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Simple Math

 


 
 
Cardio Calcs

FitnessMath.com Cardio Calcs includes equations that relate to intensity of activity.

The Karvonen forumula uses Age an Resting Heart to calculate and estimated target heart rate range.

Numerous Google equations provide answers for energy and exertion. The heart is exercised best when it is raised above resting level (1 MET, which 3.5 ml O2/kg body wgt/minute).

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Here is the calculation (Heart Rate Reserve Method or Karvonen Formula) for males and females.

Determine Maximal Heart Rate (HRmax): Males 220-age; Females 226-age

Determine Standing Resting Heart Rate (HRrest): Take pulse; record per minute (6 seconds X 10, 15 seconds X 4, or one full minute)

Calculate Heart Rate Rate Reserve: HRmax - HRrest

Use the following equations to calculate the lower and upper ranges of the Target Heart Rate Range (in this case 50% lower and 85% higher range:

THR50% Heart Rate Reserve = (HRmax - HRrest) * .50 + HRrest

THR85% Heart Rate Reserve = (HRmax - HRrest) * .85 + HRrest

MALE
Male Target Heart Rate Range

Enter your age:

Enter your resting heart rate:

Enter either your lower limit percentage or upper limit percentage in decimal form and click on Calculate:
[Lower limit percentage, such as 55%, 60% (e.g., .55, .60)]
[Upper limit percentage, such as 70%, 85% (e.g., .70, .85)]

Click calculate to see your respective Target Heart Rate Range:
               Your result: Beats per Minute

FEMALE
Female Target Heart Rate Range
Enter your age:

Enter your resting heart rate:

Enter either your lower limit percentage or upper limit percentage in decimal form and click on Calculate:
[Lower limit percentage, such as 55%, 60% (e.g., .55, .60)]
[Upper limit percentage, such as 70%, 85% (e.g., .70, .85)]

Click calculate to see your respective Target Heart Rate Range:

               Your result: Beats per Minute

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EXAMPLE: For male age 40 with HRrest of 72 beats per minute
Here is an example completed calculation (Heart Rate Reserve Method or Karvonen Formula) used in the form above to calculate Target Heart Rate (THR) for apparently healthy individuals. The example shows a calculation of 50 to 85% Heart Rate Reserve):

HRmax = 220 - 40 = 180 beats per minute

Heart Rate Reserve = 180 - 72 = 108 (You don't really need to calculate Heart Rate Reserve separately since it is part of the equation below:

THR50% Heart Rate Reserve = (180 - 72) * .50 + 72 = 126

THR85% Heart Rate Reserve = (180 - 72) * .85 + 72 = 164

THR Range = 126 to 164 beats per minute

GOOGLE CALCULATORS

METS TO O2 CONSUMPTION
What is the relative oxygen consumption of 9 METs?

This is really asking what is the oxygen consumption of someone exerting themselves at 9 times resting level. Energy cost of sitting quietly is about 3.5 ml O2/kg/min, which is 1 MET:
(You can substitute the '9' with other numbers.)


Relative oxygen consumption is the oxygen consumed per kg of body weight per minute. It is reported in units of ml O2/kg/min. Every person has a maximum oxygen consumption, which is commonly given as a rating of physical fitness. Higher VO2max, as it is called, shows better fitness. Beyond the VO2max, the exerciser can no longer deliver oxygen in steady state and anaerobic metabolism kicks in to keep up the workload for a limited time.


O2 CONSUMPTION TO METS
How do you convert relative oxygen consumption to METS?

Simply divide relative oxygen consumption by 3.5 ml O2/kg/min

Answer should be 4.54 METs

 

O2 CONSUMPTION TO KCAL/MIN
How many calories burned per minute from relative oxygen consumption?

The key is to convert ml O2/kg/min to Liters consumed per minute ... a human being burns about 5 kcal per Liter. The example below is for a 200 lb person.
You can replace the '15.89' (ml O2/kg/min) and the '200' (lbs).


Final answer should be 7.2 in kcal/minute or calories/minute
(15.89 ml O2/kg/min X 200/2.2046233 lbs/kg X 5 kcal/Liter X .001 L/ml)


KCAL/MIN TO O2 CONSUMPTION
What is your relative oxygen consumption at a given kcal/minute?

In the expression below you can replace the '7' (kcal value) and the '200' (lb body weight) values:


7 kcal/min X 1000 ml/L X (1 Liter/5 kcal) X (2.204623 lbs/kg)/200 lbs
=15 ml O2/kg/min

 

O2 CONSUMPTION STEPPING
What is your relative oxygen consumption for stepping exercise?

In the expression below you can replace the '8' (step height inches) and the '40' (steps per minute -- remember both horizontal & vertical) values:


Horizontal component = stepping rate X .35 ml O2/kg/min
Vertical component = step height (meters) X step rate X 2.39 ml O2/kg/min
(Resting component is installed as part of each of the vertical and horizontal components)

1 inch = .0254 meters
40 steps/min X .35 ml O2/kg/min + 8 inches X .0254 meters/inch X 40 X 2.39 ml O2/kg/min = 33.4 ml O2/kg/min

 

KCAL PER MINUTE STEPPING
How many kcal/minute burned during stepping?

