Let's take a different approach and look at the physics number of moving the mass of a 66 kg person 1000 m up.
The equation for energy expenditure is force x distance or, in this case, mass x acceleration x distance. Plugging in the numbers at 66 x 9.8 x 1000, you get
Wow! That's a lot. However, that is not calories which are the energy ...
Short answer: Each 100m of elevation gain is as much effort as 0.8km of running (in terms of calories). Depending on speed, terrain, inclination, climbing efficacy etc. it may go down to an equivalency running/hiking 0.4km.
Each 100m of elevation gain equals adding 0.4km to your hike, according to several hiking calculators:
10km + ...