That formula is used to find the "withstand rating" of a conductor. You will not find this in the NEC.
Here's an example of how it is used:
Copper can withstand 1-ampere for 5-seconds for every 42.25-circular mils.
So take a #8 AWG conductor. #8 = 16,510 cm / 42.25 = 391-amperes.
Using the formula. 391 x 391 x 5 = 764,405 amperes ^2 (t)
To find the withstand rating, consider a 1/4 cycle overcurrent device protecting a #8 AWG conductor.
A 1/4 cycle = .0042 seconds. So, using this information and the answer from above:
The Square Root of 764,405 / .0042 = 13,491 amperes for 1/4 cycle.
What does this mean? If the circuit has an available fault current exceeding 13,491 amperes and the overcurrent device does not open faster than 1/4 cycle, the #8 conductor will fail.
