Lot Coverage Impervious Area Calculator

Purpose and model boundary

This calculator checks a lot you draw against two zoning limits you enter. You draw the lot's outline on a grid and up to five areas on it, each a building, a paved area such as a driveway, path or patio, or a deck, and say which each one is. The spreadsheet returns the lot coverage (the share of the lot under buildings), the impervious share (the share of the lot under buildings and every other hard surface) and the floor area ratio (FAR), and says whether the lot coverage and the impervious share are within the limits you entered. FAR is reported, not checked against a limit.

It is not a survey, a zoning determination or legal advice. Your zoning code decides what counts toward lot coverage and impervious area, how floor area is measured and what the limits are. The calculator does not check setbacks, yards, building height, a floor area ratio limit or any other rule.

Inputs and units

The drawing is the first input. Its outline is sent as an ordered list of up to 100 corner points and each exclusion as an ordered list of up to 20 points, exactly as on the Area Calculator, which measures the same drawing. The US/Metric switch on the drawing chooses the unit the coordinates are written in, feet for US and metres for Metric, and the unit of every area. The shares and FAR have no unit, so the switch does not change them.

The inputs beside the drawing are:

• Exclusion 1 to Exclusion 5: what each drawn exclusion is, a Building, Paving or a Deck. Exclusion k is the exclusion the drawing numbers k, and the page shows its type only while it is drawn: a drawing with two exclusions shows two types, and one with none shows none. The drawing never renumbers, so after you delete Exclusion 2 of three the page shows Exclusion 1 and Exclusion 3. Every exclusion starts as a Building. A type belongs to its shape: deleting a shape returns its type to Building, a shape drawn afterwards takes the lowest free number and starts as a Building, and Undo brings a deleted shape back with its type. Starting over clears every type back to Building, and an imported drawing's shapes start as Buildings, except one that is exactly, point for point, a shape you had drawn, which keeps its type; so check each exclusion's type after drawing, deleting or importing. Choosing a worked example sets the type of each exclusion it draws, and Undo after it brings back the types you had. The type of an exclusion that is not drawn is sent as Building and does nothing.
• Lot coverage limit: the largest share of the lot your zoning code lets buildings cover.
• Impervious limit: the largest share of the lot your zoning code lets buildings and every other hard surface cover.
• Floors per building: the number of floors every building on the lot has.

The limits start at 35% and 45% and the floors at 1. They are the values the requirement's worked examples use, not values from any zoning code: enter your own code's limits.

Governing relationships

Every area is measured from the drawing by the shoelace formula, exactly as on the Area Calculator. For a polygon with points (x₁, y₁) to (xₙ, yₙ) in drawing order:

Area = ½ × |Σ (xᵢ₋₁ × yᵢ − xᵢ × yᵢ₋₁)| for i = 1 to n, where point 0 is point n

Lot area = the area of the lot outline

Exclusion k area = the area of exclusion k, or 0 when it is not drawn

Building footprint = the sum of the Exclusion k areas whose type is Building

Impervious area = Exclusion 1 area + … + Exclusion 5 area

Pervious area = Lot area − Impervious area

Lot coverage = Building footprint ÷ Lot area

Impervious share = Impervious area ÷ Lot area

FAR = Floors per building × Building footprint ÷ Lot area

Lot coverage within limit = Yes when ROUND(Lot coverage, 6) ≤ Lot coverage limit, otherwise No

Impervious within limit = Yes when ROUND(Impervious share, 6) ≤ Impervious limit, otherwise No

Only a Building counts toward lot coverage and FAR; every type counts as impervious. Paving and a Deck therefore count the same way in this calculator: toward the impervious share and not toward lot coverage.

Calculation sequence

1. The spreadsheet measures the lot area and the area of each exclusion, and subtracts the exclusions from the lot to give the pervious area.
2. It adds the areas of the exclusions whose type is Building to give the building footprint, and the areas of all five to give the impervious area.
3. It divides the building footprint and the impervious area by the lot area to give the lot coverage and the impervious share, and multiplies the building footprint by the floors per building before dividing by the lot area to give FAR. None of the three is rounded.
4. Each verdict rounds its share to six decimals and compares it with its limit: Yes at or below the limit, No above it. The six-decimal step keeps the spreadsheet's arithmetic from turning a share that is exactly on its limit into one a hair above it, and nothing coarser is compared. A 45.5 by 77 ft building on a 100 by 100 ft lot covers 35.035% of it: that is 35.0% to one decimal, but it is above a 35% limit, so Lot coverage within limit reads No. A 70 by 50 ft building on the same lot covers exactly 35.000% and reads Yes.
5. The status line is chosen, as described below. When it begins NOT VALID:, the shares, FAR, the building footprint and the impervious area read zero and both verdicts read NOT VALID.

