Pool Volume Liner Calculator

Purpose and model boundary

This calculator estimates the water and the liner for a swimming pool you draw. You draw the pool's outline on a grid and mark up to five islands inside the water that hold none, such as a planter or a rock island. The spreadsheet measures the net water area from the drawing and the length of the outline from the points you drew, and with the depth at each end and a fill rate you type it returns the water the pool holds in US gallons or litres, the liner area for the floor and the walls, the coping length around the outline and the time to fill the pool from empty. It is not a pool design, and it does not size a pump, dose chemicals, estimate heating or price anything. Excavation, the shell, steps, plumbing, the deck and labour are not estimated.

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 island 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 points are written in, feet for US and metres for Metric, and the unit of every result.

Draw an island, a planter or anything else that stands inside the water and holds none as an exclusion. Draw a notch, a step or a spa at the pool's edge into the outline itself, not as an exclusion: the outline is what the coping and the liner walls follow.

The inputs beside the drawing are:

• Shallow-end depth: the water depth at the shallow end, in feet (US) or metres (Metric). 0 is allowed, for a beach entry.
• Deep-end depth: the water depth at the deep end, in feet (US) or metres (Metric). It must be greater than zero and at least the shallow-end depth. For one depth throughout, enter the same depth at both ends.
• Fill rate: how fast the pool is filled, in US gallons per minute (US) or litres per minute (Metric).

Every input has one input for each system, each with its own default: 3.5 ft at the shallow end, 8 ft at the deep end and 10 gpm in US, and 1.2 m, 2.0 m and 40 L/min in Metric. The two sets are the figures of two different worked examples, not conversions of each other: 3.5 ft is 1.07 m, not 1.2; 8 ft is 2.44 m, not 2.0; and 10 gpm is 37.9 L/min, not 40. Switching between US and Metric shows the other system's inputs with their own values and never converts a number you typed; the value you typed for the system you left is kept for when you switch back, and it is not sent while it is hidden. The spreadsheet reads only the inputs of the selected system.

The defaults are the figures of the worked examples this calculator was built against, not values from a code, a standard or a manufacturer, so review them before use: measure your pool's depths, and time your own supply to find its fill rate.

Governing relationships

The net water area is the area of the outline less the area of each island, each measured by the shoelace formula exactly as on the Area Calculator:

Net water area = Gross area − (Exclusion 1 area + … + Exclusion 5 area)

The floor is taken to slope evenly from the shallow end to the deep end, so every figure uses the average of the two depths; for one depth throughout, both ends are the same:

Average depth = (shallow-end depth + deep-end depth) ÷ 2

Cubic volume = net water area × average depth, in cubic feet (US) or cubic metres (Metric)

Pool volume (US, gal) = cubic volume × 1,728 ÷ 231

Pool volume (Metric, L) = cubic volume × 1,000

The perimeter of the pool is measured by the spreadsheet from the drawn points: the straight distance from each point to the next, closing back from the last point to the first, around the outline only. Each side from (x₁, y₁) to (x₂, y₂) is √((x₂ − x₁)² + (y₂ − y₁)²) long:

Perimeter = side 1 + side 2 + … + side n, where side n closes the outline

The drawing tool's own perimeter is never used. The liner covers the flat floor and the walls up to the water depth, and the coping runs along the outline:

Liner area = net water area + perimeter × average depth

Coping length = perimeter

Fill time (hours) = pool volume ÷ fill rate ÷ 60, with the pool volume in US gallons and the fill rate in gallons per minute (US), or in litres and litres per minute (Metric)

The constants are exact: 1,728 cubic inches in a cubic foot and 231 cubic inches in a US gallon, so a cubic foot holds 1,728 ÷ 231 US gallons, about 7.48; 1,000 litres in a cubic metre; and 60 minutes in an hour. The spreadsheet keeps the fraction 1,728 ÷ 231 rather than a rounded 7.48, which would miss the printed volumes of three of the four US worked examples. Nothing is rounded in the spreadsheet: the fill time is computed from the unrounded volume.

Calculation sequence

1. The spreadsheet measures the gross area of the outline and the area of each island, and subtracts the islands to give the net water area.
2. It reads the shallow-end depth, the deep-end depth and the fill rate of the selected system.
3. Average depth: the two depths added and halved.
4. Cubic volume: the net water area times the average depth, in cubic feet (US) or cubic metres (Metric).
5. Pool volume: the cubic volume in US gallons (× 1,728 ÷ 231) or litres (× 1,000).
6. Fill time: the pool volume over the fill rate, over 60 minutes to the hour.
7. Perimeter: the straight distance from each outline point to the one before it, and from the first point to the last, added up. The islands' edges are not in it.
8. Liner area: the net water area plus the perimeter times the average depth. Coping length: the perimeter.
9. The status line is chosen, as described below. When it begins NOT VALID:, every computed figure reads zero; the net, gross and exclusion areas are still measured from the drawing.

