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We have some estimats on the density of the bodies in the main belt. E.g. What's the (particle) density of the asteroid belt?

How much of this is discovered? And how strongly does discovery correlate with the size of the body?

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Taemyr
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    "How much" is a bit vague. I would suggest the question be changed to "What is the smallest size to which all asteroid belt objects have been discovered?" It's still a bit tricky, as there could be a large object that is pitch black that is not discovered, but it's closer to an answerable question. – PearsonArtPhoto Jul 07 '15 at 13:44
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    "What percentage of the total mass" might be answerable. – Jerard Puckett Jul 07 '15 at 19:19
  • Any of it that has not been "discovered" is therefore still unknown. So all of the known asteroid belt has been discovered. – Anton Feb 08 '18 at 17:03

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The total mass of the asteroid belt can be estimated from the effect the belt has on the major planets. The total mass is estimated to be $2.8×10^{21}$ to $3.2×10^{21}$ kilograms. About 1/3 of this is concentrated in Ceres alone.

From Hidden Mass in the Asteroid Belt (2002):

These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).

How much of it is discovered by number of objects is a more complex question. For one, new discoveries are made daily. See this video (highly recommended) that charts the number of discovered asteroids from 1980-2010.
In 1980, about 8000 asteroids were known. By 2010, around 530,000 asteroids were discovered. Now (July 2015), the number's over 680,000. Estimates suggest that there are about a billion asteroids larger than 100 m.
Page pointing to a list of currently known asteroids (updated daily).
(note: the link is an html page hosted on an FTP server. When you open this page, you get a local copy of the page, but the links to the data seem to work okay. The full list is 50 Mb)

Discovering an asteroid is one thing, determining its mass is more complex. Of the discovered asteroids (lists here), we only have decent estimates for a few. For many, we've no idea how big they are.

There is some correlation between asteroid size and discovery, but other factors come into play as well.

  • albedo (in visible light, radar or IR, in which many recent discoveries were made)
  • location (see the video, with discoveries concentrated in regions that are visible from asteroid location programs on Earth by night)

In summary, we have an idea of how much mass is present in the asteroid belt, but into how many bodies that mass is divided remains a big question.

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