Worked example 11.7.1.1 of the requirements is a 60 by 100 ft lot, 6,000 sq ft, with a 1,200 sq ft house marked Building and a driveway and a patio of 360 and 168 sq ft marked Paving: lot coverage 1,200 ÷ 6,000 = 20.0%, impervious share 1,728 ÷ 6,000 = 28.8% and FAR 1 × 1,200 ÷ 6,000 = 0.20, both within 35% and 45%. Worked example 11.7.1.4 is a 50 by 120 ft lot, 6,000 sq ft, with a 1,500 sq ft house and a 160 sq ft shed, both Buildings, and 740 sq ft of paving: lot coverage 1,660 ÷ 6,000 = 27.7% is within 35%, but the impervious share 2,400 ÷ 6,000 = 40.0% is above a 35% impervious limit, so Impervious within limit reads No.

The drawing the page opens with is a placeholder, a 20 by 15 ft outline with nothing drawn on it: 300 sq ft, both shares 0.0%, FAR 0.00 and both verdicts Yes. Draw your lot, or choose a worked example, before reading a verdict.

Outputs and interpretation

Lot coverage and Impervious share, their verdicts Lot coverage within limit and Impervious within limit, and the Floor area ratio (FAR) are the headline results. The two shares are percentages to one decimal and FAR a ratio to two decimals, but the spreadsheet returns them unrounded, and each verdict reads its unrounded share: a share of 35.0% can read No against a 35% limit, as the example above shows. Building footprint and Impervious area are the areas behind the two shares, and Lot area, under "From the drawing", is the area they are shares of. The pervious area and the area of each exclusion are returned by the calculation but not printed on the page. The areas are in square feet (US) or square metres (Metric), to two decimals. Each share also has a bar from 0% to 100%, and FAR a bar from 0 to 1; a FAR above 1, as with several floors, shows its number and no bar.

A result belongs to the drawing and the inputs it was calculated for. When you change either after pressing Calculate, an exclusion's type included, the result is kept but marked stale until you press Calculate again; changing the value back makes it current again. Switching between US and Metric changes what is sent, so it marks the result stale too.

Validation and status logic

The drawing tool checks every edit to the drawing before it is kept, with the Area Calculator's rules: at least three points per shape, no two consecutive points in the same place, no wall crossing another wall of its shape, every exclusion inside the outline, no two exclusions overlapping, and at most five exclusions. Touching is allowed. A refused edit leaves the drawing as it was, and an imported drawing is refused as a whole if any rule fails.

That rule is why one worked example differs from the plan the requirements print. Worked example 11.7.1.3, the five-sided lot, prints a driveway whose corner lies 2 ft beyond the lot's angled side, so about 2 sq ft of it is outside the lot and the drawing tool refuses the plan. The worked example here moves the driveway 2 ft back inside, where its corner touches the lot line. Every figure of the example is unchanged: 5,850 sq ft of lot, a 900 sq ft house and a 360 sq ft driveway, 15.4% lot coverage, 21.5% impervious and FAR 0.15.

The drawing tool always writes a shape's points into consecutive rows, with both coordinates of every point; the spreadsheet refuses a request that leaves a blank row between them, or gives a point of the outline or of an exclusion only one coordinate.

The status line is the spreadsheet's own verdict, the first of these that applies:

• NOT VALID: choose US or Metric
• NOT VALID: draw at least three outline points
• NOT VALID: every outline point needs both coordinates
• NOT VALID: every point of exclusion 1 needs both coordinates
• NOT VALID: every point of exclusion 2 needs both coordinates
• NOT VALID: every point of exclusion 3 needs both coordinates
• NOT VALID: every point of exclusion 4 needs both coordinates
• NOT VALID: every point of exclusion 5 needs both coordinates
• NOT VALID: each exclusion needs zero or at least three complete points
• NOT VALID: outline and exclusion points must fill consecutive rows, with no blank row between them
• NOT VALID: the lot outline encloses no area
• NOT VALID: the exclusions add up to more than the lot
• NOT VALID: each exclusion type must be Building, Paving or Deck
• NOT VALID: floors must be a whole number of at least one
• NOT VALID: enter a lot coverage limit between 0% and 100%
• NOT VALID: enter an impervious limit between 0% and 100%
• CHECK: lot coverage and the impervious share are both above their limits
• CHECK: lot coverage is above its limit
• CHECK: the impervious share is above its limit
• CHECK: no exclusion is marked Building, so lot coverage and FAR are zero
• OK

