Short answer: A lot. Long answer: It depends on a multitude of factors, including body weight, pack weight, elevation gain/loss, terrain, and more.
Here's a quick round-up of a few online estimates (and guesstimates), plus some useful tools, for gauging your total caloric burn on your next backpacking adventure:
Backpacker Magazine suggests a simple calorie estimate based on body weight and the general intensity of the day's activity. For a strenuous day of backpacking with a "heavy" pack (no weight range specified), they suggest 25to 30 calories per pound of body weight. Using my 185-pound self as a proxy, that's 4,625 to 5,550 calories.
Caloriesperhour.com offers easy-to-use resources for estimating calorie burn for more than a hundred different activities. Using their activity calculator for "Hiking—climbing hills, 21-42 pound load" and assuming eight hours of activity, I would burn 5,371 calories. If I were carrying more than 42 pounds, the estimate jumps to 6,042 calories.
The Mayo Clinic lists calories burned per hour for a variety of activities, including backpacking (though no pack weight is identified). According to the site, a 160-pound person burns 511 calories per hour and a 200-pound person burns 637 calories per hour. For eight hours of activity, that would be 4,088 to 5,096 calories, depending on weight.
Fitwatch.com offers five backpacking categories to choose from. According to the site, for backpacking for eight hours with a "moderate" load, I would burn 5,639 calories. With a "moderate to heavy" load, I would burn 6,344 calories.
As you'll notice, estimates vary pretty markedly. For the criteria I used (185-pound person backpacking for eight hours with a moderate to heavy load), estimates range from roughly 4,600 calories to more than 6,300 calories.
Based on my personal experience, I would say that range is a reasonable approximation, with steeper and more strenuous terrain leaning toward the high end, and easy to moderate terrain toward the low end.
“Equipped” is an AMC Outdoors blog, written by Matt Heid.