Calories burn rate calculation - scientific studies

Calories burn rate calculation - scientific studies

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There are many online calculators for measuring walking/running/bicycling calories burn rate. They differ in input parameters like some might need my weight as well as height and some don't. Almost none take into account duration of the exercise (and this is crucial in my opinion).

So my question here is: Where are these formulas (used in these calculators) coming from? Any scientific studies perhaps? Are they reliable?

Also I would like to know what is the most accurate method available for measuring the burn rate (I'm only interested in the scientific part, not going to do this myself).

Disclaimer: Not my field but I'm doing my best.

We often measure the calories consumed indirectly by measuring the quantity of oxygen consumed. As we have a reserve of ATP(ATP is a molecule, a stock of ATP is some kind of battery of our body) in our body, at very short term the oxygen consumption is not necessarily perfectly correlated with energy use but at a longer term it works perfectly fine. Seek for further information on the Citric Acid Cycle to understand why the oxygen consumption is directly related to the energy created (which is itself at a long enough term directly related to energy use). If I am not mistaken a bunch of seconds should probably be a long enough term (time to consume all ATP at the start of an important effort) but I would appreciate if someone could give a reference for that.

For small animals we often put the animal in a chamber and calculate the energy consumption by measuring the volume of CO2 that they expire. For this purpose we have to measure the volume of CO2 at the entrance and at the exit (of the chamber) to measure the difference. For humans, we often put a mask on the face of the "cobaye". We allow him to breath normally without doing any effort for a while and then we ask him to run/bike/whatever on a home trainer.

I don't know much about such studies but it is important to 1) know the variance in energy consumption in the population for a typical exercice 2) understand that lab condition probably differ in various ways from person-to-person real life condition (no wind, no dust, stress of the experimentator, discomfort of the mask,… ).

As I have no idea concerning the variance in the population I cannot tell how representative are the summary values that we can find on many popular websites but I would tend to think that given the experimentation, these numbers has probably been fairly accurately measured.

BMR Calculator: Learn Your Basal Metabolic Rate for Weight Loss

Basal metabolic rate (BMR) is the amount of energy expended while at rest. Use this calculator to find out your BMR and determine your caloric needs.

Everybody requires a minimum number of calories to live. This minimum number is called the basal metabolic rate (BMR). Your BMR is the number of calories your organs need to function while you perform no activity whatsoever—like if you stayed in bed all day.

If you're looking to lose weight, build muscle, or maintain your weight, this information can help you calculate the number of calories you need so you can make more informed decisions about your nutrition and exercise. Use this calculator to learn your BMR and the next steps to move toward your fitness goals!

Resting Metabolic Rate Calculator

Now that you know the approximate number of calories your body needs to survive, here are your next steps.

1. Pick a Workout Program

If you're trying to burn more calories or lose weight, a systematic training program is a must! Here are the most popular ones from BodyFit:

2. Calculate Your Calories

Your RMR is important, but it isn't how many calories you're actually burning each day.'s calorie calculator gives a more complete portrayal of your calorie needs based on your current lifestyle and your physique and fitness goals.

3. Learn About the Best Fat-Loss Supplements.

Supplements can help you reach your goals faster once you have your calories and training in place. Krissy Kendall, Ph.D., shares her recommendations in the article, "5 Ways to Up Your Fat-Loss Supplement Game."

4. Join a fitness community.

For over 10 years, members of BodySpace have been helping each other build their best bodies. Join a fitness community that's over 2 million people strong!

How did we calculate your BMR?'s resting metabolic rate calculator uses the Harris-Benedict equation, which is considered by many experts to be the most accurate RMR and BMR calculation for most types of people. Here's how it works:

For men: BMR = 66.5 + (13.75 x weight in kg) + (5.003 x height in cm) - (6.755 x age in years)

For women: BMR = 655.1 + (9.563 x weight in kg) + (1.850 x height in cm) - (4.676 x age in years)

Bear in mind that this doesn't take your activity level into account!

How Can I Burn More Calories Throughout the Day?

When you're looking to lose weight, it's tempting to simply try to work out harder and more often. But that's not your only option! What is known as non-exercise activity thermogenesis, or NEAT, has been shown in studies to be effective in weight loss and management, as well.