A CHECK: verdict comes with the figures; a NOT VALID: verdict is shown in place of them.

Assumptions and limitations

• Every exclusion counts as impervious, whatever its type. A pool, a garden bed or pervious pavers drawn as an exclusion count as impervious, so leave undrawn any area your code treats as pervious.
• Only a Building counts toward lot coverage and FAR. Codes differ: some count decks, porches, pools or sheds toward coverage. Mark such an area Building if yours does.
• One floor count applies to every building, so a lot with a two-storey house and a one-storey garage has its FAR overstated. The floor area here is each building's footprint times that count, not the floor area a code measures, which can include or leave out basements, attics, garages and upper-floor overhangs.
• Setbacks, yards, building height, a floor area ratio limit and typed floor areas are not modelled.
• The lot is measured as a flat plan area; a sloping lot is measured as its footprint.
• Walls are straight lines between points; a curved lot line is drawn as short straight segments, which cut slightly inside the curve.
• The spreadsheet trusts the drawing tool to keep every exclusion inside the lot and apart from the others and does not check either itself, so this calculator is offered on its web page only, where the drawing tool enforces them.
• Drawing needs a mouse, a pen or a touch screen; a drawing prepared elsewhere can be loaded with Import.

Restrictions and non-computing states

This calculator accepts an exclusion type of Building, Paving or Deck, a whole number of floors of at least one, and limits from 0% to 100%. The drawing tool refuses any edit that would leave a shape outside its limits. Nothing is sent until you press Calculate, and pressing it again on an unchanged drawing with unchanged inputs sends nothing.

Errors and warnings

A blank required input keeps Calculate from sending, and pressing it names the input and moves to it. If the calculation service refuses an input, the status line names it and the input is marked until you change it. If the service does not answer, the page says so, keeps your drawing, your inputs and the last result, and lets you press Calculate again. A CHECK: status means the figures are returned with a reason to look again; a NOT VALID: status means they cannot be computed and none are shown.

Sources and further reading

• New York City Department of City Planning, Zoning Resolution of the City of New York, Section 12-10, Definitions. zr.planning.nyc.gov. One city's definitions, shown as an example and not as the rule where you are: lot coverage is the part of a zoning lot that, viewed directly from above, is covered by a building; lot area is the area of the zoning lot; and the floor area ratio is the total floor area on the lot, summed over its buildings, divided by the lot area.
• American Society of Planning Officials, Floor Area Ratio, Planning Advisory Service Information Report No. 111 (June 1958). planning.org. The floor area ratio as floor area divided by lot area, so that a ratio of 1.0 allows as much floor area as there is lot, however the building is shaped or stacked.
• Beth Yount, "Impervious Surfaces and Stormwater Impacts," Penn State Extension. extension.psu.edu. Impervious surfaces as hard surfaces that do not let water pass into the soil, among them roofs, driveways, sidewalks, patios, decks and swimming pools, which is why every exclusion here counts as impervious.
• Eric W. Weisstein, "Polygon Area," MathWorld, Wolfram Research. mathworld.wolfram.com/PolygonArea.html. The shoelace formula for the area of a polygon from the coordinates of its corners, with the condition it needs, a flat polygon whose sides do not cross, which the spreadsheet uses to measure the lot and each exclusion, as on the Area Calculator.
• National Institute of Standards and Technology, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, Appendix B.8. nist.gov. The exact inch (2.54 cm) and foot (0.3048 m) behind the drawing's two systems.

The 35% and 45% limits and the one floor the page starts with are the values the requirement's worked examples use, not values from these sources or from any zoning code. These sources describe the terms and the measurement; they do not set a limit for your lot or certify its result. Your zoning code decides what counts toward lot coverage and impervious area, how floor area is measured and what the limits are: check a result against it before relying on it.