Paver Patio Calculator

Purpose and model boundary

This calculator estimates the materials for a paver patio you draw. You draw the patio's outline on a grid and mark up to five areas inside it that are left unpaved, such as a column, a bed or a planter. The spreadsheet measures the net patio area from the drawing and returns the pavers to order with a pattern waste allowance, the gravel base and the bedding sand under them, the length of edge restraint along the outline, and the bags of polymeric sand for the joints. It is not a paving or base design, and it does not price anything. Excavation, geotextile, cutting layouts, borders, steps, drainage, labour and delivery 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 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 result.

The inputs beside the drawing are:

• Paver length and Paver width: the size of one paver, in inches (US) or centimetres (Metric). The footprint is the same whichever side you call the length.
• Joint width: the gap between neighbouring pavers, in inches (US) or centimetres (Metric); 0 means pavers laid tight.
• Pattern waste: extra pavers for cuts and breakage, as a percentage of the pavers that exactly cover the net patio area. It applies to the pavers only.
• Gravel base depth: the compacted gravel under the bedding sand, in inches (US) or centimetres (Metric). Enter 0 if the pavers go on an existing slab.
• Bedding sand depth: the sand layer the pavers are set in, in inches (US) or centimetres (Metric).

Every input except the pattern waste has one input for each system, each with its own default: a 9 by 6 in paver with a 0.125 in (1/8 in) joint, a 4 in gravel base and 1 in of bedding sand in US, and a 20 by 10 cm paver with a 0.3 cm (3 mm) joint, a 10 cm base and 3 cm of sand in Metric. The two sets are the figures of two different worked examples, not conversions of each other: 4 in is 10.16 cm, not 10; 1 in is 2.54 cm, not 3; and 1/8 in is 0.3175 cm, not 0.3. 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 pattern waste (default 10%) is the same in both systems.

Typical pattern waste allowances are 10% for a straight or an offset (running bond) pattern, 15% for a diagonal pattern and 20% for herringbone. 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: enter your paver's size and joint, the pattern you are laying, and the depths your supplier or designer calls for.

Governing relationships

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

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

One paver covers its own size plus one joint on its length and one on its width:

Paver footprint with joint (US, sq ft) = (paver length + joint width) × (paver width + joint width) ÷ 144, with all three in inches

Paver footprint with joint (Metric, m²) = (paver length + joint width) × (paver width + joint width) ÷ 10,000, with all three in centimetres

With the net patio area in square feet (US) or square metres (Metric):

Pavers before waste = net patio area ÷ paver footprint with joint

Pavers to order = net patio area ÷ paver footprint with joint × (1 + pattern waste), rounded up to a whole paver

Gravel base (US, cu yd) = net patio area × gravel base depth in inches ÷ 12 ÷ 27

Gravel base (Metric, m³) = net patio area × gravel base depth in centimetres ÷ 100

Bedding sand (US, cu yd) = net patio area × bedding sand depth in inches ÷ 12 ÷ 27

Bedding sand (Metric, m³) = net patio area × bedding sand depth in centimetres ÷ 100

Polymeric sand bags = net patio area ÷ the area one bag covers, rounded up to a whole bag, where one bag covers 80 sq ft of paving (US) or 7.4322432 m² (Metric)

The edge restraint is the length of the outline: the sum of the straight distances between consecutive drawn points, including the side that closes the outline from the last point back to the first. Each side from (x₁, y₁) to (x₂, y₂) is √((x₂ − x₁)² + (y₂ − y₁)²) long:

Edge restraint length = side 1 + side 2 + … + side n, where side n closes the outline

It is measured by the spreadsheet from the points the drawing sends; the drawing tool's own perimeter is never used. Exclusions are not edged: a column or a wall needs no restraint around it, and a free-standing bed or tree ring needs its own, which is not counted. The edge restraint includes every side of the outline, so it includes any side against a wall, where you may need none.