NEAT options include things like:

  • Walking rather than driving short distances
  • Parking farther from a store in a parking lot
  • Doing yard work or housework

These activities may not feel like they "count," but they definitely do! Doing them on a regular basis, in addition to a strategic, progressive approach to training, can help you burn more calories and lose more weight, with no negative impact on your workout recovery.

In addition to simply being more active, lifting weights and eating more protein can also result in raising your metabolism and burning more calories throughout the day, according to registered dietician and powerlifter Paul Salter.

Looking for even more zero-effort calorie burners? Try including the best metabolism-boosting foods in your diet!

How Can I Use My RMR to Lose Fat or Gain Muscle?

Once you use your RMR or BMR to determine your TDEE (total daily energy expenditure), you can make sure that the nutrition plan you follow is appropriate for your level of energy expenditure and that it isn't giving you too many or too few calories. Being armed with this knowledge, rather than guesstimating or blindly following a plan without scaling it to your individual needs, can make or break your muscle gains or fat loss.

Get Systematic About Your Results

Once you have your calories locked in, you can apply a similarly strategic approach to the rest of your training and nutrition. These popular calculators can help you work systematically to your fitness goals!

How Many Calories Do You Need?

Many people seek to lose weight, and often the easiest way to do this is to consume fewer calories each day. But how many calories does the body actually need in order to be healthy? This largely depends on the amount of physical activity a person performs each day, and regardless of this, is different for all people &ndash there are many different factors involved, not all of which are well-understood or known.

Some factors that influence the number of calories a person needs to remain healthy include age, weight, height, sex, levels of physical activity, and overall general health. For example, a physically active 25-year-old male that is 6 feet in height requires considerably higher calorie intake than a 5-foot-tall, sedentary 70-year-old woman. Though it differs depending on age and activity level, adult males generally require 2,000-3000 calories per day to maintain weight while adult females need around 1,600-2,400 according to the U.S Department of Health.

The body does not require many calories to simply survive. However, consuming too few calories results in the body functioning poorly, since it will only use calories for functions essential to survival, and ignore those necessary for general health and well-being. Harvard Health Publications suggests women get at least 1,200 calories and men get at least 1,500 calories a day unless supervised by doctors. As such, it is highly recommended that a person attempting to lose weight monitors their body's caloric necessities and adjusts it as necessary to maintain its nutritional needs.

Fitness trackers accurately measure heart rate but not calories burned

A Stanford inquiry into the accuracy of seven wristband activity monitors showed that six out of seven devices measured heart rate within 5 percent. None, however, measured energy expenditure well.

Euan Ashley and his team conducted a study to determine how accurately seven types of fitness trackers measure heart rate and energy expenditure.
Paul Sakuma

Millions of people wear some kind of wristband activity tracker and use the device to monitor their own exercise and health, often sharing the data with their physician. But is the data accurate?

Such people can take heart in knowing that if the device is measuring heart rate, it’s probably doing a good job, a team of researchers at the Stanford University School of Medicine reports. But if it's measuring energy expenditure, it’s probably off by a significant amount.

An evaluation of seven devices in a diverse group of 60 volunteers showed that six of the devices measured heart rate with an error rate of less than 5 percent. The team evaluated the Apple Watch, Basis Peak, Fitbit Surge, Microsoft Band, Mio Alpha 2, PulseOn and the Samsung Gear S2. Some devices were more accurate than others, and factors such as skin color and body mass index affected the measurements.

In contrast, none of the seven devices measured energy expenditure accurately, the study found. Even the most accurate device was off by an average of 27 percent. And the least accurate was off by 93 percent.

“People are basing life decisions on the data provided by these devices,” said Euan Ashley, DPhil, FRCP, professor of cardiovascular medicine, of genetics and of biomedical data science at Stanford. But consumer devices aren’t held to the same standards as medical-grade devices, and it’s hard for doctors to know what to make of heart-rate data and other data from a patient’s wearable device, he said.

