Calculations

Question 1

SLOPE = “Rise” over “Run” or RISE/RUN

Answer 1

In the figure on the left SLOPE=RISE/RUN = 20m/5,000m = 0.004 when multiplied by 100 = 0.4% slope.

In the topographic map figure on the right, realize that “Rise” is the difference in elevation from the top to bottom. So determine the elevation of the top of the hill (859 feet) and subtract the elevation at the bottom of the run at Equation Creek (note that CI = Contour interval), so the elevation change is 859 feet – 680 feet or 179 feet. The “Run” is the horizontal distance from the top elevation to the

lowest elevation, or in this example it is twice the length of the indicated 1 mile interval, or 2 miles = 2 x 5,280 feet/mile = 10,560 feet. Therefore, the SLOPE = RISE/RUN = 859 feet–680 feet/2 miles = 179 feet/10,560 feet = 0.017 when multiplied by 100 = 1.7% slope.

Question 2

FLOOR AREA RATIO (FAR)

Answer 2

FLOOR AREA RATIO = Building area/Lot area

Question 3

Example to Calculate FAR

Answer 3

In the figure example below, there is a long way to calculate the FAR using the above formula or a faster, more visual method to use on the figure to get to the floor area ratio.

Using the formula method to calculate floor area ratio of the building, FAR = Building area/lot area
= 100 feet x 200 feet x 8 (stories) / 200 feet x 200 feet
= 160,000 square feet / 40,000 square feet
= 4

To use the visual method on a figure like the one on the left, you need to first realize that a FAR = 1 is equivalent to a one-story building spread out over the entirety of a lot site. Here, there are 8 stories on half the lot area. If those stories were spread out over the entire site, the result would be a 4-story building covering the entire site, or by definition, a floor area ration (FAR) of 1.

For non-figure based floor area ratios where the building and lot areas are given (or can be calculated), generally use the formula method and write it down as working through this method will result in a correct calculation of floor area ratio.

Question 4

DENSITY

Answer 4

For planning, density basically refers to a measure of the amount of development per area. The general formula for residential density (as opposed to nonresidential/commercial density which is typically regulated/calculated by floor area ratio) is, at its simplest:

DENSITY (units/acre) = # Dwelling units / overall acreage of site

Question 5

Gross Density

Answer 5

includes the acreage for associated infrastructure, parks, roads, sidewalks and public right-of-ways, etc.

Question 6

Net Density

Answer 6

excludes the acreage needed for associated infrastructure, parks, roads, sidewalks and public right-of-ways, etc.

Question 7

Density Example

Answer 7

EXAMPLE: Using the same figure used earlier for the floor area ratio calculation, let’s start with the assumption that each of the eight floors of the building contains six residential units, or 48 dwelling units overall in the building. The lot area is 200 feet x 200 feet = 40,000 square feet or 0.9183 acre (i.e. 40,000 square feet / 43,560 square feet per acre = 0.9183 acre).

Therefore, using the Gross Density formula: DENSITY = # Dwelling units / overall acreage of site
= 48 dwelling units / 0.9183 acre
= 43.56 dwelling units per acre