Calculating Calories Burned based on Average Heart Rate

PS....

I wrote:
> There is no correlation between "heart rate" per se (or percentage of
> max heart rate) and calories burned.

I still believe that statement to be correct. But some years ago,
apparently I did derive a general formula -- perhaps something similiar
to what an HRM might rely on. I posted the following explanation
(edited).

I have not found an online calculator. But I have derived the
following formulas, based on data gleaned from the web. (See footnote
[1].)

kCal = V02max * (%MHR - 37) * 0.000075 * time

VO2max is in ml/min. Time is in minutes. %MHR is the number of
percent, not a fraction. For example, "50" means 50% or 0.50.

Ideally, estimate your VO2max and MHR using any of the fitness tests
for that purpose [8]. Alternatively (with much less accuracy),
estimate your VO2max and MHR with the following formulas. (Note: The
VO2max formulas are my own, derived from published formulas. See
footnote [4].)

male VO2max = (54 - 0.34*age) * weight

female VO2max = (42 - 0.28*age) * weight

MHR = 220 - age, or any other formula or method

Weight is in kg. Weight{kg} = weight{lb} / 2.2.

Footnote 4 has a gender-independent formula for VO2max. However, it
introduces a 10-20% computational "error".

All formulas are based on statistical regressions, so there is inherent
statistical "error" ("+/- X"). I cannot estimate the standard error
because I do not know the std err for the underlying data. I suspect
that the above is similar to how HRMs compute calories. One HRM vendor
indicates that their estimate is +/- 30-40%(!) [5]. I expect that is
typical.

Example #1:

30-year-old 70-kg male walking 4 MPH at 62% MHR.

(54 - 0.34*30 ml/kg/min) * (70 kg) * (62 - 37 %MHR) *
(0.000075 kCal/ml) * (30 min) = 172 kCal

Example #2:

30-year-old 60-kg female walking 4 MPH at 70% MHR.

(42 - 0.28*30 ml/kg/min) * (60 kg) * (70 - 37 %MHR) *
(0.000075 kCal/ml) * (30 min) = 150 kCal

These example results are similar to results based on the Compendium
[9].


-----
Footnotes

[1] kCal = VO2{ml/min} * kCal/ml * weight{kg} * time{min} [10]

VO2{ml/min} = VO2max{ml/min} * (%V02max / 100)

%V02max = (%MHR - 37) / 0.64 [2]

kCal/ml = 4.8 kCal / 1000 ml [3]

Note that %VO2max and %MHR are the number of percent, not a
fraction. For example, "50" means 50% or 0.50.

[2] Swain (1994)
http://www.brianmac.demon.co.uk/maxhr.htm

[3] http://courses.washington.edu/conj/vo2_2004.htm

[4] My own formula, based on regression analysis of modified Leger [6]
and ACSM estimate of VO2max for "average" male and female [7]. For age
20-60. For age 60+, compute using 60.

Gender-independent formula:

VO2max{ml/min} = (47 - 0.28*age) * weight{kg}

10-12% error for male; 14-20% error for female.

[5] Posting dated Apr 29, 2004 9:24 AM at

http://forums.runnersworld.com/thread.jspa?threadID=175758&tstart=15

[6] Leger (1982)
http://www.janatrains.com/default.asp?id=19
http://www.brianmac.demon.co.uk/beep.htm

Original Leger, averaged over all ages and both genders, yields a
regression formula similar to Swain, namely:

%V02max = (%MHR - 36) / 0.57

Therefore, I arbitrarily modified Leger to fit the Swain
regression, namely:

%MHR = 45.6 + (0.64 * %VO2max) - 0.41*age + 0.0038*VO2max*age +
1.55*gender

where gender is 1 for male and 2 for female.

[7] ACSM estimate of VO2max, hardcopy, original source unknown.
Provided by the director of a fitness center.

[8] http://www.brianmac.demon.co.uk/vo2max.htm

[9] http://prevention.sph.sc.edu/Tools/Compendium_tracking.pdf
[defunct]
http://www.solutionsinfitness.com/kcalexpenditure.htm
http://www.caloriesperhour.com/index_burn.html

[10] http://www.solutionsinfitness.com/kcalexpenditure.htm
 >> Stay informed about: Calculating Calories Burned based on Average Heart Rate 

Proctologically Violated©® wrote:
> Didn't follow all of your post (will later)

I have to say: neither do I(!). That is, I follow the equations as
written, but I cannot imagine how I derived them from the published
formulas. I am not sure I can stand behind them without some
confirmation.

