What is a safe height for a 8 week old kitten to fall from?
I don't know that there is a safe height. Falling wrong from a very low height can have fatal consequences.
That being said, kittens are fairly low mass and their bones are actually pretty flexible. It would not surprise me to hear people tell stories of seeing a kitten fall from 10 feet (3.048 m) or more without any ill effects.
However that is not the same as saying it is safe for a kitten to fall from 10 feet (3.048 m). If a kitten fell from height but seemed to walk away with no lasting effects, I would not worry about it. But I also would not go encouraging a kitten to jump off a balcony or dropping one, except in case of an emergency where the alternative is certain death.
Agreed - kittens can be very resilient and fearless, but that doesn't mean they can't injure themselves from a fall. It all depends on whether they manage to land well.
The very first night I had my kitten Julius he was in a safe room upstairs. I was rather ill, and hadn't covered the upstairs railing. Going into his room he ran out past me and tried to circle outside the bannister rail and fell to the tile, some 12-15 feet. Shocked but unharmed. Years later got some new kittens and put cardboard over all the bannisters and halfway down the stairs and one *climbed the cardboard* and fell. Also unhurt. Sometimes you can't win with the little stinkers.
As a very conservative rule, kittens can safely jump down from the same height they can jump up to. Anything higher, i.e. requiring climbing rather than jumping, may be unsafe. Even minor injuries in a kitten that young aren't good and could have lasting effects (and expensive vet bills).
My most recent kitten taught himself to climb up onto my bed, but he sprained one of his front paws jumping back down—onto carpet! Once he recovered, I made him some steps (stacked cardboard boxes) to get up and down safely.