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### Calculating Maximum Heart Rates by Age

```Date: 08/08/2005 at 17:46:05
From: Alex
Subject: Heart Rate

Find the heart rate of a 15 year old at 85% intensity.  I'm not sure
if I am supposed to add or multiply.

```

```
Date: 08/08/2005 at 22:51:44
From: Doctor Wilko
Subject: Re: Heart Rate

Hi Alex,

Thanks for writing to Dr. Math!

While the true way of measuring maximum heart rate (MHR) probably
involves stress tests done by cardiologists/exercise physiologists,
there are formulas we can use as rules of thumb to estimate our
maximum heart rates, which in turn will allow us to calculate our
target/training heart rates (in this case, 85%).

A well-known formula that I've seen used for determining maximum heart
rate is

A)  220 - (age) = MHR (in beats per minute)

The true maximum heart rates of individuals probably aren't linear as
this formula suggests.  This formula may overestimate the MHR of
younger people and underestimate the MHR of older people.

The author of this website,

Maximum Heart Rate
http://www.brianmac.demon.co.uk/maxhr.htm

also references these formulas:

B)  206.3 - (0.711 * Age) = MHR

C)  217  - (0.85 * Age)  = MHR

While formula A above will probably give you the answer you're looking
for, let's calculate the 85% intensity (of MHR) from all three
formulas to see how they compare.

To do this, we'll calculate

1.  The MHR using each of the three formulas above, and then

2.  Take 85% of each MHR

Formula A:

220 - 15 = 205 (MHR)

205 * 0.85 = 174.25 (85% of MHR)
======

Formula B:

206.3 - (0.711 * 15) = 195.64 (MHR)

195.64 * 0.85 = 166.29 (85% of MHR)
======

Formula C:

217  - (0.85 * 15)  = 204.25 (MHR)

204.25 * 0.85 = 173.61 (85% of MHR)
======

Using these three formulas as an estimate of an average 15-year-old's
maximum heart rate, you can say that his/her 85% intensity level is
somewhere between 166 and 175 beats per minute.

Notice that in each case we found 85% by multiplying the MHR by 0.85,
which is the easiest way to find a percent of a number.

Another useful and probably more accurate formula for determining
one's training heart rate is the Karvonen Formula, which is based on
an individual's resting heart rate.  For more on this, check out

http://www.primusweb.com/fitnesspartner/library/activity/thr.htm

And here are a couple more links you might find interesting:

The Walking Site
http://www.thewalkingsite.com/thr.html

Measuring Exercise Intensity
http://www.ginmiller.com/gmf04/artinfo/targetheart1.htm

Does this help?  Please write back if you have further questions.

- Doctor Wilko, The Math Forum
http://mathforum.org/dr.math/
```
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