For the drawing the page opens with, the canvas's 20 by 15 ft rectangle of 300 sq ft with the US defaults: the average depth is (3.5 + 8) ÷ 2 = 5.75 ft, so the pool holds 300 × 5.75 = 1,725 cu ft, which is 1,725 × 1,728 ÷ 231 = 12,903.9 US gallons; the outline's four sides give 70 ft, so the liner is 300 + 70 × 5.75 = 702.5 sq ft and the coping 70 ft; and at 10 gpm the pool fills in 12,903.9 ÷ 10 ÷ 60 = 21.51 hours. Worked example 11.7.5.1, a 32 by 16 ft pool at the same depths and rate, holds 22,023 gallons, needs 1,064 sq ft of liner and 96 ft of coping and fills in 36.70 hours; the fill time comes from the unrounded 22,022.6 gallons. Worked example 11.7.5.3 is an eight-sided pool of 490 sq ft, 5 ft deep throughout, whose outline of cut corners measures 84.4267 ft, shown as 84.43, so its liner is 490 + 84.4267 × 5 = 912.13 sq ft. In Metric, worked example 11.7.5.4 is a 10 by 5 m pool, 1.2 m deep at the shallow end and 2.0 m at the deep end, filled at 40 L/min: (1.2 + 2.0) ÷ 2 = 1.6 m, 50 × 1.6 = 80 m³ or 80,000 L, 50 + 30 × 1.6 = 98 m² of liner, 30 m of coping and 80,000 ÷ 40 ÷ 60 = 33.33 hours. Worked example 11.7.5.5 is a 20 by 12 ft plunge pool, 4.5 ft deep throughout, around a 4 by 4 ft planter: 224 sq ft of water, 7,540 gallons, and 224 + 64 × 4.5 = 512 sq ft of liner along the 64 ft outline, which is also its coping. The liner is not the gross floor's 240 + 64 × 4.5 = 528 sq ft, and neither it nor the coping includes the planter's walls or its 16 ft edge.

Outputs and interpretation

Pool volume, Liner area, Coping length and Fill time are the four headline results. Pool volume is in US gallons (US) or litres (Metric), shown as a whole number; Liner area is in square feet or square metres, Coping length in feet or metres, and Fill time in hours in both systems, each shown to two decimals.

Average depth, in feet or metres, and Cubic volume, in cubic feet or cubic metres, are the two steps every figure is built on, each shown to two decimals. Net water area is the area the volume, the liner floor and the fill time are computed from, and Gross area and Exclusion 1 area to Exclusion 5 area show how the drawing arrives at it, 0 for an exclusion slot you did not use; they are in square feet (US) or square metres (Metric). Every figure is computed from unrounded values, so a figure worked out by hand from the ones shown on the page can differ in its last place.

A result belongs to the drawing and the inputs it was calculated for. When you change either after pressing Calculate, 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. A refused edit leaves the drawing as it was, and an imported drawing is refused as a whole if any rule fails. The drawing tool always writes a shape's points into consecutive rows, each point with both its X and its Y; the spreadsheet refuses a request that leaves a blank row between them, because the perimeter is measured from each point to the next, or that gives a point of the outline or of an exclusion only one of the two.

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 pool outline encloses no area
• NOT VALID: the exclusions leave no water area
• NOT VALID: enter a shallow-end depth of zero or more
• NOT VALID: deep-end depth must be greater than zero
• NOT VALID: shallow-end depth cannot be greater than deep-end depth; for one depth throughout, enter it at both ends
• NOT VALID: fill rate must be greater than zero
• CHECK: the liner and coping follow the outline only; add the walls and edge of any island or planter drawn as an exclusion
• OK

The checks on the depths and the fill rate read the selected system's inputs only. The shallow end may not be deeper than the deep end; that keeps the two labels meaning what they say, and swapping two depths you entered the wrong way round would change no figure. The CHECK: line applies whenever an exclusion is drawn, because the liner and the coping then leave out the island's walls and edge, material you would otherwise under-order: worked example 11.7.5.5, a plunge pool around a planter, reads CHECK:; the default pool and examples 11.7.5.1 to 11.7.5.4, which leave nothing out, read OK. A zero shallow-end depth is valid and raises no check. A CHECK: verdict comes with the figures; a NOT VALID: verdict is shown in place of them.

Assumptions and limitations

• The floor is taken to slope evenly between the two ends, and the liner floor is measured flat as the net water area; a sloping floor's true area is slightly larger, so the liner needs slightly more than the figure says.
• The liner walls stop at the water depth. There is no allowance for freeboard between the water and the coping, for the liner's overlap or for waste.
• There is no transition depth and no depth zones: every figure uses the average of the two ends.
• The liner and the coping follow the outline only. An island's or planter's walls and edge are not included, and the status says so whenever one is drawn.
• Walls are straight lines between points; a curved edge is drawn as short straight segments, which cut slightly inside the curve and shorten the coping and the liner walls slightly.
• No chemicals, heating, pump sizing or pricing are estimated.
• The spreadsheet trusts the drawing tool to keep exclusions inside the outline and apart from each other 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 depths and a fill rate of zero or more. A deep-end depth or a fill rate of zero, and a shallow end deeper than the deep end, are refused by the status line; a shallow-end depth of zero is accepted. An input of the system that is not selected is not read. 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

• National Institute of Standards and Technology, NIST Handbook 44 (2023), Appendix C, General Tables of Units of Measurement. nist.gov. The exact definitions behind the volume constants: 1,728 cubic inches make a cubic foot and 231 cubic inches a US gallon, so a cubic foot holds 1,728 ÷ 231 US gallons; and the litre is a special name for the cubic decimetre, 1,000 of which make a cubic metre.
• 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 foot (0.3048 m) and inch (2.54 cm) behind the drawing's two systems, and the factors that relate the US gallon (3.785412 L) and the cubic foot to the cubic metre.
• Eric W. Weisstein, "Polygon Area," MathWorld, Wolfram Research. mathworld.wolfram.com/PolygonArea.html. The shoelace formula for the area of a polygon from the points of its corners, with the condition it needs, a flat polygon whose sides do not cross, which the spreadsheet uses to measure the pool and each island, as on the Area Calculator.

The default depths and fill rates are the figures of the worked examples this calculator was built against, not values from these sources or from any code, standard or manufacturer; each system has its own. These sources describe the units and the measurement; they do not certify a particular pool or its result. Measure your pool's depths, time your own supply for its fill rate, and check the figures before ordering a liner or coping.