A paper reporting the researchers’ findings was published online May 24 in the Journal of Personalized Medicine. Ashley is the senior author. Lead authorship is shared by graduate student Anna Shcherbina, visiting assistant professor Mikael Mattsson, PhD, and senior research scientist Daryl Waggott.

Hard for consumers to know device accuracy

Manufacturers may test the accuracy of activity devices extensively, said Ashley, but it’s hard for consumers to know how accurate such information is or the process that the manufacturers used in testing the devices. So Ashley and his colleagues set out to independently evaluate activity trackers that met criteria such as measuring both heart rate and energy expenditure and being commercially available.

Study participants wore the fitness trackers while walking or running on a treadmill and while pedaling on a stationary bicycle.
Paul Sakuma

“For a lay user, in a non-medical setting, we want to keep that error under 10 percent,” Shcherbina said.

Sixty volunteers, including 31 women and 29 men, wore the seven devices while walking or running on treadmills or using stationary bicycles. Each volunteer’s heart was measured with a medical-grade electrocardiograph. Metabolic rate was estimated with an instrument for measuring the oxygen and carbon dioxide in breath — a good proxy for metabolism and energy expenditure. Results from the wearable devices were then compared to the measurements from the two “gold standard” instruments.

“The heart rate measurements performed far better than we expected,” said Ashley, “but the energy expenditure measures were way off the mark. The magnitude of just how bad they were surprised me.”

Heart-rate data reliable

The take-home message, he said, is that a user can pretty much rely on a fitness tracker’s heart rate measurements. But basing the number of doughnuts you eat on how many calories your device says you burned is a really bad idea, he said.

Neither Ashley nor Shcherbina could be sure why energy-expenditure measures were so far off. Each device uses its own proprietary algorithm for calculating energy expenditure, they said. It’s likely the algorithms are making assumptions that don’t fit individuals very well, said Shcherbina. “All we can do is see how the devices perform against the gold-standard clinical measures,” she said. “My take on this is that it’s very hard to train an algorithm that would be accurate across a wide variety of people because energy expenditure is variable based on someone’s fitness level, height and weight, etc.” Heart rate, she said, is measured directly, whereas energy expenditure must be measured indirectly through proxy calculations.

Ashley’s team saw a need to make their evaluations of wearable devices open to the research community, so they created a website that shows their own data. They welcome others to upload data related to device performance.

The team is already working on the next iteration of their study, in which they are evaluating the devices while volunteers wear them as they go about a normal day, including exercising in the open, instead of walking or running on a laboratory treadmill. “In phase two,” said Shcherbina, “we actually want a fully portable study. So volunteers’ ECG will be portable and their energy calculation will also be done with a portable machine.”

The work is an example of Stanford Medicine’s focus on precision health, the goal of which is to anticipate and prevent disease in the healthy and precisely diagnose and treat disease in the ill.

Other Stanford co-authors are clinical nurse specialist Heidi Salisbury, RN, MSN clinical exercise physiologist Jeffrey Christle, PhD Trevor Hastie, PhD, professor of statistics and of biomedical data science and Matthew Wheeler, MD, PhD, clinical assistant professor of cardiovascular medicine. Ashley is also a member of the Stanford Cardiovascular Institute, the Stanford Child Health Research Institute and Stanford Bio-X. Hastie is a member of CHRI, Bio-X, the Stanford Cancer Institute and the Stanford Neurosciences Institute.

Stanford’s departments of Medicine, of Genetics and of Biomedical Data Science supported the work.

A windowless lab

For the new study, the researchers wanted to examine how the body's internal clock affected metabolism, separate from people's activity levels, or their sleep and eating habits.

To do this, they recruited seven people to (voluntarily!) spend more than a month in a laboratory without knowing what time of day it was outside. The lab rooms had no clocks or windows, and participants didn't have access to phones or the internet. In addition, the people were assigned specific schedules of when they could sleep, wake up and eat.

Critically, each night they went to bed 4 hours later than the night before, and they kept this up for three weeks. These time shifts are what a person would experience if they traveled around the globe in a week.

"Because they were doing the equivalent of circling the globe every week, their body's internal clock could not keep up," Duffy said. This meant that the body's clock "oscillated at its own pace," or kept its own internal time without relying on external cues, Duffy said. "This allowed us to measure metabolic rate at all different 'biological' times of day," she said. ("Biological" time refers to the time according to a person's internal clock, regardless of the actual time of day or whether a person was sleeping or awake.)

The study found that people's resting energy expenditure, or how many calories they burned, was lowest in the late biological night, when people experience a dip in their core body temperature. Energy expenditure was highest about 12 hours later, in the biological afternoon/evening. Overall, people burned about 130 more calories in the biological afternoon and evening, compared with the early biological morning.

Future studies should explore whether these periodic changes in people's resting metabolic rate contribute to weight gain among people who don't keep regular schedules, the researchers said.

For now, people trying to lose weight should try to keep regular sleep and eating schedules, which are important for overall health, the researchers said.

The researchers also plan to look at how people's appetite and response to food varies with the time of day as well as how the timing of sleep influences those responses.

The Beginner’s Guide to Fitness

Learn the Benefits of Exercise & Get in Shape

You've probably read a bunch of articles about the benefits of exercise, or watched several videos in YouTube to guide you in your 20-minute workout just before you go to work but you're still here and clicked this article looking for something new that might help you to be encouraged and stick with an exercise routine. Don't worry, we got you covered!

Most people are aware that they should exercise — and yet for some reason, most don't do it. Adopting a methodical approach can help you succeed. In attaining your goal in losing your weight, aside from determination, consistency is a great factor. Hence, the importance of setting a realistic goals and a workout plan to guide you along the way.

The Why's of Exercise

Making exercise as part of your daily routine is easier said than done. A lot of people I know, cannot stick with their work out. They started so eager at first but was not able to continue it. There are many factors that contribute as to why a person don't exercise nearly enough like work, stress, lack of time and lack of motivation. That is why it is important to know and ask yourself in the first place why you want to embark to the road of fitness.

Understanding your motivation — your primary purpose for starting a fitness routine — will help you to be inspired and determind to stick up with your plan when unexpected obstacles cause you to think about quitting.

Figure out which of the many reasons to exercise is vital to you. Then always keep it in your mind the very reason why you started your fitness journey whenever you think of quitting.

7 Physical and Physiological Benefits of Exercise

Here are some reasons that might motivate you to get started. Just reading this list will motivate you to never blow off a gym session again or your daily workout.

Even a Little Exercise Might Make Us Happier

Our activity affects our mental health. Working out leads to changes in your brain, such as increased blood flow and the creation of new neural pathways. Hormones such as endorphins, serotonin, dopamine, and testosterone are also released in response to increased physical activity.

Studies by US Department of Health have shown that 30 to 60 minutes of exercise, 3 to 5 times per week will give you significant mental health benefits.

Another study by The University of Vermont found that just 20 minutes of exercise a day can boost someone's mood for up to 12 hours. So next time you're feeling down, go for a 20 minute run or gym session and reap the rewards for the next 11 hours. It is a better solution than drinking alcohol or chasing artificial highs that come with crashes, right?

According to Wendy Suzuki, a professor of Neural Science and Psychology in the Center for Neural Science at New York University, simply moving your body, has immediate, long-lasting and protective benefits for your brain.

Regular Exercise May Keep Your Body 30 Years &lsquoYounger'

The muscles of older men and women who have exercised for decades are indistinguishable in many ways from those of healthy 25-year-olds, according to an uplifting new study of a group of active septuagenarians.

These men and women also had much higher aerobic capacities than most people their age, the study showed, making them biologically about 30 years younger than their chronological ages, the study's authors concluded.

Working Out Affects Our Memory

In a study done at the University of British Columbia, researchers found that regular aerobic exercise, the kind that gets your heart and your sweat glands pumping, appears to boost the size of the hippocampus, the brain area involved in verbal memory and learning.

According to Michelle Voss, a neuroscientist at the University of Iowa, described the findings as &ldquointriguing.&rdquo

&ldquoThe brain regions involved here are also the regions that are thought to play a big role in the deterioration of memory with ageing. […] It would be really exciting to see this type of experiment in older adults,&rdquo she said.