> but it seems that, given a set
> of muscles used in the same way, that HR CAN be used as a measure of
> calories, and an approximately linearly proportional one, within a defined
> activity.

For a particular individual and for a particular mode of exercise, I
agree. That is why I wrote: "The statistical correlation is better
for a specific mode of exercise".

But please note that the equations that I posted rely on %MHR, not HR
per se. That makes more sense (to me) because there is a statistical
relationship between %MHR and %VO2max, and it is VO2 that can be used
as an estimate of calories burned -- really, a comparison of oxygen
intake and CO2 output. Of course, all such estimates depend a number
of assumptions, ya-da ya-da ya-da.

I am still concerned that the equations do not take mode of exercise
into account. Actually, perhaps they do. That is, the original
equations might have been based on statistical data for a particular
mode of exercise. I don't remember. Of course, the equations also do
not take individual variables into account. But that is typical of
these kinds of regression formulas. They provide an estimate for the
"average" individual, much like "220 - age" does. None of us is
"average". Ya-da ya-da ya-da.
 >> Stay informed about: Calculating Calories Burned based on Average Heart Rate 

Didn't follow all of your post (will later), but it seems that, given a set
of muscles used in the same way, that HR CAN be used as a measure of
calories, and an approximately linearly proportional one, within a defined
activity.

An interesting application would be in the case of walking and running:
One should find that in walking, when HR is plotted against speed, that the
line is non-linear, because calorie burn w/ walking speed is non-linear--it
is, supposedly, quadratic.
In a jog, the line should be linear.
In a run, it should be linear.
Can only compare within a common gait.

In anaerobic events, the situation is much harder to analyze, but probably
still holds, accounting for epoc, etc.
--
------
Mr. P.V.'d (formerly Droll Troll), Yonkers, NY

Stop Corruption in Congress & Send the Ultimate Message:
Absolutely Vote, but NOT for a Democrat or a Republican.
Ending Corruption in Congress is the *Single Best Way*
to Materially Improve Your Family's Life.
The Solution is so simple--and inexpensive!

entropic3.14decay at optonline2.718 dot net; remove pi and e to reply--ie,
all d'numbuhs

<joeu2004.DeleteThis@hotmail.com> wrote in message
news:1164874227.611272.174300@n67g2000cwd.googlegroups.com...
> PS....
>
> I wrote:
>> There is no correlation between "heart rate" per se (or percentage of
>> max heart rate) and calories burned.
>
> I still believe that statement to be correct. But some years ago,
> apparently I did derive a general formula -- perhaps something similiar
> to what an HRM might rely on. I posted the following explanation
> (edited).
>
> I have not found an online calculator. But I have derived the
> following formulas, based on data gleaned from the web. (See footnote
> [1].)
>
> kCal = V02max * (%MHR - 37) * 0.000075 * time
>
> VO2max is in ml/min. Time is in minutes. %MHR is the number of
> percent, not a fraction. For example, "50" means 50% or 0.50.
>
> Ideally, estimate your VO2max and MHR using any of the fitness tests
> for that purpose [8]. Alternatively (with much less accuracy),
> estimate your VO2max and MHR with the following formulas. (Note: The
> VO2max formulas are my own, derived from published formulas. See
> footnote [4].)
>
> male VO2max = (54 - 0.34*age) * weight
>
> female VO2max = (42 - 0.28*age) * weight
>
> MHR = 220 - age, or any other formula or method
>
> Weight is in kg. Weight{kg} = weight{lb} / 2.2.
>
> Footnote 4 has a gender-independent formula for VO2max. However, it
> introduces a 10-20% computational "error".
>
> All formulas are based on statistical regressions, so there is inherent
> statistical "error" ("+/- X"). I cannot estimate the standard error
> because I do not know the std err for the underlying data. I suspect
> that the above is similar to how HRMs compute calories. One HRM vendor
> indicates that their estimate is +/- 30-40%(!) [5]. I expect that is
> typical.
>
> Example #1:
>
> 30-year-old 70-kg male walking 4 MPH at 62% MHR.
>
> (54 - 0.34*30 ml/kg/min) * (70 kg) * (62 - 37 %MHR) *
> (0.000075 kCal/ml) * (30 min) = 172 kCal
>
> Example #2:
>
> 30-year-old 60-kg female walking 4 MPH at 70% MHR.
>
> (42 - 0.28*30 ml/kg/min) * (60 kg) * (70 - 37 %MHR) *
> (0.000075 kCal/ml) * (30 min) = 150 kCal
>
> These example results are similar to results based on the Compendium
> [9].
>
>
> -----
> Footnotes
>
> [1] kCal = VO2{ml/min} * kCal/ml * weight{kg} * time{min} [10]
>
> VO2{ml/min} = VO2max{ml/min} * (%V02max / 100)
>
> %V02max = (%MHR - 37) / 0.64 [2]
>
> kCal/ml = 4.8 kCal / 1000 ml [3]
>
> Note that %VO2max and %MHR are the number of percent, not a
> fraction. For example, "50" means 50% or 0.50.
>
> [2] Swain (1994)
> http://www.brianmac.demon.co.uk/maxhr.htm
>
> [3] http://courses.washington.edu/conj/vo2_2004.htm
>
> [4] My own formula, based on regression analysis of modified Leger [6]
> and ACSM estimate of VO2max for "average" male and female [7]. For age
> 20-60. For age 60+, compute using 60.
>
> Gender-independent formula:
>
> VO2max{ml/min} = (47 - 0.28*age) * weight{kg}
>
> 10-12% error for male; 14-20% error for female.
>
> [5] Posting dated Apr 29, 2004 9:24 AM at
>
> http://forums.runnersworld.com/thread.jspa?threadID=175758&tstart=15
>
> [6] Leger (1982)
> http://www.janatrains.com/default.asp?id=19
> http://www.brianmac.demon.co.uk/beep.htm
>
> Original Leger, averaged over all ages and both genders, yields a
> regression formula similar to Swain, namely:
>
> %V02max = (%MHR - 36) / 0.57
>
> Therefore, I arbitrarily modified Leger to fit the Swain
> regression, namely:
>
> %MHR = 45.6 + (0.64 * %VO2max) - 0.41*age + 0.0038*VO2max*age +
> 1.55*gender
>
> where gender is 1 for male and 2 for female.
>
> [7] ACSM estimate of VO2max, hardcopy, original source unknown.
> Provided by the director of a fitness center.
>
> [8] http://www.brianmac.demon.co.uk/vo2max.htm
>
> [9] http://prevention.sph.sc.edu/Tools/Compendium_tracking.pdf
> [defunct]
> http://www.solutionsinfitness.com/kcalexpenditure.htm
> http://www.caloriesperhour.com/index_burn.html
>
> [10] http://www.solutionsinfitness.com/kcalexpenditure.htm
>
>
 >> Stay informed about: Calculating Calories Burned based on Average Heart Rate 

