Level

Level is the evolutionary measure of buildings and technology. Each building and technology in needs to be built or researched from raw materials. The initial construction/research will yield a Level 1 product. This product will do the job it is intended. Each time a building/tech is upgraded it will increase another level, and become more efficient at what it does. For mines this means they will yield more resources, for engine technologies, the ships they power will get faster, and so on. With each level a building or tech increases it becomes more expensive to upgrade.

Cost
Given a base cost B and growth factor F, the cost C to upgrade a building currently at level L is calculated with this formula, with the result rounded down:

$$C=B\times F^L$$

Given a base cost B and growth factor F, the cumulative cost C to upgrade a building from level 0 to level L is calculated with this formula:

$$C_\text{cum}=B\times\frac{F^L-1}{F-1}$$

Note: The cumulative cost formula may be a few units too high. This is because the formula shown here is not affected by truncation of the decimal, whereas the first formula is. So if two levels in a technology cost 100.7 (truncated to 100) and 250.6 (truncated to 250), this formula would yield 100.7+250.6 = 351.3, but the actual result would be 100+250 = 350.

These formulae are used to calculate each resource separately. Growth factors for buildings and technologies are in the following table:

Example
To find the cost of upgrading a level 1 Metal Mine to level 2, we first get the variables B, F, and L. The base cost for a Metal Mine is 60 metal, 15 crystal. The growth factor for a Metal Mine is 1.5. The metal mine's current level is 1. Thus:

$$C_\text{metal}=60\times 1.5^1$$

$$C_\text{metal}=90$$

$$C_\text{crystal}=15\times 1.5^1$$

$$C_\text{crystal}=22$$

So, upgrading a level 1 metal mine to level 2 costs 90 metal and 22 crystal.