Exercise Slows the Aging Process

Exercise doesn't just make you feel younger—it may actually turn off the aging process in your chromosomes. It has to do with telomeres, the caps at the end of chromosomes that control aging. Telomeres become shorter as you get older, and longer telomeres are associated with longevity. Recent studies have found a link between regular exercise and the lengthening of the telomeres, suggesting that exercise can slow the clock so you live longer. &ldquoThough exercise won't guarantee you a long life, it can greatly improve your odds,&rdquo says Frisch.

It May Lengthen Your Lifespan

Becoming active slashes death risk. The greatest longevity benefits were seen among individuals who had high physical activity levels at the start of the study and increased them even more with time.

Alexander Mok, a doctoral researcher at the University of Cambridge in the United Kingdom said that these highly active people were 42% less likely to die prematurely from any cause. Mok and colleagues conclude: &ldquoThese results are encouraging, not least for middle-aged and older adults with existing cardiovascular disease and cancer, who can still gain substantial longevity benefits by becoming more active, lending further support to the broad public health benefits of physical activity.&rdquo

He also added that it is never too late to start exercising, as becoming more active may lengthen lifespan &ldquoregardless of past activity levels.&rdquo

Exercise Relieves Stress

A long outdoor run in the forest or scenic hike can distract you from anxiety and worries. But there may be a physiological reason exercise lowers stress levels.

According to studies, the endorphin release prompted by a workout has a relaxing effect and reduces anxiety. Also, more meditative forms of exercise, such as yoga or Tai Chi, encourage mindfulness along with moving your body. Staying in the moment so you focus on your breathing and heart rate make it a lot harder to mentally freak out about a stressful work project or that fight you had last night with a friend.

Exercise Boosts Your Mood

You've heard of runner's high, and that blissful mood boost can happen during any sweat-inducing cardio workout. It seems to come down to endorphins: the body chemicals your system cranks out when you're active.

&ldquoEndorphins are like natural opiates,&rdquo says Eric Sternlicht, PhD, associate professor of kinesiology at Chapman University.

Some evidence shows that gym sessions can trigger changes in other neurotransmitters linked to pleasurable feelings, such as dopamine. And the confidence kick you get helps you feel happier too.

The 5 Most Effective Exercises for Weight Loss and Fitness

Now that you're motivated to start on your work out plan, it is now the time to put things in action. Here are the most popular exercises for weight loss. Find what suits your schedule and work on it.

High Intensity Interval Training

To max out the benefits of your workout, intensity is the key. HIIT i.e. High Intensity Interval Training involves short intervals of exercise at almost your maximum effort, followed by longer recovery periods. The secret to HIIT is in how hard you work during your intense intervals. The result? Your body's fat-burning potential shoots up and the pounds melt away. High-intensity exercise increases the release of growth hormones, which mobilize fat to be used as fuel.

So your 20-minute workout ends up burning more calories throughout the day than a long, easy jog around the block. Robin, instructor at Soul to Sole Academy suggests, &ldquoHIIT forces your muscles to work harder, burn more fuel, perform better. It's a smart strategy to help you lose weight fast.&rdquo

Strength Training

It's a misconception that doing weights bulks you up, it in fact also helps you slim down and revs up your metabolism permanently. So head to the weight room, and when you feel like quitting, ask yourself why you started. The secret to shedding pounds is actually to build muscles. Go on, workout with weights. Another option is circuit training, which involves moving quickly from one exercise to the next, and burns 30% more calories than a typical weight workout. It blasts fat and sculpts muscle, burning up to 10 calories a minute.


Did you know that if you include 30 minutes of brisk walking to your daily routine you could burn about 150 calories a day? When you want to shed serious weight, walking doesn't even cross your mind. Well, it should. Walking is the easiest weight loss exercise, and low intensity of course. If you're a beginner, start by walking 3 days per week for at least 20 minutes and then gradually increase the frequency and duration of your walks until you are walking 30-60 minutes per day and six times a week. Now put on your walking shoes, turn on the music and walk off your weight.


If the gym isn't your thing, then just dance! Zumba is a feel-good way to improve your fitness and an effective way of incorporating exercise into your daily routine. Zumba is all about loosening up and burning calories. No wonder, it has been found to help relieve stress, increase energy and improve strength. It incorporates vigourous exercise and high intensity movement which helps sculpt the body.

