The simple but difficult physics of losing weight

by John Quiggin on June 25, 2020

As Eszter said in her post on health living,, everyone has their own story and their own health. That’s true, but we are all subject to the same physical laws. So, here’s my story and some thoughts on the physics.

I managed to lose about 12 Kg over a couple of years, almost entirely through exercise.

The basic physics is simple
(1) weight loss = (kilojoules burnt – kilojoules consumed)*k,
(2) kilojoules burnt = base metabolism + work done

where k ≃ 0.025 is a constant reflecting the rate at which your body converts kilojoules of food energy into kilograms of fat. If you can alter the right hand side of (1) through any combination of diet and exercise then you will lose weight.

The problem is that altering either of these, or even altering while holding the other constant is really hard. Dieting makes you tired and slows your metabolism. Exercise increases your appetite, and also encourages you to flop once you stop exercising. All that’s because your body isn’t evolved to lose weight easily. Hunger and fatigue are both adaptations to stop you doing that. And, even if you can shift (1) enough to lose some weight, (2) puts a limit on how much you can lose. Balance is restored by the fact that your lighter body takes less energy to maintain and move around.

The crucial thing is to find some change for which you have both the willpower to adopt it initially and the willingness to maintain it indefinitely. For me, as I said, that’s been exercise. I aim to burn 4000 kj (about 1000 calories) a day in addition to base metabolism, which implies about 100 minutes of vigorous aerobic exercise. That’s logistically feasible for someone with flexible working hours and no kids at home, but very difficult otherwise. And it takes a long while to get to the point where you really enjoy it. That’s why the experts mostly recommend working on diet. But, if you can manage it, I think exercise is the better way to go.



Declan Kenny 06.25.20 at 9:34 am

I am a big fan of the science of this debate, and without doubt, exercise is key. But it goes in tandem with diet, and by diet, I mean simply what you eat each day. As you have already alluded to, the body is cute enough to react to what you do as regards exercise, but it has less control over what you feed it. As an over-50s bloke who exercises regularly and has been doing so for years, I would suggest that diet is more important than exercise. But both together is the key. And as you also touch on, whatever lifestyle you adopt (where lifestyle equals exercise plus diet) needs to be sustaiable or it all falls apart. Best of luck with your journey.


Tim Worstall 06.25.20 at 10:08 am

The trigger for me was being put on the blood pressure pills. Along with the “If you lose that weight – chortle chortle – maybe you can come off them again.”

The weight loss being similar to JQ’s above. Achieved with less strenuous exercise, 30 to 40 minutes 5 times weekly does it but also some diet change. The largest of which was switching from the ever present bottle of soda pop and a glass on the desk to a fizzy mineral water and a glass.

Off the pills and 5 inches down in waist size (for some years now, it’s stuck that routine has) but all rather aided by having such a lousily sugared diet in the first place.


Kit 06.25.20 at 10:12 am

There are two aspects to weight loss that I’d encourage you to look into:

1) the subtle yet crucial distinction between weight loss and fat loss.

2) how to manage your macros (protein, fat, and carbs) in order to best reduce muscle loss, keep your energy levels high, and avoid feeling hungry.

While there might not be a royal road to getting in shape, there are countless pitfalls that can be avoided.


reason 06.25.20 at 1:42 pm

I’m not convinced that that simple calculation is all there is to it. There is some evidence that your degree of satiation is a function not of number of calories consumed but of protein. And high fibre foods can fool your satiation feeling as well, and calorific drinks work in the other direction. My experience as someone who has always done masses of sport is that diet is more important than exercise. But there is a twist – the more excercise you do the more you demand better food.


Matt 06.25.20 at 1:50 pm

And it takes a long while to get to the point where you really enjoy it. That’s why the experts mostly recommend working on diet. But, if you can manage it, I think exercise is the better way to go.

With notice that everyone is different, I’ll add that, for me, getting used to regular exercise is a lot easier than dieting. I don’t do strenuous exercise every day, but I do try to do it at least a few times a week (with modest exercise every day.) For me, even when I am doing it regularly, the first few minutes often seem hard, but after that, easy. And, I actually look forward to it. That’s a lot different than “dieting” as that’s normally understood! As for changing one’s diet, I think that learning to not snack is the biggest key for most people. This is not easy, especially with common lifestyles. But, here, being active can help, too, as if you are doing something else, it’s harder to snack. For most people, simply cutting out snacking will help a lot.

