Formula for calculating user experience - ruby-on-rails

Question

I would like (without using a gem) to create a level and experience point system for my users.
When creating his account, he starts level 0 with 0 experience points. To reach level 1 he will need 10 additional points, for a total of 10 points. For level 3 he will need 30 additional points, for a total of 60 experience points. Each additional level requires 10 more experience points. (see example below).
Level | Total XP | XP for next level|
----------------------------------------|
0 | 0 | 10 |
1 | 10 | 20 |
2 | 30 | 30 |
3 | 60 | 40 |
4 | 100 | 50 |
5 | 150 | 60 |
etc...
I would like an xp column in my user table that would represent the total experience of a user.
In my view I would like to display its level. But what is the formula for calculating this?
Let's imagine that my user has 157 experience points in total. Which corresponds to a level 5. How to calculate a level only via the total experience points and how to calculate this regardless of its total experience point whether it is 38 like 369 or 4393.

Answer 1

I'm not sure if this is exactly what you wanted. It's more of an algorithm than a formula, but here is a method that will return the proper level based on the experience given. Think of the bar variable like the bar you have to get over to meet a new level, and think of the step variable like the amount of experience added between each level (as you describe in your right-most column).
def calculate_level(experience)
level = 0
bar = 10
step = 10
while experience >= bar
level += 1
step += 10
bar += step
end
level
end
Example output:
irb> calculate_level(0) # => 0
irb> calculate_level(9) # => 0
irb> calculate_level(10) # => 1
irb> calculate_level(11) # => 1
irb> calculate_level(29) # => 1
irb> calculate_level(30) # => 2
irb> calculate_level(31) # => 2
irb> calculate_level(59) # => 2
irb> calculate_level(60) # => 3
irb> calculate_level(61) # => 3
irb> calculate_level(99) # => 3
irb> calculate_level(100) # => 4
irb> calculate_level(101) # => 4
irb> calculate_level(149) # => 4
irb> calculate_level(150) # => 5
irb> calculate_level(151) # => 5

Answer 2

Calculate the inverse of my above comment and take the floor:
def calculate_level experience
(Math.sqrt(0.2 * experience + 0.25) - 0.5).floor
end

Answer 3

You can use such "formula"
def calculate_level(experience)
(1..).find { |i| (experience -= 10 * i).negative? } - 1
end
Just decrease experience on 10x steps every time and check if result is not negative
calculate_level(0)
# => 0
calculate_level(9)
# => 0
calculate_level(10)
# => 1
calculate_level(11)
# => 1
calculate_level(29)
# => 1
calculate_level(30)
# => 2
calculate_level(31)
# => 2
calculate_level(59)
# => 2
calculate_level(60)
# => 3
calculate_level(61)
# => 3
calculate_level(99)
# => 3
calculate_level(100)
# => 4
calculate_level(101)
# => 4
calculate_level(149)
# => 4
calculate_level(150)
# => 5
calculate_level(151)
# => 5
calculate_level(209)
# => 5
calculate_level(210)
# => 6