Handheld shutter speeds? Whats safe?

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Hey all. Can anyone advise on the maximum shutter speeds that are safe to use without a tripod (handheld)? I've been playing it safe so far (1/80 max or roundabouts) but i'm sure you can go lower safely -- without getting shake. I'm at the end of my stay in NZ so probably should have asked this a while ago.. but meh .. bring on Sydney and Thailand

Ta.

 

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Thanks guys. The inverse of focal length thing was something i could vaguely remember, but i thought it was to do with something else (god knows what). That should give me a bit more freedom, knowing that for sure now.