At the heart of this issue is a single unit of measurement—the calorie—and some seemingly straightforward arithmetic. “To lose weight, you must use up more calories than you take in,” according to the Centers for Disease Control and Prevention. Dieters like Nash and Haelle could eat all their meals at McDonald’s and still lose weight, provided they burn enough calories, says Marion Nestle, a professor of nutrition, food studies, and public health at New York University. “Really, that’s all it takes.”

But Nash and Haelle do not find weight control so simple. And part of the problem goes way beyond individual self-control. The numbers logged in Nash’s Fitbit, or printed on the food labels that Haelle reads religiously, are at best good guesses. Worse yet, as scientists are increasingly finding, some of those calorie counts are flat-out wrong—off by more than enough, for instance, to wipe out the calories Haelle burns by running an extra mile on a treadmill. A calorie isn’t just a calorie. And our mistaken faith in the power of this seemingly simple measurement may be hindering the fight against obesity.

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The process of counting calories begins in an anonymous office block in Maryland. The building is home to the Beltsville Human Nutrition Research Center, a facility run by the U.S. Department of Agriculture. When we visit, the kitchen staff are preparing dinner for people enrolled in a study. Plastic dinner trays are laid out with meatloaf, mashed potatoes, corn, brown bread, a chocolate-chip scone, vanilla yogurt and a can of tomato juice. The staff weigh and bag each item, sometimes adding an extra two-centimetre sliver of bread to ensure a tray’s contents add up to the exact calorie requirements of each participant. “We actually get compliments about the food,” says David Baer, a supervisory research physiologist with the department.

The work that Baer and colleagues do draws on centuries-old techniques. Nestle traces modern attempts to understand food and energy back to a French aristocrat and chemist named Antoine Lavoisier. In the early 1780s, Lavoisier developed a triple-walled metal canister large enough to house a guinea pig. Inside the walls was a layer of ice. Lavoisier knew how much energy was required to melt ice, so he could estimate the heat the animal emitted by measuring the amount of water that dripped from the canister. What Lavoisier didn’t realize—and never had time to find out, as he was put to the guillotine during the Revolution—was that measuring the heat emitted by his guinea pigs was a way to estimate the amount of energy they had extracted from the food they were digesting.

Until recently, the scientists at Beltsville used what was essentially a scaled-up version of Lavoisier’s canister to estimate the energy used by humans: a small room in which a person could sleep, eat, excrete, and walk on a treadmill, while temperature sensors embedded in the walls measured the heat given off and thus the calories burned. (We now measure this energy in calories. Roughly speaking, one calorie is the heat required to raise the temperature of one kilogram of water by one degree Celsius.) Today, those “direct-heat” calorimeters have largely been replaced by “indirect-heat” systems, in which sensors measure oxygen intake and carbon-dioxide exhalations. Scientists know how much energy is used during the metabolic processes that create the carbon dioxide we breathe out, so they can work backwards to deduce that, for example, a human who has exhaled 15 liters of carbon dioxide must have used 94 calories of energy.

The facility’s three indirect calorimeters are down the halls from the research kitchen. “They’re basically nothing more than walk-in coolers, modified to allow people to live in here,” physiologist William Rumpler explains as he shows us around. Inside each white room, a single bed is folded up against the wall, alongside a toilet, sink, a small desk and chair, and a short treadmill. A couple of airlocks allow food, urine, feces, and blood samples to be passed back and forth. Apart from these reminders of the room’s purpose, the vinyl-floored, fluorescent-lit units resemble a 1970s dorm room. Rumpler explains that subjects typically spend 24 to 48 hours inside the calorimeter, following a highly structured schedule. A notice pinned to the door outlines the protocol for the latest study: