at the dawn of powered flight, men carried pocket watches on fobs. Mr. Santos-Dumont, a Brazilian rival of the Wright Brothers who lived in Paris, complained to Mr. Cartier that while using both hands to control his plane, “there was no question of him hauling a fob watch out of his waistcoat pocket to check the time,” according to a Cartier history.

Until then, wristwatches were either dainty women’s jewelry or bulky novelties worn by some military officers. Cartier soon marketed its innovation as “the Santos”—probably the first man’s wristwatch on the market.

With aviation’s surge during World War I, wristwatches became standard in the sky, on land and at sea. In peacetime, planes and pilot watches raced ahead. In 1931, Charles Lindbergh and Swiss watchmaker Longines released a model that aviators could use with a sextant and nautical almanac to calculate longitude. During World War II, planes and watches added more functions.

But another spinoff of WWII—computing—wound down watches’ role in aviation. By the 1970s planes were automating and computerized quartz watches, some with digital readouts, nearly killed mechanical watchmaking.

Aviation swooped to the rescue. In 1984, Italy’s national flying team approached Swiss watchmaker Breitling for a pilot-friendly mechanical watch.

“Mechanical watches were out of fashion,” says Breitling Vice President Jean-Paul Girardin. Fashion-mad Italians made it a hit, helping spark the pilot-watch renaissance.

Breitling, which had made watches for Britain’s Royal Air Force since 1936, pushed further skyward, sponsoring air racers, refurbishments of classic airplanes, and the first circumnavigation of the globe in a balloon. It also tries to make aviator watches that aviators find useful, like its Emergency models that include homing beacons linked to satellites.

Still, pilots can ignore even helpful functions. Billionaire aircraft-leasing pioneer Steven Udvar-Hazy, a private pilot, wears a Breitling. “But I do not use any of the tech features,” he says.

The million-dollar Richard Mille RM 039 is aimed mainly at “collectors and people who are passionate about aviation,” says Ms. Samson. The watch took three years to develop and costs so much because of its tiny components’ mechanical and metallurgical complexity. A simpler version lists for about $155,000.

Mass-market brands sell aviator watches for less than $200.

Mr. Bright, the pilot who once dreamed of a watch and sunglasses, now wears a Tissot pilot’s watch from Switzerland—though not for flying.

“Sometimes I think I could use it as a backup,” he says. “But the time’s always wrong.”