# Walking formula ?October 15, 2006 3:50 PM   Subscribe

Is there a simple formula to calculate how many calories are used during walking exercise ?

Specifically, if the following is known: weight, speed, incline (% or degrees); I'd like to be able to see (plot) the relationship between walking faster, longer or steeper.

Also, is adding additional weight (backpack) an effective way to get use more energy in the same time period ?

Thanks
posted by matholio to Health & Fitness (7 answers total)

Searching for "walking calories burned formula" turns up quite a bit of useful information.

This site has another equation, which is:
For moderate walking:
Calories burned = 0.029 x weight (lbs) x time (minutes)

For Vigorous walking:
Calories burned = 0.048 x weight (lbs) x time (minutes)
The thing that makes this difficult is that everyone has differences in metabolic rates, energy reserves, muscle mass, etc. So there is no single formula that will be perfect. Any formula will only give you approximations, but generally, the approximation is close enough for your purposes as a dieter or person in training.
posted by chrisamiller at 4:20 PM on October 15, 2006

Ankle-weights will be more effective than a backpack -- I can't tell you how to figure thie into the formula, though.
posted by winston at 4:57 PM on October 15, 2006

All of these are gross estimates. When a well trained runner hits the road doing 7 minute miles there are precious few calories burned. However, when a newbie with similar weight hits the road there will be many calories burned due to poor technique. In cycling and swimming the differences can be even more dramatic.
posted by caddis at 5:44 PM on October 15, 2006

While many of these formulas will give you a pretty good estimate and allow you to compare the relative merits of different kinds of activity, the exact number of calories burned will depend on your metabolic rate, which varies somewhat from person to person based on factors that are somewhat difficult to capture.

BTW, ankle weights are discouraged by most reponsible trainers because they put extra strain on joints and work strengthen muscles unevenly, which can contribute to injury. Stick with the backpack.
posted by decathecting at 9:06 PM on October 15, 2006

Response by poster:
Well, I thought it would be more about moving a mass (m) up an incline (i) for a distance (d) at a constant speed (s). (or similar)

Why would there be any variance because of metabolism ?
Surely it's the same formula.

I can appriciate a lighter person would need less energy to move the same distance, and that a fitter person will find that energy from different sources, and need less time to recover, but everyone has the same laws of physics.

hmm, perhaps it's more to do with math and less to do with health.

Thanks anyway.
posted by matholio at 12:18 AM on October 16, 2006

Best answer: i read somewhere a few years ago (can't remember where) about why the bicycle is such a more efficient form of transport as compared to walking or running.

if you want to look at it from a physics point of view, it's because when a person pedals a bike, their center of mass stays at the same height through the entire pedal stroke, so the energy they expend goes almost entirely into turning the wheels of the bike.

walkers/runners, on the other hand, have a center of mass that moves up and down with each step. so when someone is walking, with each step they have to do some work (in the physics sense of work = force x distance) against gravity. some fraction of the calories burned are this work; most of the rest are overhead associated with the physiology of delivering energy to your muscle cells.

so obviously the amount of energy a person spends has a great deal to do with their gait when running. you can see this in elite long-distance runners; watch their hips as they run and you'll see very little up-down motion. so form has a lot to do with the number of calories burned.

anyway, if you assume some sort of baseline rate of calorie burning associated with running with a particular gait and some particular metabolism on flat ground at a given speed, i think you can just add the physical work done against gravity in lifting your mass from height h1 to h2. this work is

W = mg(h2-h1)

the power is work / time:

P = mg(h2-h1)/t

if you take m as your mass in kg, g as the acceleration of gravity = 9.8 m/s2, t as the time you ran in seconds, and (h2-h1) is the elevation change in meters.

the number you get will be in Joules/sec, and to convert to calories per hour multiply it by 0.86. (a "food calorie" is actually 1 kilocalorie.) anyway that will give you the extra calories per hour you burned by running on a slope instead of flat ground.

the above is subject to the following caveats: the rate at which calories are burned determines the metabolic pathways that bring energy to your muscles. if your extra energy expenditure lifts you above the threshold from aerobic respiration to anaerobic then the metabolic overhead increases.

also you don't get the work back when running downhill because the chemical reactions only work in one direction. (though you do burn less as you no longer have to lift your center of mass as much with each step.) finally this doesn't include everything, like the work done in swinging your arms when you run, etc. but it's probably pretty close to a first approximation.
posted by sergeant sandwich at 3:38 AM on October 16, 2006

Response by poster: