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The VIX is quoted in terms of percentage points and translates, roughly, to the expected movement in the S&P 500 index over the next 30-day period, on an annualized basis.

For example, if the VIX is at 21, this represents an expected annualized change of 21% over the next 30 days; thus one can infer that the index option markets expect the S&P 500 to move up or down over the next 30-day period.

That is, index options are priced with the assumption of a 68% likelihood (one standard deviation) that the magnitude of the S&P 500's 30-day return will be less than 6.06% (up or down).
21% / sq. root of 12 = 6.06%
3.4646102

How do I calculate the same for 2 or 3 standard deviations?

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In this solution the empirical rule is emphasized clearly. The solution also includes one reference link for further help with the subject.

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First, remember that the "empirical rule" states that in a normal distribution, about 68% of observations fall within 1 standard deviation (sd), 95% fall within 2 sd's, and 99.7% fall within 3 sd's. (For ...

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