The equations
By using the NeherMcGrath equation found in Section 31015 of the NEC and remembering that Delta TD equals zero for 600 volt and less systems we can derive the equation used to calculate derating factors found at the bottom of Table 31016. This simple equation then can be used to increase the ampacity for conductors used at lower temperatures. For instance, the ampacity for a No. 12 copper conductor with 90 degree Centigrade insulation at zero degrees Fahrenheit is 40 amperes. This means that when we use the derating factors in Note 8 to Table 31016, we can install up to 40 No. 12 copper conductors with a 90 Centigrade insulation in the same raceway and protect each with a 20 ampere circuit breaker. How do we do this? The derating factor is 40 per cent and .4 x 40 is 16 amperes; rounding up allows the 20 ampere circuit breaker. This assumes that the branch circuit is not used to supply multiple outlets used to supply cord and plug connected portable loads.
The derivation of the equation for calculating the ambient derating factors is given below. I1 is the ampacity for a conductor at an ambient of TA1, that is 30 degrees C for Table 31016. TA2 is the new ambient for which we want to find the derating factor. In the following diagram I2 equals the new ampacity and the quantity in the radical after I1 in the last equation is the derating factor. The second diagram graphs the ampacity of a No. 12 copper conductor with 90 degree C. insulation (TC) for changes in the ambient down to 50 degrees F. (TA2). In doing the calculation 30 amperers is used for I1 and 30 degrees C is used for TA1. Remember C=5/9(F32) and TA1 and TA2 must be in degrees C.
