The Calculation Order
First, each resource is converted into power with flooring where full resource units are required. For example, every 180 pops gives 1 power, and partial progress below the next full unit does not add another power point.
Second, category caps are applied. Third, capped category power is summed. Fourth, effective power is capped at 200,000. Finally, the game selects the highest degree whose required power is less than or equal to that effective power.
Degree Thresholds
Degree 1 requires 0 power and Degree 100 requires 200,000 power. Degrees 2 through 99 follow the Bloons Wiki degree formula with JavaScript integer display rounding.
Because thresholds become farther apart at higher degrees, the same 2,000 power from one Power Totem can represent a large jump at low degrees but only part of a level near Degree 100.
Why Category Caps Matter
A category cap means extra resources in that category no longer improve Degree. For v39.0+ rules, pops and bonus income cap together at 90,000 power, cash sources cap together at 60,000, non-T5 tiers cap at 10,000, and extra Tier 5s cap at 50,000.
The final effective total also caps at 200,000. Power above that number can be displayed by a planning tool as unused, but it cannot push the Paragon beyond Degree 100.