I agree, "un-derating" is faster.One way I was taught was to find the ampacity needed instead of selecting a conductor, derate it, find out it is too small, then do it all over with the next size larger.
Lets say you have a continuous load of 17 amps. For continuous loads you need to multiply the load by 1.25, so at this point you need a conductor with an ampacity of 21.25 amps. Now lets say you need a deration of 70% because of number of conductors in the raceway. Instead of picking a conductor, derating, then seeing if it is still large enough just multiply your needed ampacity of 21.25 by the recriprocal of 70% (1/.70 = 1.43).
21.25 x 1.43 = 30.39. At this point we need a conductor with an ampacity of 30.39. If we still need to consider ambient temperature we can still multiply this value by the reciprocal of whatever adjustment is required, and that result is minimum ampacity required of our conductor. Select the one that is equal or greater than the result.
Most of us (myself included) were taught to do this the way that can involve more steps. With the 17 amp load above we will add 125% for continuous load and pick a 12 AWG @75 deg conductor because it is more than 21.25 ampacity. We will then multiply that by 70% for conductors in raceway plus derate for ambient only to find out the 12 AWG is too small and then we do it all over again with 10 AWG.
However, a bigger problem remains: most people are taught and still do the wire size determination incorrectly, just as you have. I am guilty myself. We compound the effect of the 125% factoring and derating.
I believe the part needing pointed out is the 125% factoring for continuous load is before the application of any adjustment or correction factors. Let's look at the requirements first...
210.19(A)(1) said:Where a branch circuit supplies continuous loads or any combination of continuous and noncontinuous loads, the minimum branch-circuit conductor size, before the application of any adjustment or correction factors, shall have an allowable ampacity not less than the noncontinuous load plus 125 percent of the continuous load.
215.2(A)(1) said:The minimum feeder-circuit conductor size, before the application of any adjustment or correction factors, shall have an allowable ampacity not less than the noncontinuous load plus 125 percent of the continuous load.
Restating the application example, we have a continuous load of 17A, with termination temperature limitation of 75?C, and we are going to use 90?C conductors, plus we have to derate them to 70% for 7-9 conductors in the homerun raceway.
1) 110.14(C): 17A results in 14 AWG Cu rated 20A@75?C
2) 210.19(A)(1): 17A?125%=21.25A results in 14 AWG Cu rated 25A@90?C
3) 310.15: 17A?70%=24.3A results in 14 AWG Cu rated 25A@90?C