For math nerds who also run: how fast would you be if you we

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OK, so here's how I derived the formula:

Start by finding your calories burned. I found that most online calculators, HRM's, etc., were reasonably close to the technical definition of a kilocalorie (what we call a calorie), and that is the energy required to move one kilogram a distance of one kilometer. Physics comes into play here, because any change we exact on the movement (shoes, surface, etc.) has an impact on the calories burned. But it generally is within 10% from my experience.

So to find your calories burned, divide your weight in pounds by 2.2 to convert it to kilograms. Then multiply your miles traveled by 1.61. You now have the total number of kilograms and the total number of kilometers. Multiply these two numbers and you have your estimate for calories burned. Even if you don't have a Garmin, a stand-alone HRM, etc., you can try this on your numbers and you'll probably find that the calories from this calculation and the calories given from a site like this are reasonably close.

But how "fast" were these calories burned? You burn roughly the same calories walking a mile as you do running a mile (though running faster can burn more calories), so you have in this a notion of calories per hour. If a 100 kg (220 lbs) person runs 1 kilometer in 6 minutes, they will run 10km (6.2mi) per hour, so their km is burned at a rate of 1000 cal/hour. Most of my runs are actually around this rate of calories per hour, and several years ago I ran a mile at a rate that was equivalent to over 1200 calories per hour.

To get calories per hour, take your calories burned and divide by the number of minutes you worked out (calories per minute), then multiply by 60 for calories per hour.

But if you were carrying less weight, you would not be propelling as much in your run, and so you would not burn as many calories going the same distance. In the example above, someone who 75 kg (165 lbs) running at the same pace would only burn 750 calories per hour. But what if they exerted more energy so that they were burning calories at the same 1000 calories per hour rate? Then the missing piece is to find out how far they need to go to burn 1000 calories.

The 75 kg person burns approximately 75 calories per kilometer, so it would take about 13-1/3 km to burn 1000 calories. This is 8.28 miles, which is a pace of 7.24 minutes per mile. Note that your calculator will give you HUNDREDTHS of a minute, not seconds. So 7.24 is NOT 7'24". To find out how many seconds .24 is, simply multiply it by 60 and you get 14.4. This gives you 14.4" ... the 220-pounder running a 9:41 mile, then, could conceivably exert the same muscular effort on a 165-pound body and run the same distance in approximately 7:14 per mile.

Obviously all of this does not take into account physical fitness. The 220-pound runner will probably be in better shape when they are 165 pounds and so if anything can be encouraged that their mile time might be FASTER than this.

If this doesn't make sense, think of it this way. Consider two people who both weigh 165 pounds and are in the same physical condition. If one of them straps 55 pounds (25kg) to their back and then they both run a mile at the same effort level, it would stand to reason that the one with the extra weight will go slower. To keep the same pace as his friend, the weight-laden runner will have to exert more energy.

So ... using all metric measurements, then, here's a summary of the stuff above:

Weight times distance traveled = calories
Calories divided by minutes, then multiplied by 60 = calories per hour (what I refer to as "effort level" in my training log)

Take effort figure (cals/hour) and divide by your desired weight (again, in kg). This is how far you would need to go IN ONE HOUR to burn the same calories at your goal weight. This figure is in km, so if you need miles, reconvert this by dividing by 1.61.

Divide: 60 ÷ distance you need to go at goal weight.

This figure is how fast you would need to run each mile to burn calories at the same rate, so if you exert the same level of effort when you're lighter, you should be able to run this fast.

WE'RE ALMOST TO THE SIMPLIFIED FORMULA ...

60 / { 1.61 * [ (weight) * (distance) * 60 ] / (length of run) } / (desired weight in kg)

There are so many fractions in there it makes most of us want to throw up a little in our mouths a little bit, but it simplifies to this:

1.61 * desired weight * time of run ... all divided by total calories just burned