(one problem with moderate exercise alone, especially for people not used to getting much exercise, is that it’s enough to make them feel hungrier, but not enough to burn that may calories. So, the extra burn is often more than made up for by extra eating. This is why strenuous exercise is often better, I think. But again, different things will work for different people.)


Trader Joe 06.25.20 at 2:28 pm

Thanks to many for some thoughtful suggestions. I’ll pitch in with my own formula which I’d describe as a very slow, very-long term approach to lowering weight and improving overall health. I’ll add in one other variable, the role of sleep.

I began this about 5 years ago when I noticed my blood-pressure was up and my waist size had gotten to the high end of my normal range and didn’t seem to be going back down (since University I’d maintainted the same pants waist size, it would get snug by the end of winter after limited outdoor activity and normally go back down). I’m sure much of this was metabolism driven by ageing. I had also developed sleep apnea which impacts so many bodily systems.

The sleep issue was easily solved in my case with a night guard and that almost instantly pushed my BP back to normal levels.

Exercise I take a 5 day approach. Monday I run, Tuesday I walk, Wednesday I do light weights, stretches, yoga and then Thursday and Friday I walk and Run respectively. Saturday and Sunday I don’t purposely do anything, but will use them as “make-up” days when schedule prevents doing my normal routine. I’ll swap the schedules a bit owing to time constraints but have found I can’t run on back to back days so that’s my limiting factor.

Each workout is aimed at about 500 calories so Runs are usually around 30mins whereas walks take more like an hour. My mood, general energy level and health govern the intensity – some days you feel great and get done quicker than average, other days not and it takes a bit longer. Roughly its 3.5-4.0 hours per week.

My motivation is simple – I enjoy beer and basically grant myself 1 beer for each 250 calories I burn. If I do the full week – in theory I can have 10 beers. Since apart from maybe holiday time I rarely drink 10 beers in a week, the excess is weight loss, but as JQ notes manifests in better caloric burn.

On diet I try to reduce sugar and processed food to a minimum. I grant myself a couple of exceptions, but never more than 1x per week.

Twice a year – during Lent and from October 1-US Thanksgiving I go all in on no-carbs, reduced calories. The rest of the year I eat as I choose and emphasize portion control.
Like Eszter said in her piece, once you know what a portion should look like you quickly realize how often you’ve taken more. Even something basic like a chicken breast can range from about 1 serving to nearly 3. Once I fixed portion control in my mind for meals I regularly eat it gave me a bit of ‘extra’ available for situations where portion is harder to gauge like restaurants, dinner parties or less familiar foods.

The first year I followed this I found I was thinking about diet and exercise all the time. After that, enough of it became routine that it wasn’t a big deal. My weight has dropped about 10% cumulatively over the 5 years (about 10kg) but my general level of health and activity is just simply better as measured by heart rate, BP, cholesterol etc. I now see weight as more the outcome of good habit and less as some number I need to attack or defend.

That’s my 2cents. It works for me and I find it pretty easy, maybe others would too.


wp200 06.25.20 at 2:39 pm

You can also increase base metabolism.

Mammals have brown fat, special fat that helps maintain temperature by burning calories when you’re cold without any ATP production in the mitochondria of the fat cells.

Brown fat is activated by cold.

In my work as a nuclear medicine physician it’s just a hindrance when brown fat activity obscures tumor activity in PET scans, but rest assured that the industry is looking for a way to pharmaceutically activate brown fat. Or, you could choose to be cold by not wearing enough clothes. Not sure this would work in Brisbane though.


steven t johnson 06.25.20 at 3:17 pm

Equation (1) is mystifying. So far as I know, k is not a constant, which seems to be acknowledged verbally by claims dieting lowers metabolism. Even more puzzling, k, as a factor in weight loss, should be the rate at which the body converts fat into energy, rather than the reverse. Converting energy into fat isn’t weight loss. The definition of k given above makes more sense to me if you write (kilojoules consumed – kilojoules burnt)*k. A negative value times this k would indicate weight loss I should think.

The thing about k not being a constant is not just that k may vary from person to person. The thing is, that the the rise in k as energy intake drops varies even more, which is why so many people don’t get the same effects from dieting (or exercise.)

The time required seems a little optimistic in regards to everyone, judging from these figures.