I'll have to psych myself up to take a good gander at your equations.
It is very interesting tho.

In the meantime, what do you think of calculating calories via pure
mechanical force x dist, or the much easier delta m g h?
I think this is a viable alternative for anaerobic, mechanically simple
activies, such as most lifts, kneebends, other calisthenics.
--
------
Mr. P.V.'d (formerly Droll Troll), Yonkers, NY

Stop Corruption in Congress & Send the Ultimate Message:
Absolutely Vote, but NOT for a Democrat or a Republican.
Ending Corruption in Congress is the *Single Best Way*
to Materially Improve Your Family's Life.
The Solution is so simple--and inexpensive!

entropic3.14decay at optonline2.718 dot net; remove pi and e to reply--ie,
all d'numbuhs

<joeu2004.RemoveThis@hotmail.com> wrote in message
news:1165080189.140962.176100@79g2000cws.googlegroups.com...
Proctologically Violated©® wrote:
> Didn't follow all of your post (will later)

I have to say: neither do I(!). That is, I follow the equations as
written, but I cannot imagine how I derived them from the published
formulas. I am not sure I can stand behind them without some
confirmation.

> but it seems that, given a set
> of muscles used in the same way, that HR CAN be used as a measure of
> calories, and an approximately linearly proportional one, within a defined
> activity.

For a particular individual and for a particular mode of exercise, I
agree. That is why I wrote: "The statistical correlation is better
for a specific mode of exercise".

But please note that the equations that I posted rely on %MHR, not HR
per se. That makes more sense (to me) because there is a statistical
relationship between %MHR and %VO2max, and it is VO2 that can be used
as an estimate of calories burned -- really, a comparison of oxygen
intake and CO2 output. Of course, all such estimates depend a number
of assumptions, ya-da ya-da ya-da.

I am still concerned that the equations do not take mode of exercise
into account. Actually, perhaps they do. That is, the original
equations might have been based on statistical data for a particular
mode of exercise. I don't remember. Of course, the equations also do
not take individual variables into account. But that is typical of
these kinds of regression formulas. They provide an estimate for the
"average" individual, much like "220 - age" does. None of us is
"average". Ya-da ya-da ya-da.
 >> Stay informed about: Calculating Calories Burned based on Average Heart Rate