In the expression below you can replace the '8' (step height inches), the '40' (steps per minute -- remember both horizontal & vertical), and the '137' (weight in lbs) values:


40 steps/minute X .35 ml O2/kg/min + 8 inch step height X .0254 meters/inch X 40 steps/minute X 2.39 ml O2/kg/min X 137 lbs/2.204623 lbs/kg * 5 kcal/Liter O2 consumed X .001 Liters/ml = 20 kcal/min

 

O2 CONSUMPTION TREADMILL WALK
What is the relative oxygen consumption of walking 3 mph at a 3% treadmill grade?

In the expression below we are adding a resting component, horizontal component and a vertical component of oxygen consumption:


In this formula you can replace '3.0' (both mph)
and .03 (percent grade) with your numbers.

Resting component = +3.5 ml O2/kg/min
Horizontal component =
Speed (meters/min) X .1 ml (O2/kg/min)/(m/min)
Vertical component = Grade X speed m/min X 1.8 ml O2/kg/min
1 mph = 26.8224 meters/minute.
Horizontal component oxygen consumption = .1 ml (O2/kg/min)/(m/min)
Vertical component oxygen consumption = 1.8 ml O2/kg/min/(m/min)

3.5 + (3.0 *26.8224)*.1 +.03 * (3.0 *26.8224) * 1.8 = 15.89
EXAMPLE answer in the equation should read 15.89 (ml O2/kg/min)

 

KCAL PER MINUTE TREADMILL WALK
How many kcal/minute burned during walking on treadmill?

In the expression below we are adding a resting component, horizontal component and a vertical component of oxygen consumption and converting to kcal/minute (about 5 kcal per Liter O2 consumed for total body weight -- 200 lb in this example):


In this formula you can replace '3.0' (both horizontal and vertical mph)
and .03 (percent grade) and 200 (body weight in lbs) with your numbers.

Resting component = +3.5 ml O2/kg/min
Horizontal component =
Speed (meters/min) X .1 ml (O2/kg/min)/(m/min)
Vertical component = Grade X speed m/min X 1.8 ml O2/kg/min
1 mph = 26.8224 meters/minute.
Horizontal component oxygen consumption = .1 ml (O2/kg/min)/(m/min)
Vertical component oxygen consumption = 1.8 ml O2/kg/min/(m/min)
Conversion to kcal/per min (200 lbs/2.204623 lbs/kg) * 5 kcal/L* .001 L/ml

(3.5 + (3.0 *26.8224)*.1 +.03 * (3.0 *26.8224) * 1.8) * (200/2.204623)*5*.001 =7.2
EXAMPLE answer in the equation should read 7.2 kcal


O2 CONSUMPTION RUN/JOG TREADMILL
What is your relative oxygen consumption for a run/jog on treadmill?

In the expression below you can replace the '6.0' (mph in horizontal and vertical component) and the '.03' (grade).


Resting component = 3.5 ml O2/kg/min
Horizontal component = Speed (meters/min) X .2 ml (O2/kg/min)/(m/min)
Vertical component = Grade X speed (m/min) X .9 ml O2/kg/min
1 mph = 26.8224 meters/minute.
Horizontal component oxygen consumption = .1 ml (O2/kg/min)/(m/min)
Vertical component oxygen consumption = 1.8 ml O2/kg/min/(m/min)

3.5 + (6.0 * 26.8224 * 0.2) + (.03 * 6.0 * 26.8224 * 0.9) = 40.0 ml O2/kg/min

EXAMPLE answer in the equation should read 40.0 ml O2/kg/min

 

 

KCAL PER MIN RUN/JOG TREADMILL
How many kcal/minute burned during in run or jog on treadmill?

In the expression below we are adding a resting component, horizontal component and a vertical component of oxygen consumption and converting to kcal/minute (about 5 kcal per Liter O2 consumed for total body weight -- 200 lb in this example) You can replace the '6.0' (mph in horizontal and vertical component) the '.03' (grade), and the '200' (weight in lbs) values:


Resting component = 3.5 ml O2/kg/min
Horizontal component = Speed (meters/min) X .2 ml (O2/kg/min)/(m/min)
Vertical component = Grade X speed (m/min) X .9 ml O2/kg/min
1 mph = 26.8224 meters/minute.
Horizontal component oxygen consumption = .2 ml (O2/kg/min)/(m/min)
Vertical component oxygen consumption = 0.9 ml O2/kg/min/(m/min)
Conversion to kcal/per min (200 lbs/2.204623 lbs/kg) * 5 kcal/L* .001 L/ml

3.5+(6.0*26.8224*0.2)+(.03*6.0*26.8224*0.9)*(200/2.204623)*5*.001 = 18 kcal per minute

EXAMPLE answer in the equation should read 18 kcal/min

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*Some calculations may not be appropriate for certain individuals. This site is intended for use as an educational tool, not a clinical tool. Always check with your physician before starting an exercise program.

FitnessMath.com © Copyright 2006 Apriori, Inc. AA-ER.com

 

 

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