How do I calculate Standard Deviation from range and mean

[RonPurewal]

There's no such formula.

Remember, standard deviation represents a kind of 'average' (not a literal average, but something along those lines) of how far your data are from the mean of the set.
If you move some values closer to that mean, then, to preserve the same SD, you must move other data points farther from it. In so doing, you may well change the range of the set.
In other words, if some data points are moved, then, to keep the SD the same, you may have to change the range of the set.

For instance, there's going to be some x > 1 for which the set -x, 0, 0, x has the same standard deviation as the set -1, -1, 1, 1. (In terms of the concepts above"”If you start with -1, -1, 1, 1 and move the two middle values from -1 and 1 to 0 and 0, then you must move the two outer values farther away from 0.)
These sets have different ranges, but the same SD.

[RonPurewal]

Of course, there's one notable exception: If SD = 0, then range = 0, and vice versa. (If either range or SD is zero, then every datum in your set is the same value.)