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Dear David,

What a great question. It has taken me awhile to marshal the answers and formulae appropriate. Most of my experts were adamant that they would rather bike fifty miles than run it and all said they would rather run on the flat instead of uphill. Of course, we all knew it but ferreting out the real answers took time.

Fuel processing, weight bearing, incline, size in square meters, time , temperature, are involved and probably more factors then you want to know.  Turns out you must take into consideration body mass or weight while running.  ACSM says it is important while running but not while cycling. Walking formula is ml/min/kg but cycling with the seat holding you up is ml/min. 

Incline  is important and the ACMS energy consumption formula for incline is: ml/kg/min= [speed (m/min)x 0.1] [speed (m/min) x 1.8 x % grade].  

More calories are used for running because of the bodyweight used to propel that distance.  Mass x distance = calories burned/energy.  

One correspondent allowed as how it might make 50 kcal difference and reminded us that one donut is 200.

Experts employed; James J., Eugene, OR; Susan K.,Editor, Running and Fitness;  Bethesda, MD; Adam G., MS Exercise Physiologist < the real formulae>;William J., Orthopaedic Surgeon and Squash Player.  

George L. Dixon, Jr., M.D.