How this calculator works
The ACSM walking equation estimates oxygen use from speed and grade: a horizontal term of 0.1 mL/kg/min per metre per minute, a vertical term of 1.8 mL/kg/min per metre per minute for each unit of grade, and 3.5 mL/kg/min for resting. This page adds backpack mass to body mass because you carry both up the hill. Grade is elevation gain divided by horizontal distance, so a 400 m climb over 8 km is 5 percent. The result is gross energy use, and the equivalent fat mass uses the common 7,700 kcal per kilogram approximation. The equation is not validated for very steep terrain, scrambling or downhill walking.
Formula
Speed (m/min) = distance / time in minutes. Grade = elevation gain / distance. VO2 (mL/kg/min) = 0.1 x speed + 1.8 x speed x grade + 3.5. kcal/min = VO2 x total mass (kg) x 5 / 1000. Calories = kcal/min x minutes. Fat equivalent = calories / 7,700.
Worked example
An 8 km hike with 400 m of gain in 2 hours, a 70 kg hiker and a 10 kg pack: speed is 66.67 m/min, grade is 0.05, VO2 is 6.67 + 6.00 + 3.5 = 16.17 mL/kg/min. That is 16.17 x 80 x 5 / 1000 = 6.47 kcal/min, or 776 kcal over 120 minutes, equivalent to about 0.101 kg of fat. A flat 5 km walk in 1 hour at 60 kg uses 3.55 kcal/min, or 213 kcal.
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Frequently asked questions
Why does the pack matter?
Every kilogram has to be lifted up the hill. The model multiplies oxygen use per kilogram by total mass, so adding 10 kg to a 70 kg hiker raises the estimate by about 14 percent for the same pace.
Does downhill hiking burn the same?
It burns less than uphill for the same distance, though eccentric muscle work means it is not free. The ACSM equation with a positive grade does not model descending, so the estimate is least reliable on a loop with big descents.
Should I use moving time or total time?
Use moving time if you want the energy cost of walking. Including long rest stops lowers the average speed and also adds resting energy, which the equation already includes for the whole period, so a mixed value is approximate.