I can't remember the correct formula for figuring how many amps at 14.5 VDC a # 4 fine wire cable will work safely with
I can remember Ohms law but not any thing else on figuring the safe loads on low DC voltage
All help will be greatly appreciated
Maybe even posting the math with the formula may help others on here later

Depends on the length as well, a handy chart, no math needed.

https://www.bluesea.com/resources/1437

Length? An electric guy once told me the length is more important than the gage in determining amp capacity. I believe him. There are charts if you Google around. There are plenty of race cars using 4ga for the main power cable. Once the engine is running, it's plenty for anything else going on.

I'd find a new electric guy. Both are important. The wire gauge determines resistance per unit length. Obviously you then multiply by length to get total resistance! Then you figure out voltage drop by multiplying the resistance by the current. (Ohm's law).

A very short piece of small gauge wire is known as a "fuse" and it works by melting

In response to Cab's question: at 77F, 4 ga. wire has a resistance of 0.25 milliohms per foot. (At 122F it's about 0.28).
So... how much voltage drop are you willing to tolerate, how long is the wire and how much current is passing through it?

Incidentally a "12 volt" system with an alternator is around 13.8 volts which also varies with temperature (higher voltage in colder weather). If you're not running an alternator then your battery voltage will be dropping with time also

Edited to add: 14.5 volts, take a SWAG (Scientific Wild-Ass Guess) that you are OK with 0.5 volt drop, and the cable is six feet long? That's 0.25 * 6 = 1.5 milliohm.
1.5 milliohm will drop 0.5 volt if 333 amps are flowing. (0.5/0.0015 = 333).
Unless you're using it for starter cable, you don't even need #4 most likely.
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Spoken like a true EE!

I had a incident on my S/P bracket car when I used the alternator output to feed 12V to my timing light, I hooked it up with the motor not running and then started it up. The timing light lead vibrated over sideways and grounded out the alternator output lug burning up the 10 gauge feed wire all the way back to the trunk where the two batteries are, big stinking smoking mess That ended my day of racing in Sacramento, CA at the Mopar race their.
I rewired it with 10 gauge and had a little lower output reading on my Volt gauge and I ended up calling Power Master about them rebuilding it or selling me parts for me to fix it, they wanted to know what gauge feed wire I was using and insisted that I needed a #4 gauge feed wire and to ground the alternator with a # 4 wire to their grounding lug to a threaded connection on the block
I was going to use two #6 wires to feed the batteries, one to each battery but he insisted on one #4 instead. I've grounded and am ready to install the #4 wire now back to the batteries today, probably less than 10 Ft total length.
Thanks to all for the help, I should have paid more attention in basic electricity math class back in 1975 That or dug out one of my old text books on basic electricity

True, and of course both are important, but how much amperage will that short piece of wire pass before melting (or carry with no issues) vs the same size wire 17' long?

And the "electric guys" I was having the conversation with was a person who has wired hundreds of cars including the most complex of Pro Mods where weight is everything and the wire size used for specific loads and lengths is just what is needed and no more. And an engineer who is a pioneer in the industry, owns a company you've heard of, and has designed and sold components to racers for many years, maybe even stuff in your car. I don't pay attention to just anyone.

So, a 4ga cable at 4' long is not the same capacity as a 4ga at 18' long, and can be reduced in size accordingly. That's the point I was trying to make.

Then perhaps you misunderstood him. A flat statement such as "gauge is more important than length" is just plain wrong, which is obvious from the equations.
I've wired a few cars and many houses in my day too. Not to mention electronic devices of all sizes and power capability.
MarkZ - EE '81 (and amateur wrench-turner for about that long too). How did you guess?

Experts in aerodynamics also proclaimed that bumblebees could not fly... and yet, there they are.

That is not correct. Ampacity does not change. Voltage drop does.

So after getting some clarification from "my guys" I see where I was not entirely correct in some of my understanding of some of this, and I don't want to go through life ignorant, nor can I go for a Masters in everything I need to know a little bit about. So, length is important, but there are other considerations.

OP's question was how many amps at 14.5V with 4ga cable.

Again, what length and also what voltage drop can you tolerate?

Using 60A for an alternator line and 150A for a starter - the only things on a race car that would require that heavy of a conductor...

4ga voltage drop at 13.8V...

60A - 5' long - 13.72V
60A - 15' long - 13.57V
150A - 5' long - 13.61V
150A - 15' long - 13.24V

8ga @ 60A goes to 13.61V @ 5' long & 13.23 @ 15' long.
10ga " " " " 13.50v " " " " 12.90 " " "

Conversely, if you want no more than a 2% drop at 60A, maximum lengths are - 18' for 4ga; 11' for 6ga; 7' for 8ga; 4' for 10ga.
at a 5% drop at 60A, maximum lengths are - 46' for 4ga; 29' for 6ga; 18' for 8ga; 11' for 10ga; 7' for 12ga.

Keep in mind, for an alternator rated at 60A output to get close to that, the battery would have to be dead as a stone and/or the electrical load of everything running in the car would have to be near that. Unlikely unless you have a serious sound system. I've used 8ga for an alternator line to the trunk, in carbureted race cars with the typical electronics, with acceptable results. Charging the battery to 100% in between weekends was included.

I had forgot about the wire gauge and length affects on DC voltage
I started working in telephone outside plant in 1965 when we used open wire on arms that was .108 copper weld wire, copper over steel in the out lying lightly populated areas instead of more expensive cable. All the telephone cable we used back then varied in gauge size from 26 gauge for close into the offices up to 19 gauge for the furthest away.
Gauge and length go hand in hand
For my deal I'm sure the #4 gauge from the alternator to the batteries in the trunk, maybe15 ft. total length, is over kill but I would rather have it to big than to small.
Thanks to all of you for your help and input
Hopefully this post will help more than just me

Just use a fusible link at the alternator end of that wire. Don;t want to burn up anything if there is a short.

People disagree, but I'm anal about weight. 2 and 4 gauge is battery cable to me. You won't lose much from the alternator with that.

I was surprised to hear the Power Master tech say to use #4 gauge wire for their 100 amp alternators, I was ready to use two #6 as I have a lot of that size wire in stock but I ended up deciding to follow his suggestion on this
This car has run me through the hoops a bunch so why not follow the "experts" suggestions and hopefully prevent future problems

The rating will vary depending on ambient air temp & type of wire insulation; since insulation in a concern (how hot it gets).
Most wire tables will shown various temps for factoring the final amp rating. Open air or enclosed also considerations. Wire in an engine bay not the same as say the trunk. Bundled or single wire.

If I remember correctly, My friend, a master electrician, said that 2 wires of the same gauge, one being solid wire, and one being very fine multible strands, the stranded wire will carry more amps because more of the electrons move in the outer diameter part of each strand of wire and less in the inner diameter of the wire?

I've heard that same theory probably in one of the college classes I took years ago.
Same theory on fibre optic, all the light signals travel on the outside edges
On my deal with the race car I hope I'll never find out that , the charging wire to the battery, it is to big or to small

The frequency determines the amount of "skin effect" of the current, and DC has no frequency..

Fine strand welding cable will conduct more current (less drop) than same gauge coarse strand automotive type battery cable. It's all I use and have never had an issue using the smaller cable.

This is true when you are talking about AC currents. The phenomenon is the skin effect and as the frequency of the AC current increases the wire become more resistive due to the current mostly flows on the outer diameter of the wire as opposed to uniformly thought it. The reason the stranded wire can carry more current is that the stranded wire has a larger total surface area where the current can travel compared to the single wire.