In particular, it is difficult to understand how all this exercise doesn’t mainly increase muscle mass. Converting fat into muscle seems a worthy goal in itself, but it’s not weight reduction per se. The wear and tear on the joints seem to be omitted too.

Nevertheless, time spent exercising is time not spent eating. Of course, this applies to all sorts of activities. The inferior people who spend too much time at home because they like TV in preference to travel, gallery openings, theater or opera or ballet, skiing trips, business trips, travel to conferences and all manner of better things to do with your time will be apt to gain weight because they’re not as active. Worthwhile lives are much less prone perhaps to comfort eating? I suspect this kind of thing is why many young men gain weight after getting married, for instance.

That brings up the question of how people could be so wrong-headed as to get fat in the first place. It is hard to lose weight, though women may tell me differently when they think about their return to normal after childbirth. Episodes of depression and stress are not generally deemed to be acceptable reasons for bad habits, like increased smoking and drinking and eating.


steven t johnson 06.25.20 at 3:23 pm

PS The amount of energy released by digestion does seem to have a great deal to do with the microbiota in the gut. This is something of a trendy research topic, so it’s a matter of “Watch this space!” rather than to be hasty. Still it’s hard to see how will can affect that


Anonymous 06.25.20 at 6:49 pm

As a >80-yr-old, one who has exercised vigorously all my life (marathons in my 40s, handball (or fives) from age 10 to 75, I have a different experience. Back surgery and a detached quad keeps me from running or even jogging, but I still try to shuffle along a running path or the beach for a few hundred yards; and a replaced shoulder and rotator cuff surgery has made handball all but out of the question. Now both my wife and I continue to have 3-4 sessions with various trainers. My weight hasn’t changed much over the years, but is down slightly from when I was most active. On the other hand, my wife, also active all her life (perhaps not as strenuous as my activity) has put on a few pounds and is having a hell of a time in losing them. Our diets are pretty much (weight-proportional) what everyone recommends for our ages. Let’s face it, there’s a (hormonal?) difference in the sexes that has a major role to play.


tm 06.25.20 at 8:15 pm

“I managed to lose about 12 Kg over a couple of years, almost entirely through exercise.”

Are you sure no change in your diet was involved? Do you know what your daily calorie intake is? I’m just curious. I agree that the physics seems simple enough, but then I observe that I seem to eat more than most people I know, do little exercise, and my weight stays within a narrow band, and I just can’t explain why.


oldster 06.25.20 at 9:05 pm

Isn’t the main gap in the equation due to the fact that “consumed” can either mean “put into the mouth and swallowed,” or it can mean “absorbed into the digestion and processed through the liver”?

There’s a difference: if your gut takes in some calories but passes them through without their being absorbed into the bloodstream, then those calories are not “consumed” in a way that affects the caloric balance between consumption and expenditure.

The equation is relevant to the second sense of “consumed”, not the first sense. But we can only directly measure the first sense, not the second sense.

This is why, as Steven Johnson notes, issues of gut flora are going to turn out to be very important. Some people simply poop out a lot of the calories that they swallow; others extract every last calorie from their food and pass it on to their liver.


Adam Hammond 06.25.20 at 9:49 pm

I was a college athlete who wrecked my knees and became a scientist (biophysics). I also gained quite a bit of fat once I couldn’t run around all day. I am very confident that science does not yet have anything of quality to offer us on the subject of weight loss. It is a matter of behavior and genetics interacting with a complex environment. That is not our strong suit, to put it mildly.

However, medical scientists do have some nice solid evidence that regular exercise is good for you, in study after study. It doesn’t even have to be strenuous or take much time. SOME regular exercise is hugely beneficial compared to none. While it seems obvious, that is an important piece of information to take in. Set aside your desire to lose weight and consider just being healthier. Don’t conflate the two things.

Once you have done SOME exercise for a year, you may find that you want to push yourself … or not … you are already much improved. I continue to find it much easier to motivate my exercise regimen after making this shift in my thinking.

Many fat people are very healthy. Many thin people are very unhealthy. While obesity is a risk factor for a whole host of diseases, overall mortality statistics don’t show an average lower life expectancy correlated to obesity*. That counter-intuitive finding may be because overweight people are more likely to be eating well and exercising — attempting to lose weight, but just getting healthier instead.

