There are numerous online calorie calculators for running (e.g. from runners world). What is the underlying formula for calculating energy expenditure while running? This post has an excellent answer for the analog of calories burned throughout the day.
Worth noting, without data from an ECG (heart rate monitor) and face mask based gas analyzers, along with details of the gradient, wind speed, and surface there aren't any accurate equations.
The best you can do is to estimate a VO2 (mL·kg-1·min-1) figure, and convert that into a Kcal one:
Note: respiratoryExchangeRatio is 5.0 for blood sugars, but drops to 4.86 for freeing energy from fat, so if the run is of more than a few min's use this.
Personally I prefer the ACMS Running VO2max equation, as it's relatively simple, will give a number that's accurate within: +/-14.5%, though the conversion to Kcal will multiply the error by a bit, and it's recommended in the paper: Energy Expenditure of Walking and Running: Comparison with Prediction Equations, Hall et Al, 2003
So we have:
The Léger equations is simpler, but does not account for gradient:
Though a not dissimilar degree of accuracy is claimed by the MET tables and formula, and is even simpler:
Where MET is short for Metabolic Equivalent of Task, and is just an abstract way to quantify the relative energy cost of an activity, a number of sites offer MET estimates for specific activities eg.
I googled a bit and stumbled upon the following formula. The source claims it's from Journal of Sports Sciences.
This is the most comprehensive (and quite recent) formula I could find, which takes in account many factors that others don't (age, heart rate etc.). Hope it helps :)
It depends, there are quite a few different formulas available, depending on who was doing the research, and when it was performed. To some extent, the method used to determine the calories burned can have an effect on the formula.
That is a link to a published study from Syracuse University, comparing several different methods of calculating calorie burn. If you are looking at a watch, treadmill or other device that is measuring it for you, somewhere in their literature they should be describing what method they are using.