To get a good answer to this question, you need to define what you mean by strength (as well as hardness). Between tensile strength and indentation hardness, as CoryPad has stated, there are fairly well defined correlations. These tend to be material-specific, so you need to make sure you are looking at the right correlation.
On the other hand, there are different types of strength (other than tensile strength) and hardness (other than indention hardness). For example, there is impact strength, compressive strength, chemical strength, magnetic strength, and so on. The correlation between these other types of strength to the indention hardness is much less than that for tensile strength (for some, there is no correlation).
As far as hardness goes, many a machinist has told me that 321 stainless is difficult to machine because it is so hard. 321 SS has relatively low indentation hardness (and correspondingly, tensile strength), however. The machinists know what they are talking about, however, they just do not mean indention hardness when they say that 321 is hard, they mean that it dulls their tools more quickly and gives them more pushback than low-allloy steels. The correlation between this type of hardness and those other types of strength is even more nebulous.