That, my friend, is the million dollar question….. LOL
Is he a jumper? Mine can jump from a periscope position, with no effort, up to and over her head (ears!) height when standing up.
So definitely tall enough for him to stand up and then I would add another 50% on top of his stretch height (or 100% if the gates were up against a wall (to push off like a cat jumps – trust me, I found out the hard way!!! LOL))
You can always buy the cover / netting to go over it which will prevent him from being tempted to jump.
I bought one which has 8 individual pieces (gates, one of which has a door in) which are held together by drop pins that can go into the grass. You can then choose if you have a big space or not. and have an L shape, an octoganal shape, a square, a rectangle…… the shapes are endless! LOL

Our Tossu, a one-year-old 4,5kg New Zealand Red male, once jumped a 105cm puppy pen fence with ease right before my very eyes. Our French lop girl, on the other hand, doesn’t jump out of even a 40cm puppy pen. It shouldn’t come as a surprise that bunnies can and will jump incredible heights when properly motivated, but it does depend on the rabbit a bit!

If you do have a jumper on your hands, I would highly recommend covering the pen with a clothes-pinned sheet or something, or you’ll soon have an escapee rabbit! There’s no puppy pen in the world high enough to contain a rabbit who really wants to get over it. They’ve even been known to climb fences, as opposed to just jumping over it.

I would personally recommend 60cm as a minimum, just for the sake of safety

Pippi and Gina both need a 4′ or 120 cm high run wall indoors to keep them in their allocated halves of the dining room. 3′ or 90 cm isn’t even a challenge for either of them, and neither of them are that big, with Gina being around 4 lb and Pippi just over 5 lb. Outdoors all four buns are kept in two enclosed metal runs.

And redbun is right, some bunnies can climb up like a cat, Gina does.

Oh yes def 60cm… 40 cm!!?? Mine would just step over that like Bunzilla without even engaging her super hopping powers! LOL

Put the top on straight away though, don’t let him jump out even once, ‘cos once they get the juicy taste of freedom, they magically bounce even higher…!! LOL

mine can hop over 90 cm without a secure roof, but it does depend on the bunny.

This is what I use outside, this is from a screen shot from the manufacturers image.

These aren’t too bad for price, fold flat, and are easy enough to move around on the grass

They are fairly secure, though a determined bunny could still burrow out! I had a cat come and sit on top once, it was soon a very wet cat, and the buns, though jittery weren’t too badly scared.

I’ve messaged you a link

I bought Olly the highest pen I could find, its really a dog pen, he can jump 3 foot but, he’s not bothered about jumping now for some reason.

Is a soft cover – like a sheet or blanket sufficient enough to keep them from wanting to jump out? Or do you all suggest a hard cover?