As I'm sure many have likely guessed, whether through gut feeling or experimentation, the exp needed per level is exponential, and likely a part of why the game feels slow and grindy to some.

So, I actually stumbled upon what might be the answer to this based on a random mod I found on the nexus. It seems that the formulae for leveling is 200 (the exp to hit level 2 from level 1), plus 75 multiplied by the next level, multiplied by 1.015, or thereabouts.

So in the case to hit level 3, the total exp needed should be about (200 (1.015(75x3)), or about 428 exp.

In other words, it's meant to be an exponential curve where leveling is faster at the start, but significantly slows down as you approach higher levels, which I'm not the biggest fan of personally. For example, I gained about 7 levels just from entering a console command that removes the exponential multiplier, since it seems to be retroactive.

The link to the mod page where I found this info

Here's the important stuff from the mod page

"setgs fXPStart 500
// Changes how much exp you need to level up from 1-> 2 to 500 (default 200)

setgs fXPBase 10
// Changes the Increment to exp needed per level to 10 (default 75)

setgs fXPExpMult 0
// Stops fXPBase from increasing in increments of 5 as you level (default 0.0015)"

Thus, where I got the figures for 200 base exp, the 75 per level, and the multiplicative modifier on experience.

These all apply retroactively to a save once you load, whether by saving and loading, entering a new area, etc. The above reduces the amount of exp significantly, to if I had to guess the levels of fallout leveling. Personally not a fan of the settings as it gave me over 20 levels from the above combination. In contrast, as I mentioned earlier, just adding the exponential multiplier gave me about 7 levels, and reduced the exp I need to level by... 600 exp or so?

Whether you enjoy the current leveling pace or not, I figured this might be helpful for anyone who wants to mess with experience, whether to experiment, give themselves an easier time leveling, etc.

Unfortunately, as these are console commands, I apologize to our console brethren as this won't be usable by you at this time.

EDIT: Through personal experimentation, it seems changing the multiplier and not the formulae for leveling will put you in an EXP debt that you have to overcome. In which case, I highly recommend to use this command to fix the exp debt: Player.modav experience <value>, with value being replaced with the number of exp you wish to gain. By messing with this, I can confirm that while leveling, you will no longer have the exponential multiplier on EXP once you continue leveling after using the fXPExpMult command.