Sanaa, the founder of Sole to Soul Academy remarks, &ldquoShake, shake, shrink- that's our motto. Before you know it, you'll be losing tons of calories and yet, your energy levels will be soaring! In the midst of squats, twists, multiple dance routines and upbeat music, you'll actually have fun.&rdquo


Swimming workouts burn fat, trim inches and help you get stronger, fitter and healthier than ever. Swimming vigorously can burn up to 500-700 calories an hour, whether you do a breaststroke or freestyle. It's a highly effective form of exercise for weight loss and toning. Swimming engages all of the major muscle groups, from your abdominals and back muscles to your arms, legs, hips and glutes. It can be your sole form of fitness but can effectively compliment other exercises like walking and running as well.

The Workout Plan

We can agree that indeed, exercise is easier said than done. That eager spirit on your first day or second day to achieve your &lsquobody goals' might not be there on the next day. Here comes the part that you need to put your hearts in. It is important to stay motivated until it becomes your habit, you should not just think for the short-term. Your ultimate goal should be to exercise for your life. Without a workout plan, your attempt to your fitness journey might not be successful therefore it is important to have one. Also getting in shape is a lot easier if you have a guide.

Creating a program that suits your body type, lifestyle and schedule is essential. According to Brad Schoenfeld, an assistant professor of exercise science and director of the Human Performance Laboratory at Lehman College in New York, &ldquoIf you're walking around the gym unsure of what to do, then chances are you won't get the most of out of your time there.&rdquo

Those who fail to plan, plan to fail, said Dr. Schoenfeld, paraphrasing a famous quote.

Most people dread the thought of workout. But if you find something that you find enjoyable while doing your exercise then it is highly probable that you you'll love working out and quitting will never be an option. Research suggests it's more likely to last. &ldquoWe know that when people do activities that they enjoy, they're more likely to stick with them,&rdquo said Ms. Johnson of the Mayo Clinic.

Some ideas that you may find enjoyable are the following: trying out the 7-Minute Workout, joining a running club, signing up for CrossFit, playing a team sport you enjoyed as a child, or participating in Zumba.

The ok routine you keep is far better than the perfect routine you give up on.

Whatever reason you have in your mind on why you want to start a fitness routine, what is important is the determination and consistency because the benefits are for long term. Study suggests that 10 years after an exercise, benefits persist. Your body will thank you for what you are doing right now.

We may, in part, be building a physiological reserve, Dr. Kraus says. Raise aerobic capacity or improve insulin sensitivity with exercise, and even as those measures decline later with inactivity and age, we will be better off than if we had never worked out.

Exercise also probably leaves long-lasting imprints on our genes and cells that affect health, Dr. Kraus says.

The Ultimate Backpacking Calorie Estimator

In a special session on military physiology at last week&rsquos American College of Sports Medicine conference, two teams of researchers presented new data on something called the &ldquoPandolf equation,&rdquo which has been used since the 1970s to estimate how much energy it takes to hump a pack. A British team explored how load distribution patterns affect the estimates, since modern soldiers carry weight in different places thanks to things like body armor, instead of having their full load crammed into a backpack. And a U.S. Army team looked into differences between men and women, since women are now filling combat roles that require carrying heavy loads.

The results of these studies are mildly interesting. (In brief, modern soldiers burn more energy than the equation predicts, because it&rsquos more efficient to carry loads on your back. And men burn more energy than women while carrying a given weight, but the equation isn&rsquot quite right for either.)

But the real revelation to me was the original Pandolf question. Here&rsquos a simple tool that tells you how many calories you&rsquore burning as a function of your weight, your pack&rsquos weight, your hiking speed, the incline of the slope you&rsquore walking on, and the nature of the terrain. Amazing! Even if it has some mild inaccuracies in the absolute numbers it calculates, it offers an objective way of answering some of the logistical questions that you face when planning a backpacking trip. How much extra energy will it cost you to haul an optional luxury like your camp chair? How much will you slow down on a prolonged climb or in sandy terrain if you maintain a roughly constant effort level? What&rsquos the most efficient speed if you&rsquore carrying a particularly heavy pack? Or a particularly light one?

