onald Kirkendall, an exercise physiologist at the University of North Carolina, will never forget the time he put a heart-rate monitor on a member of the United States rowing team and asked the man to row as hard as he could for six minutes.

The standard formula for calculating how fast a human heart can beat calls for subtracting the person's age from 220. The rower was in his mid- 20's.

Just getting the heart to its actual maximum rate is an immense effort and holding it there for even a minute is so painful that it is all but inconceivable for anyone who is not supremely motivated, Dr. Kirkendall said. But this rower confounded the predictions.

"His pulse rate hit 200 at 90 seconds into the test," Dr. Kirkendall said. "And he held it there for the rest of the test." A local cardiologist was looking on in astonishment and told Dr. Kirkendall, "You know, there's not a textbook in the world that says a person could have done that."

But maybe, some physiologists and cardiologists are saying, the textbooks are wrong.

The question of how to find maximum heart rates is not just of academic interest, medical experts say. The formula for calculating the maximum rate has become a standard in cardiology and in fitness programs, and an entire industry has grown up around it, with monitors sold to individuals and built into exercise equipment.

"There is a need, a clinical and societal need, to estimate the maximum heart rate," said Dr. Douglas Seals, an exercise physiologist at the University of Colorado.

Doctors use the formula when they test patients for heart disease, asking them to walk on treadmills while the speed and incline are gradually increased until their heart rates reach 85 percent of the predicted maximums.

The idea is to look for signs, like chest pain or a sudden drop in the heart rate, indicating that the heart is not getting enough blood. But if doctors underestimate how fast the person's heart can beat, they may stop the test too soon, Dr. Seals noted.

Personal trainers and exercise instructors design fitness programs around the maximum heart rate, often telling people to wear heart rate monitors and then to exercise at 80 to 90 percent of the maximum in brief spurts to build aerobic capacity and at 65 percent to 75 percent to build endurance.

Some heart monitors built into exercise machines even shut the machines down if an exerciser exceeds 90 percent of the predicted maximum. But if the heart rate formula is wrong, these exercise prescriptions are misguided.

"If you're trying to improve their aerobic fitness or to train for certain endurance events, then you want to know with a reasonable accuracy what intensity you're exercising at," Dr. Seals said. "If your estimate is 10 or 20 beats too low, then you're pretty far off."

Exercise physiologists say, however, that being pretty far off is more common than most people expect.

"The more information we have, the more we realize that that formula is just a very rough consideration," said Dr. Jack H. Wilmore, an exercise physiologist at Texas A&M.

And while Dr. Seals is now proposing a new formula to use as a general guide, he and others say it is simplistic to rely on a single formula to predict the maximum heart rates of individuals.

The common formula was devised in 1970 by Dr. William Haskell, then a young physician in the federal Public Health Service and his mentor, Dr. Samuel Fox, who led the service's program on heart disease. They were trying to determine how strenuously heart disease patients could exercise.

In preparation for a medical meeting , Dr. Haskell culled data from about 10 published studies in which people of different ages had been tested to find their maximum heart rates.

The subjects were never meant to be a representative sample of the population, said Dr. Haskell, who is now a professor of medicine at Stanford. Most were under 55 and some were smokers or had heart disease.

On an airplane traveling to the meeting, Dr. Haskell pulled out his data and showed them to Dr. Fox. "We drew a line through the points and I said, `Gee, if you extrapolate that out it looks like at age 20, the heart rate maximum is 200 and at age 40 it's 180 and at age 60 it's 160," Dr. Haskell said.

At that point, Dr. Fox suggested a formula: maximum heart rate equals 220 minus age.

But, exercise physiologists said, these data, like virtually all exercise data, had limitations. They relied on volunteers who most likely were not representative of the general population. "It's whoever came in the door," Dr. Kirkendall said.

In addition, he and others said, gauging maximum heart rates for people who are not used to exercising is often difficult because many prematurely stop the test.

As the treadmill hills get steeper, people who are not used to exercise will notice that their calves are aching. "They will say they can't go any further," Dr. Kirkendall said.

In addition, Dr. Wilmore, the exercise physiologist, said it was clear from the scattered data points that maximum heart rates could vary widely from the formula. "If it says 150, it could be 180 and it could be 120," Dr. Wilmore said.

But the formula quickly entered the medical literature. Even though it was almost always presented as an average maximum rate, the absolute numbers took on an air of received wisdom in part, medical scientists said, because the time was right.

Doctors urging heart patients to exercise wanted a way to gauge exercise intensity. At the same time, exercise gurus, promoting aerobic exercise to the public, were asking how hard people should push themselves to improve their cardiovascular fitness. Suddenly, there was a desire for a simple formula to estimate maximum heart rates.

"You tell people to exercise at a moderate intensity," Dr. Haskell said. "Well, what's a moderate intensity?"

Soon, there was a worldwide heart-rate monitor industry, led by Polar Electro Inc, of Oulu, Finland, selling more than 750,000 monitors a year in the United States and citing the "220 minus your age" formula as a guide for training.