I have a 85x90 barn with gutters on each end. 4 downspouts on each side.

Being on top of a mostly flat hill that I plan on discing/conditioning into a riding arena as well as using for horse pens, I'd like to pipe the water away from the barn so we don't get any standing water/ponds/mud right at the edge of the barns.

Thinking I can tie each of the gutters into a common line on each side and pipe it away from the barn into ditch/creek- what size pipe do I run? 4" 6", should my wife measure the pipe and tell me? Bigger is better?
Madisonville TX area.

4" is certainly adequate for what comes off at each downspout. If they all tie into a single pipe to go to the creek,I'd go with 6" from that point on. 85 x 90 is a lot of roof.

We'll round up to 8,000 SF, divide by 4 & say each gutter handles 2k SF.
A 4" per hour rainfall event can be handled by a 6" gutter/pipe pretty easily.
That rate of rainfall has a chance of occurring probably once every few decades, so you should be good.

FYI I plugged your drainage into my runoff calculator for this, so not spitballing. This is what it is.

If you are going to combine 2 downspouts into 1 pipe then I would recommend upsizing the main pipe to be at least 6". I just built my house and I had two downspouts that tied into a single 4" drain line and it was not enough capacity and the water started backing up the gutter. A 6" main drain pipe can handle the capacity of two 4" pipes. Since I changed out my main branch to 6" I no longer have any drainage issues.

Sounds like you'll be set up to capture the rainfall after you tie down spots into trunk lines.

Just need a big cistern and you're nearly set

Thanks Apache -

Now looking at cost - 2 of the 4" poly lines somehow workout cheaper than 1-6" poly line for the 100' I'd need/want. Safe to run 2 and just do half of each side into one? - Basically 2000 sq ft per 4" line?

Each 2000 SF area will need a 6" pipe to handle all the water in a 4"/HR Rainfall event.

If you drop down to a 4" pipe, you'll handle the majority of rains but you'll have some overflow in serious rainfall. Probably not that big a deal & you can just avoid riding for a day or two after heavy runoff.

You might look at some other piping options:
SDR pipe (sewer and drain)
ADS pipe (corrugated flexible drain pipe)

Both are available in 4" and 6" diameter and cheaper than Poly. ADS is very easy to work with & they make adapters for gutter connections. Try a sprinkler supply house in College Station, I think there is a Ewing outlet there.