Beach Run Calorie Burn Estimation

PoohAA

Wow, running on a beach, just wow. I did it barefoot because screw getting sand in my shoes, sand is practically designed for bare feet. I know that's backwards, but you get it...

So my question is: is there a way to estimate calories burned during a beach run more accurately? I have used runkeeper, mapmyfitness, rundouble, nike+, etc., and I haven't seen anything that might account for the increased effort of running in sand vs level ground. I guess a related question would be how this compares to running on trails?

(Basic stats were: I usually run a 9:30-11:00 min mile, varies greatly depending on temperature, and today's pace was 12:30-13:30 in the sand. I ran for a longer time than usual and shorter distance too , maybe even more effort than usual)