The Floor Area Ratio is the total building square footage (building area) divided by the site size square footage (site area).
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, as would be found in a multiple-story building.
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, regardless of how that area is distributed horizontally and vertically. Thus, many jurisdictions have found it uneccessary to include hard height limitations when using Floor Area Ratio calculations.
Japan has extensively adopted the Floor Area Ratio in the zoning system since 1970. The evaluation of the adoption is, however, controversial: some say that it has deteriorated the skylines and building lines in Japanese cities; others claim that it has protected the residential environments.
Andres Duany, 2000, notes 1) abdicating to floor area ratios (market forces) is the opposite of aiming a community toward something more than the sum of its parts. 2) FAR, a poor predictor of physical form, should not be used when the objective is to conserve and enhance neighborhood character. Whereas traditional design standards (height, lot coverage and setbacks or build-to lines) enable anyone to make reasonably accurate predictions, recognize violations, and feel secure in their investment decisions. And lastly, 3) if FAR is carelessly combined with traditional setbacks, assembled lots have a considerable advantage over individual lots, which has a negative effect on fine grained cities and the diversity of ownership.
Area Ratio is the cross reference between two figures after they have been divided by the denominator of the previous shape.