As per J.K. Rowling herself:
Why are some people in the wizarding world (e.g., Harry) called 'half-blood' even though both their parents were magical?
The expressions 'pure-blood', 'half-blood' and 'Muggle-born' have been coined by people to whom these distinctions matter, and express their originators' prejudices. As far as somebody like Lucius Malfoy is concerned, for instance, a Muggle-born is as 'bad' as a Muggle. Therefore Harry would be considered only 'half' wizard, because of his mother's grandparents.
If you think this is far-fetched, look at some of the real charts the Nazis used to show what constituted 'Aryan' or 'Jewish' blood. I saw one in the Holocaust Museum in Washington when I had already devised the 'pure-blood', 'half-blood' and 'Muggle-born' definitions, and was chilled to see that the Nazis used precisely the same warped logic as the Death Eaters. A single Jewish grandparent 'polluted' the blood, according to their propaganda.
Therefore, as per JKR, the official Third Reich formula-like rules were in effect:
In Germany itself, the Ahnenpass and Nuremberg Laws classified people as Jews if they descended from three or four Jewish grandparents. A person with one or two Jewish grandparents was a Mischling, a crossbreed, of "mixed blood". (source)
Of course, as usual, the bosses got to make any exceptions they wanted - e.g. Voldemort was certainly not considered "half-blood inferior" by his own rules. Same as with Nazis - quoting my completely unrelated answer on Skeptics.SE:
These events (Erhard Milch being issued a German Blood Certificate) prompted Hermann Göring to say famously "Wer Jude ist, bestimme ich" ("I decide who is a Jew")