[
ukbouldering.com]
Bertuzzi et al¹ found that climbing a 10-m gym route required 17 to 23 kcal, depending on the difficulty of the route and the skill of the climber. Watts et al.² found that climbers' total energy expenditure while climbing was in the range of 10.4–11.2 kcal/min. A reasonable estimate of resting metabolic rate is 1.2 kcal/min. Subtracting this figure from Watts' results gives a net energy of rock climbing of 9.2–10.0 kcal/min. If we assume that a 10-m gym route takes about 2 min. to climb, then Bertuzzi's and Watts' results are quite comparable.
Looking at Bertuzzi's results more closely, they found that highly skilled climbers burned 17.1, 19.3, and 22.0 kcal climbing routes rated 5.10a, 5.11b, and 5.12b, respectively.
So, say that in a day of climbing you can complete 10 5.11b routes. Then, in that day, you will have burned 193 kcal climbing. That's equivalent to jogging a whole 19 minutes. On the other hand, if dropping down to 5.10a would allow you to climb 20 routes in a day, then you would burn 20 × 17.1 = 342 kcal.