The Floor Space Index (FSI) or Floor Area Ratio (FAR) is the ratio of the total floor area of buildings on a certain location to the size of the land of that location.
As a formula: Floor Area Ratio = (Total covered area on all floors of all buildings on a certain plot)/(Area of the plot)
Thus, an FSI of 2.0 would indicate that the total floor area of a building is two times the gross area of the plot on which it is constructed
Floor Area Ratio in zoning
The Floor Area Ratio can be used in zoning to limit the amount that can be built in a certain area. For example, if the relevant zoning ordinance permits construction on a parcel, and construction must adhere to a .1 floor area ratio, then the total area of all floors in all buildings constructed on the parcel must be no more than one-tenth the area of the parcel itself.
A builder can plan for either a single-story building consuming the entire allowable area in one floor, or a multi-story building that rises higher above the plane of the land, but which must consequently result in a smaller footprint than would a single-story building of the same total floor area. By combining the horizontal and vertical limits into a single figure, some flexibility is permitted in building design, while achieving a hard limit on at least one measure of overall size. One advantage to fixing this parameter, as opposed to others such as height, width, or length, is that floor area correlates well with other considerations relevant to zoning regulation, such as total parking that would be required for an office building, total number of units that might be available for residential use, total load on municipal services, etc. The amounts of these things tend to be constant for a given total floor area, regardess of how that area is distributed horizontally and vertically.
http://www.carfree.com/far.html (picture refers)
A FAR of 1.0
The illustration above shows a Floor Area Ratio (FAR) of 1.0. This simply means that, if the area of the plot is 100 square meters, then 100 square meters of gross floor area has been built on the plot. The illustration above shows a 4-story building covering 1/4 of the site, giving a FAR of 1.0. Four floors of 25 square meters each are built on a site of 100 square meters.
The reference design for carfree cities is based on a FAR of 1.5. Here are some ways to get to a FAR of 1.5:
Build a 2-story building on 75% of the site (2 x 0.75 = 1.5)
Build a 3-story building on 50% of the site (3 x 0.5 = 1.5)
Build a 4-story building on 37.5% of the site (4 x 0.375 = 1.5)
It will be noted that a FAR of 1.5 is quite high, although this density is not unusual in Venice or central Paris, and is considerably exceeded in most of Manhattan. It requires 4-story buildings and narrow streets with modest interior courtyards. (Higher buildings would leave more room for streets and gardens, but buildings higher than 4 stories are not desirable because they are expensive to construct and unpleasant to live in.)