Ladder/steps in oak, plank dimensions?

1 2/3’ would be about 21 inches. In oak you could probably get away with 4/4 (1”) surfaced to 7/8” since the pieces are narrow and that short. Cut the rough material oversized a bit and joint and plane. Make sure the grain isn’t too wild and there aren’t any knots. Probably depends on the weight limit you are looking for.

Take a piece of 3/4 oak 24” long and put it up on a block at each end and stand on it. If it flexes more than you want, go thicker.

Starting with 5/4 and surfacing or gluing up two pieces of thinner stock and surfacing that down to 1” might be better. I assume you are going to dado the treads into the rails for support.

-- Michael Murphy, Woodland, CA.

I was sitting there doing this myself so I spent a bit of time checking out some rough lumber to see what can be done.
I find that the rough lumber in my area is not actually 4/4, it’s more like 15/16 inches. By the time you take the warp or wobble off this dimension of lumber is almost impossible to get 3/4 inch stock from it.
I’ve decided that I’ll go for 5/4 when I can find it.
I’m planning a mobile latter much like a library ladder for my shop so I’m looking for a full finished four-inch width for the rails and a full four-inch width for the stair treads. I plan to dado stair into the rails and reinforce the unit with quarter inch rod under each stair. I might be able to go lighter than this but I’m fairly hefty myself and toting a box of 50 or 60 pounds down that ladder is stretching the limits of lighter lumber.
Good luck with yours,

-- A mind, like a home, is furnished by its owner