How many calories you burn doing arm exercises depends on what kind of arm exercise you do. Other factors that can effect the caloric burn include your body weight, your level of exertion, even the temperature and your mood at the time.
According to fitness resource website Nutristrategy, a 155 pound person will burn 123 calories in 30 minutes of pushups at a light pace with plenty of rest periods. At a vigorous pace, the burn increases to 281 calories in half an hour.
A vigorous, 30-minute session of arm exercises in the weight room will burn 211 calories off a 155 pound man. A lighter session with lower weights and longer rest periods will burn about 105 calories.
Working a punching bag exercises the biceps, triceps, forearms and shoulders. A 155 pound man burns about 211 calories in 30 minutes of bag work. Sparring moves the burn up to just over 317 calories per half hour.