Level (Fallout 4)

Levels are the player character's measure of progress within the SPECIAL character system $$

Gameplay
Levels are a quantifiable measure of experience and abilities. They are determined by the number of Experience Points the player character has earned throughout the game's events. Each time the player character levels up, they have the option to modify skills. Therefore, the player character becomes more equipped to navigate challenges with each level gained.

Calculation
The number of points to earn in level n in order to progress to the next are:
 * $$\Delta\mathrm{XP}_n=75\cdot(n-1)+200\,.$$

Simplified:
 * $$\Delta\mathrm{XP}_n=75n+125\,.$$

The XP thresholds for level n are thus:
 * $$XP_n=37.5\cdot n^2+87.5\cdot n-124\,.$$