I have 100 amp breaker with a 4 wire 8-3 running from main breaker box little over 100ft to a 125amp sub panel will this work or is 8-3 to small also I'm going to have 1 30 amp double pole breaker for 220 AC/heat window unit and three 20amp breaker for plugs and lights coming out of the sub panel it's self
A 125A subpanel being fed by a smaller breaker is absolutely fine. If anything, make sure the panel is big enough in terms of the number of spaces. More spaces are dirt cheap when buying the panel, running out of spaces is expensive. I generally go straight for 200A panels even if I mean to feed it off 60A - I'm a bit of a zealot about spaces.
Your 100A breaker is a wild mismatch for your #8 cable. Not even close.
You have several options depending on your circumstances, all radical.
Change the breaker to 40A
A subpanel is not a service. Wiring to a subpanel gets its ampacity off the same table as branch circuits, the common NEC 310.15(B)(16). Since you must pull out of the 60C table, that puts you at 40A.
Revisit the air conditioner/heater load. I find it astonishing that a window air conditioner could possibly be 6kw and draw the same as a massive whole-house unit, unless it uses resistive heating instead of heat-pump heating. Maybe it can work on a 20A circuit. There is a narrow exception for certain motors, hence ThreePhaseEel's question about your motor nameplate on the A/C unit. You should shoot him a pic of the nameplate.
If you really want the circuit to be 100A, then upsize your cable to 1/0 aluminum. (Running large copper such a distance is just a waste of money, and invites dissimilar-metal corrosion since the lugs you connect to will be aluminum.)
While this is the minimum size for 100A, it will also satisfy voltage-drop concerns as its drop will only be about 2%.
Beast of both worlds: 100A on the #8
This is beast mode, and not for the amateur who likes living. Great care must be taken in installation to keep the super-zappy stuff away from loved ones.
If the cost of replacing the cable is prohibitive, and you need most of 100A, then your only remaining option is to "step it up" for transmission with transformers.
The power involved is 24,000 watts. This happens at 240V@100A, 480V@50A, or 600V@40A. 40A is within the current limit of your wire.
So you get two 25,000 VA transformers that have 600V on the primary (@41 amps) and 120/240 on the secondary (@104 amps). These things are not cheap, but can sometimes be had used. Canada's 575V is close enough IMO. Transformers are bidirectional, so the house's 100A breaker goes to the 240V secondary of one transformer. This steps up to 600V on the primary, which is attached to the long cable. The other end of the cable goes to the other transformer's 600V primary. Its secondary gives 120/240V.
The transformer isolates, so it must be treated as its own separate service, and the neutral must be bonded to a local grounding rod and the grounding system, since the subpanel now counts as a main panel. Now you can use the service feeder table for sizing your wires (#2 aluminum) between transformer and now-main panel.
Of the works, only a tiny bit is 600V, and that is isolated, so a person has a chance to survive casual touch. Still, the installation should be designed to minimize exposure, e.g. Have the wire go straight to the transformer, no splices or reroutes, and put the transformer in an enclosure or outside.
You have a 125 Amp Sub panel fed with a 100 AMP breaker with a 100 foot feed.
You want to get to 100 feet at 100 AMP (your panel is rated 125 - I would install for that if my main service panel could handle the additional 25 amp ) NEC 310.15 (B) (2011 version). Shows that the feed wires will need to be at least #4 (copper) or #2 (Aluminum) at 100 AMPS - at 125 you move up 2 gauges to #2 and 1/0 respectively. Your 8-3 is about 40 amps load and will melt before that 100 Amp breaker trips.
Ratings for 120/240 volts, 3-Wire, Single-Phase Dwelling
Services— See NEC Table 310.15 (B)(7)
These are permitted ratings for Dwelling Unit service and feeder conductors
which carry the total load of the dwelling.
NEC 210.19 Conductors — Minimum Ampacity and Size (A) Branch Circuit Not More Than 600 Volts. (1) General. Branch-circuit conductors shall have an ampacity not less than the maximum load to be served. 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.
I posted the excerpt of the text for search engines, but posted the picture for the table.