(Also, if you are still drinking sugary drinks, including fruit juice, you should stop. That is a pretty solid health finding too.)

since this claim seems ridiculous, I will include one hasty reference, but there are many:


chpooter 06.25.20 at 10:29 pm

One extra step in the exercise equation is to workout before breakfast as there is some evidence that exercise on an empty stomach burns more fat.


steven t johnson 06.26.20 at 1:15 pm

In equation (2) “base metabolism” is not a quantity at all. If it means “basal metabolic rate” or “resting metabolic rate,” then it needs to be multiplied by time resting to become a quantity to add to work done. Work done implicitly is the product of rate of energy used*time working. This is all fairly trivial. But if you substitute equation (2) into equation (1) it’s not clear how basal metabolic rate and k aren’t inadvertently double counting the same thing.

Oldster seems to be correct, but waiting for multiple confirmations over a period of time is prudent for laymen reading about new science. Also, dieting by itself tends to dramatically increase the amount of calories absorbed. There’s no evidence this is due to a change in the intestinal flora. This suggests no magic cure for obesity, however defined, by managing the gut.


Cian 06.26.20 at 2:38 pm

I am no expert, but when I looked into the research a few years ago it seemed like that while exercise is a good idea for lots of reasons it doesn’t particularly help with weight loss. The advice seemed to be exercise for the benefits (blood pressure, cognitive ability, energy levels, immunity, etc), but diet is the key to weight loss.

My own experience has been that the way you eat and what you eat is far more important than counting calories. Replacing simple carbs with complex carbs and high fibre foods makes a big difference, as does cutting out sugary drinks entirely. And trying to change snacking habits is useful. I try to eat either vegetables, or seeds, or hummus – and that again makes a big difference. It’s a lot harder to do though if you have a house filled with snack food…

I also find that if I eat complex carbs I’m less likely to get hungry and high fibre foods tend to fill me up so I don’t really want to eat anything else.


Cian 06.26.20 at 2:41 pm

I do hate the modern thing where exercise has to be painful though. I run because I enjoy running, but I don’t see the point in trying to push myself, or break targets. If you enjoy doing that then fine, but honestly just doing something seems to be enough.


HankP 06.26.20 at 6:53 pm

I’m in the process of losing weight after some medical issues had me recumbent and not exercising for several months. I think exercise is important for a variety of reasons and I do ~30 minutes of aerobic/weights a day, but I think it is a very difficult way of losing weight for most people. Look at it this way, to burn 100 calories requires ~15 minutes of running, while not eating 100 calories is two strips of bacon or 1/2 cup of rice. If you stay away from starches and processed foods and eat something filling like a salad I think dietary restrictions are a better way to go for most people.


John Quiggin 06.27.20 at 4:29 am

Cian @17 “the modern thing where exercise has to be painful though” I associate “no pain, no gain” with the 1970s, and with the fact that everyone who ran then seemed to wreck their knees.

Like you my rule is “it has to be enjoyable”. I’m willing to put up with a bit of muscle soreness, because I know it’s part of the process of building strength and goes away soon. But any sign of joint pain or just plain exhaustion and I stop


divelly 06.27.20 at 8:47 pm

Don’t see any good advice here.
Obesity good.
Exercise good.
Sleep good.
Sugar bad.
Smoking bad.
My Great Grandmother’s oldest brother Jimmy survived on Corned Beef and Irish Whisky and lived to 98.
“Eat food.Not too much.Mostly plants.”


AnthonyB 06.30.20 at 1:16 am

In the U.S., people talk about the Covid-15: the fifteen pounds gained during lockdown as a result of eating comfort food. I, on the other hand, during lockdown have lost ten pounds due to eating my own vegetarian food at lunchtime as opposed to restaurant vegetarian food. It’s completely a matter of portion size. At home I have a modest plate of whatever, but when I used to leave my office to bring food back to my desk, I would end up with a 1-lb. platter of Middle Eastern fare (rice, hummus, vegetables, slaw, olives, feta, etc.). When I would go out for a cheese sandwich, it would be enormous compared to what I make at home. Weird portion size is a specifically American thing but at home, Americans don’t serve the ridiculous portions they expect (for economic reasons?) from restaurants.


Silverlake bodhisattva 06.30.20 at 6:48 am

I believe the titular gorilla in Daniel Pinkwater’s now-long-out-of-print opus, “Fat Elliot and The Gorilla” summarized the equation as “Eat less stuff. Eat better stuff. Move around more.”

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