The constants are exact: 144 square inches in a square foot, 10,000 square centimetres in a square metre, 12 inches in a foot, 27 cubic feet in a cubic yard (a yard is 3 feet) and 100 centimetres in a metre. The 80 sq ft a bag of polymeric sand covers is not a figure the requirement states: it is the round figure its five worked examples all admit. A bag that covers a different area changes the count in proportion. In Metric the same bag is the 80 sq ft converted exactly, 7.4322432 m² (80 × 0.09290304 m², a square foot being exactly 0.3048 m squared), not a rounder metric figure. The pattern waste applies once, to the pavers, before the rounding up; the gravel, the sand and the polymeric sand carry no waste allowance and no compaction factor.

Calculation sequence

1. The spreadsheet measures the gross area of the outline and the area of each exclusion, and subtracts the exclusions to give the net patio area.
2. It reads the paver length, paver width, joint width, gravel base depth and bedding sand depth of the selected system, and the pattern waste.
3. Paver footprint with joint: the paver's length and width, each with one joint added, multiplied, in square feet (US) or square metres (Metric).
4. Pavers before waste: the net patio area over the footprint, not rounded.
5. Pavers to order: the pavers before waste times one plus the pattern waste, rounded to six decimals and then up to a whole paver. The six-decimal step keeps a figure that is whole on paper whole in the spreadsheet: the default 300 sq ft patio in 9 by 6 in pavers laid tight is exactly 800 pavers, 880 with 10% waste, but the spreadsheet's arithmetic gives 880.0000000000001, and without the step it would order 881.
6. Gravel base and bedding sand: the net patio area times each depth, in cubic yards (US) or cubic metres (Metric). Neither is rounded.
7. Edge restraint length: the straight distance from each outline point to the one before it, and from the first point to the last, added up.
8. Polymeric sand bags: the net patio area over the area one bag covers, rounded to six decimals and then up to a whole bag.
9. The status line is chosen, as described below. When it begins NOT VALID:, every computed quantity reads zero; the net, gross and exclusion areas are still measured from the drawing.

For the drawing the page opens with, worked example 11.7.4.1, a 20 by 15 ft patio of 300 sq ft with the US defaults: one paver covers (9 + 0.125) × (6 + 0.125) ÷ 144 = 0.3881 sq ft, so 772.9 pavers cover the patio exactly and 851 are ordered with 10% waste; 300 × 4 ÷ 12 ÷ 27 = 3.70 cu yd of gravel and 300 × 1 ÷ 12 ÷ 27 = 0.93 cu yd of bedding sand; the outline's four sides give 70 ft of edge restraint; and 300 ÷ 80 = 3.75, so 4 bags of polymeric sand. Worked example 11.7.4.3 draws a 300 sq ft patio with two 45 degree corners and lays it in herringbone at 20% waste: 928 pavers and 67.48 ft of edge restraint, of which 10 ft is the side that closes the outline. Worked example 11.7.4.4 draws a T-shaped 400 sq ft patio in 12 by 12 in pavers: 431 pavers, 4.94 cu yd of gravel, 1.23 cu yd of sand, 100 ft of edge restraint and exactly 5 bags, where rounding up adds nothing. In Metric, worked example 11.7.4.5 is a 6 by 4.5 m patio around a 60 cm column and a cabinet against the wall, 25.44 m² net, with the Metric defaults: one paver covers (20 + 0.3) × (10 + 0.3) ÷ 10,000 = 0.020909 m², so 1,339 pavers, 2.54 m³ of gravel, 0.76 m³ of sand, 21 m of edge restraint along the outline alone and 4 bags.

Outputs and interpretation

Pavers to order, Gravel base, Bedding sand, Edge restraint length and Polymeric sand bags are the five headline results: the things you buy. Pavers to order and Polymeric sand bags are whole numbers. Gravel base and Bedding sand are in cubic yards (US) or cubic metres (Metric), and Edge restraint length in feet (US) or metres (Metric), each shown to two decimals.

Pavers before waste is the number of pavers that exactly cover the net patio area, shown to one decimal, before the pattern waste and before rounding up; Paver footprint with joint is the area one paver covers, in square feet (US) or square metres (Metric), shown to two decimals, so a 20 by 10 cm paver's 0.020909 m² reads 0.02 m² while every quantity is computed from the unrounded figure. Net patio area is the area every quantity is 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). The whole numbers are counted from the unrounded figures, so they can differ from a count made from the figures shown on the page.

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, with both coordinates of every point; the spreadsheet refuses a request that leaves a blank row between them, because the edge restraint is measured from each point to the next, or that 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 patio outline encloses no area
• NOT VALID: the exclusions leave no patio area
• NOT VALID: paver length must be greater than zero
• NOT VALID: paver width must be greater than zero
• NOT VALID: enter a joint width of zero or more
• NOT VALID: enter a pattern waste between 0% and 100%
• NOT VALID: enter a gravel base depth of zero or more
• NOT VALID: enter a bedding sand depth of zero or more
• CHECK: gravel base depth is zero, so no base gravel is estimated
• CHECK: bedding sand depth is zero, so no bedding sand is estimated
• CHECK: the edge restraint follows the outline only; add restraint around any bed or planter drawn as an exclusion
• OK

The checks on the paver size, the joint and the two depths read the selected system's inputs only. The last CHECK: line applies whenever an exclusion is drawn, because the edge restraint is then shorter than the edges the paving has: worked examples 11.7.4.2, an L-shaped patio around a column, and 11.7.4.5, a patio around a column and a cabinet, read CHECK:; the default patio and examples 11.7.4.3 and 11.7.4.4, which leave nothing out, read OK. A zero joint and a zero pattern waste are valid and raise no check. A CHECK: verdict comes with the figures; a NOT VALID: verdict is shown in place of them.

Assumptions and limitations

• The patio is measured as a flat plan area; a sloping patio is measured as its footprint, so it needs slightly more of everything than the figures say.
• The gravel base and the bedding sand are each one depth throughout, and their volumes are as laid: there is no allowance for compaction or waste, so add depth or order extra as your supplier advises.
• The pattern waste is one percentage for the whole patio. The calculator does not lay out cuts, soldier courses or borders, and it does not vary the waste with the shape of the edges or the number of exclusions.
• The edge restraint runs along the outline only. It is not measured around exclusions, and it includes sides against a wall or a house, where you may need none.
• The polymeric sand coverage of 80 sq ft per bag is an assumption, not a product's figure; coverage varies with the product, the joint width and the paver size. A bag that covers a different area changes the count in proportion.
• Walls are straight lines between points; a curved edge is drawn as short straight segments, which cut slightly inside the curve and shorten the edge restraint slightly.
• 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 a paver length and width, a joint width and the two depths of zero or more, and a pattern waste from 0% to 100%; a paver length or width of zero is refused by the status line. 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, 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, from which 12 inches make a foot and 144 square inches a square foot; the exact square foot, 0.09290304 m², by which the Metric bag coverage is converted; and the cubic yard (0.7645549 m³), which is 27 cubic feet.
• Bureau International des Poids et Mesures, The International System of Units (SI), 9th edition (2019), and its table of SI prefixes. bipm.org. The prefix behind the Metric paver size, joint and depths: a centimetre is a hundredth of a metre, so a square metre is 10,000 square centimetres.
• 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 patio and each exclusion, as on the Area Calculator.

The default paver size, joint width, pattern waste, gravel base depth and bedding sand depth, and the 80 sq ft a bag of polymeric sand is counted to cover, are the figures of the worked examples this calculator was built against, not values from these sources or from any code, standard or manufacturer. These sources describe the units and the measurement; they do not certify a particular patio or its result. Use your paver's size and joint, the base and bedding depths your supplier or designer calls for and the coverage printed on the polymeric sand you buy, and check the figures before ordering.