I spent some time playing around with the equation to see what it tells us, using the example of a 150-pound person carrying a 50-pound pack at 4 miles per hour on a gravel path as the reference case. The equation itself isn&rsquot particularly revealing, but for the record here it is:

M = 1.5 W + 2.0 (W + L)(L/W) 2 + n(W + L)(1.5V 2 + 0.35VG)

Here M is the metabolic rate, which is how quickly you&rsquore burning energy. This equation gives you a value in watts, but that&rsquos easy to convert to other units like calories per hour.

The inputs into the equation are:

  • W: your weight (kg)
  • L: the weight of your pack (kg)
  • V: your hiking speed (m/s)
  • G: the grade of any incline (%)
  • n: a &ldquoterrain factor&rdquo that adjusts the results for different surfaces (for example, a paved road has a terrain factor of 1.0, but a gravel road is 1.2, since it takes more calories to walk on a soft or uneven surface)

For the equation to work as written, you have to use the units I&rsquove listed above. For the remainder of this article and for the interactive calculator at the bottom of the page, I&rsquove converted to pounds for the weights and miles per hour for hiking speed.

So if you plug my reference case numbers into the equation, you find that this hypothetical hiker (let&rsquos call him &ldquoAlex H&rdquo) is burning about 555 calories per hour. That means that over a six-hour hiking day, he&rsquod be burning 3,330 calories. That&rsquos a lot of GORP.

To be fair, not all of those calories are directly related to hiking. Notice that the equation has three terms in it. The first term reflects the energy cost of simply standing still, supporting your own weight. In this case, that&rsquos 88 calories per hour. The second term reflects the energy of standing still with a pack on. The pack adds another 17 calories per hour. And the third term is where the action is, incorporating the energy needed to walk at a given speed, with the effect of gradient and terrain included&mdashin this case, an extra 450 calories per hour.

That gives us a baseline estimate of the caloric demands of backpacking, so now we can explore what happens when the conditions change. For example, what is the effect of increasing your pack weight between 20 pounds and 100 pounds (shown along the horizontal axis)? And how does that change if you walk at different speeds from 1 mph to 5 mph (shown with different lines)?

Admittedly, the conclusions here aren&rsquot earth-shattering. The heavier your pack, the more energy you burn. At 4 mph, doubling your pack weight from 40 lbs to 80 lbs increases your calorie burn from 526 per hour to 657 per hour, an increase of about 25 percent. You pay a steeper penalty for adding 20 pounds to a heavy pack than to a light pack.

This could be useful to know for trip-planning, for example, to figure out how far you can reasonably expect to make it in a given amount of time. But if you&rsquove already decided how much distance you&rsquore going to cover, then you have to consider that the faster you hike, the less time you&rsquoll spend hiking. That means that hiking faster might sometimes actually be more efficient overall, since you&rsquore burning more calories but for a shorter time. So let&rsquos look again at the same data, but expressed as calories per mile instead of calories per hour:

Now things get a little more complex. In this case, the two worst options are the slowest (1 mph) and fastest (5 mph) hiking speeds, with the best options somewhere in the middle. Some of the lines cross each other, so it&rsquos hard to figure out why this is. To get a clearer picture, let&rsquos look at the same data one last time, but this time switch things around so that hiking speed is on the horizontal axis and pack weight is shown with different lines:

This shows that walking really slowly is inefficient, particularly if you&rsquore carrying a heavy pack. That makes sense: if you take too long to cover your distance, you&rsquore spending unnecessary time with a big pack weighing you down. So going faster is more efficient&mdashbut if you keep speeding up, the cost of trying to walk fast takes over. The sweet spot between walking too fast and supporting the pack for too long, in this sample case, is between 2 and 3 mph. The heavier your pack, the faster the optimal walking speed gets.

It&rsquos important to note that this analysis is only considering the energy cost of walking with a pack. There are other factors that make backpacking hard. For me, at least, keeping a heavy pack on for long periods of time gets uncomfortable no matter how well-fitted it is. My hips and shoulders start to fatigue and sometimes chafe. So I generally find that I prefer a faster-than-&ldquooptimal&rdquo speed, which burns some extra calories but minimizes the amount of time I need to keep the pack on. Still, these graphs give you some ideas of how the energetics of backpacking change as you adjust parameters like pack weight and walking speed.

