Vanes,
If you find a written standard that states angles that a tractor can be safely used on, do let us know. I doubt you will...this kind of data just does not seem to be out there.
You can measure the angle of your slopes. A tilt meter is probably most useful to those that are on unfamiliar territory. Still, it can't hurt to own one.
For me, 20 degrees is more than I like to be sideways on on my
B2910 Kubota. It just does not feel good. Period. But in my gut I really feel that I could be sideways on a 30 degree slope with my loaded tires if I was real careful and went real slow. But I don't have a reference point. I don't want to take my tractor to the limit and roll it to find out. Too expensive...me that is...and so is the tractor.
But slopes themselves do not tell the whole story. There are dynamic considerations that change the equation anyway. A hole on the low side or a bump on the high side when you are moving changes the situation considerably. The "safe slope" now becomes a very dangerous one.
I doubt you will find a warm and fuzzy answer to your question. You can probably cross a 20 degree slope at reasonable speed safely, but who can tell anyone that for sure? One hole, one bump, one stump...and all bets are off.
That being said, I think Powertrac is one of the rare manufacturers that does certify some of their tractors for use on steep slopes, something like 40 or 45 degrees on a couple models.
My smaller BX Kubota with front and rear tires loaded and the relatively heavy MMM on it feels much more stable on the 20 degree slopes, when sideways than the bigger tractor does. I am still trying to figure out how to tell if this is an illusion, however.
Frankly, the best way to prevent a rollover is to be aware of the dangers and try to avoid them. You can roll a tractor on flat ground too...this is the way I look at it anyway, and what I try to do myself...