I don't recall from my days in clinical psychology (and administering IQ tests to adults and children) that there was a formal definition of “genius.” However, on the Wechsler scales, 140 was where we would begin to use the term colloquially.
A score of 145 is three standard deviations above the norm. Folks with an IQ of 145 are almost literally one-in-a-thousand, as they represent a bit more than 0.1% of the population.
These are folks who may be aptly called “geniuses.”
That's not to say that folks with higher IQs aren't, well, even more “geniusy.” I remember in high school, there was one fellow with a higher IQ than me - his IQ was 160+. The difference between him and me wasn't huge, but it was noticeable and measurable.
By the way, contrary to the myths, folks with extremely high IQs (160 is four standard deviations above the norm, a score obtained by fewer than 1 in around 25,000 folks or so) don't generally get messed up in life.
My buddy from high school is a senior consultant in one of the leading consulting firms in the world, earned his masters and Ph.D. from Stanford, has a wife and a daughter, is a long-time officer in the Navy and now the Navy Reserve, having achieved the rank of Captain, and has a pretty darned nice life. No medications. No help.
I've known more than a few folks with these sorts of IQs. Some of them are messed up - like folks with much lower IQs - most are pretty successful, pretty happy, pretty fulfilled human beings.
Really, really smart folks have the ordinary panoply of problems that people generally do. My friend from high school played in the band (not a great high-status sort of activity back then), had acne and allergies, wore glasses, was slightly undersized, and like many young fellows (especially those of us in all-boys Catholic high schools) was a little socially awkward and shy around girls. He, like the rest of us, grew out of these sorts of problems, like ordinary adolescent boys, and has gone on to a very happy and successful life.
In fact, very high IQ generally correlates moderately with good social and life skills (the anecdotes related to high school nerds and geeks all notwithstanding).
sitetest
Hmmm, strange. The last course I took (granted it was over ten years ago) on psychometrics rather strongly declared that tests results of beyond three standard deviations were well outside of the target range of most IQ tests... so much so that scores beyond three standard deviations were likely to be meaningless (since the margin of error in any score at the extremes of the test would likely be higher than the score differentials between standard deviations). We were encouraged to refer to scores in that range as “3 SDs +” as opposed to putting possibly fictional monikers or scores on these results. It could very well be the tests or their accuracy have changed in the intervening time... but I always raise an eyebrow when I hear scores much about 145 (based on that info)...