There are other factors we can play around with. For example, how does calorie burn change as a function of slope? Here&rsquos some data for my reference case at slopes from 0 to 15 percent, with walking speeds from 0.5 to 4 mph shown along the horizontal axis:

Yes, it takes a lot more energy to walk uphill. But we can extract some more useful information, too. Let&rsquos say you&rsquore used to schlepping along at 4 mph with a 50-pound pack on level ground. Now you&rsquore planning a trip that will involve some prolonged uphill. What speed should you expect to maintain if you plan to expend roughly the same amount of effort (or, more specifically, the same amount of energy)? At a 5-percent grade, you&rsquod have to slow down to 2.9 mph. At a 10-percent grade, it would be 2.2 mph.

The last detail I&rsquoll pull out is the effect of terrain. All of the above calculations have used a &ldquoterrain factor&rdquo of 1.2, which is what the Pandolf equation recommends for gravel or dirt roads. But those numbers can change pretty dramatically if you&rsquore on other surfaces. A paved road has a terrain factor of 1.0 swamp has a terrain factor of 3.5. (There&rsquos been lots of research and debate on the appropriate terrain factors over the years I&rsquom using values from a 2015 paper on the topic.)

Here&rsquos the calories-per-mile data for various terrains at three different speeds between 2 and 4 mph:

You can see that bad terrain takes a disproportionately big toll at faster speeds. If you&rsquore planning a route through difficult terrain and you don&rsquot factor in a significant slowdown, you&rsquoll be pushing yourself very hard to stay on pace. If you&rsquore clipping along at 4 mph on a gravel path, then come to a section of ice (terrain factor 1.7), you&rsquoll slow down by about 15 percent to 3.4 mph if you maintain the same energy output. Sand is a little more complicated: its terrain factor is (1.5 + 1.3/V^2), meaning that it changes with hiking speed, so that the slower you go, the harder it gets.

So that&rsquos the Pandolf equation. Exactly what it tells you will depend on the specific details of your trip, which is why we&rsquove designed a simple calculator that allows you to calculate your own caloric cost. Simply plug in your weight and your pack&rsquos weight (in pounds), your hiking speed (in miles per hour), and the grade you&rsquoll be hiking on (in percent), and select one of the terrain options, and the calculator will estimate your caloric cost in calories per hour and calories per mile. Have fun playing with it. and always pack an extra day&rsquos food just in case.

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What is a burden rate? A burden rate is a ratio of indirect costs associated with hiring and maintaining employees to the direct costs of wages of those employees. The indirect costs include training, benefits, sick leave, pensions, etc.

How to calculate burden rate?

    First, determine the total indirect costs.

For this problem, the company has 20 total employees, and the average indirect cost per employee is $10,000.00 per year, so, the total would be 10,000 * 20 = $200,000.00.

The average salary per employee is $50,000 so the total direct wage costs is $1,000,000.00.

Using the formula above, the burden rate is found to be 200,000/1,000,000 = .20.

Like most biochemical systems, the brain's energy expenditure is a complex situation. Students routinely report mental exhaustion following key exams, like the SAT or MCAT. The physical toll of such tests is real, although it's likely due to a combination of stress and concentration. Researchers have found the brains of people who think for a living (or for recreation) become more efficient as using energy. We give our brains a workout when we focus on difficult or unfamiliar tasks.

Scientists have studied the effect of sugar and other carbohydrates on the body and brain. In one study, simply rinsing the mouth with a carbohydrate solution activated parts of the brain that enhance exercise performance. But, does the effect translate into improved mental performance? A review of the effects of carbohydrates and mental performance yields conflicting results. There are evidence carbohydrates (not necessarily sugar) can improve mental function. Several variables affect the outcome, including how well your body regulates blood sugar, age, time of day, the nature of the task, and the type of carbohydrate.

If you're facing a tough mental challenge and don't feel up to the task, there's a good chance a quick snack is just what you need.