Concrete Volume and Bags

Purpose and model boundary

Estimates the concrete for a schedule of slabs, strip footings, pads, piers, walls and solid stairs typed as element rows, and for a slab drawn on the page's drawing grid and poured through a 'Slab from the drawing' row. From that schedule it gives the concrete before and after waste, the whole bags and the ready-mix order with its trucks and their costs, whether the waste-adjusted order is above a ready-mix threshold you choose, a placement-temperature note, and a rebar, mesh-sheet or entered reinforcement quantity, including a slab rebar takeoff across each slab's bounding rectangle.

It is a quantity estimate. It does not determine structural adequacy, the concrete mix, the reinforcement design, the subgrade or formwork, or placement and curing procedures, and it is not a cost quote, a permit approval or an endorsement by a cited source.

Inputs and units

The element grid holds ten fixed rows; a row you do not need stays in the grid with Include set to No. Each row has an Include choice, a label, a shape, a Quantity, a Length and a Width in feet, a Depth in inches, a void deduction in cubic feet and a source note. The shape decides what the dimensions mean:

• Rectangular slab, continuous strip footing and rectangular isolated footing (a pad): Quantity × Length × Width × Depth.
• Circular pier or footing: Width is the diameter.
• Wall: Width is the wall's height and Depth its thickness.
• Solid stairs: Quantity is the number of steps, Length the tread in feet, Width the stair width in feet and Depth the riser in inches; each step is a solid block down to grade.
• Slab from the drawing: the area is the drawing's net area and Depth is the slab's thickness. Length and Width are not used; type 1 in each. Only one included row may use the drawing.

Lengths and widths are in feet, so a dimension measured in inches is typed as feet to at least four decimals: 16 in is 1.3333 ft. Worked example 11.5.1.3, a 60 ft strip footing 16 in wide and 8 in deep, needs 1.9753 cu yd of concrete before waste with the width typed as 1.3333 ft, which is 1.98 to two decimals; typed as 1.333 ft it is 1.9748, which is 1.97.

The drawing is a slab outline with up to five exclusions, such as a column or a drain that takes no concrete, drawn in feet (US) or metres (Metric). It is used only by a 'Slab from the drawing' row; without one, the drawing is not poured. Its areas are in the drawing's unit, square feet or square metres.

Every typed input is in US units, and so are the concrete, bag, cost and reinforcement results: feet, inches, cubic feet, cubic yards, dollars and degrees Fahrenheit. The waste factors are percentages. The US or Metric choice belongs to the drawing alone: a Metric drawing's net area is converted at 0.09290304 square metres per square foot and its bounding rectangle at 0.3048 metres per foot, both exact.

The supply route (bags, ready mix, or a comparison of the two), the reinforcement route (rebar grid, mesh sheets, an entered quantity, no estimate, or the slab rebar takeoff) and the temperature-note route each decide which of the other inputs apply. An input that does not apply to the chosen routes is still sent, and does not change any result. The ready-mix threshold is optional: left blank, the threshold answer reads Not evaluated and no other result changes.

Governing relationships

Each included row's gross volume, in cubic feet:

Rectangular slab, strip footing, pad or wall = Quantity × Length × Width × Depth ÷ 12

Circular pier or footing = Quantity × π × Width² ÷ 4 × Depth ÷ 12

Solid stairs = Width × Length × Depth ÷ 12 × Quantity × (Quantity + 1) ÷ 2

Slab from the drawing = Quantity × drawn net area in square feet × Depth ÷ 12

The stair formula counts step k as a solid block k risers high, so the steps together are one prism whose cross-section is the flight's stepped profile. The net concrete volume is the sum, over the included rows, of each row's gross volume less its void deduction:

Net concrete volume (cu ft) = Σ (gross volume − void deduction)

Concrete before waste (cu yd) = net concrete volume ÷ 27

Waste-adjusted order volume (cu yd) = net concrete volume × (1 + concrete waste) ÷ 27

Every whole-number count of something you buy (bags, ready-mix increments, trucks, rebar lines and stock bars) uses one counting rule, G. A count of a positive quantity is at least one; the quantity is rounded to six decimals before it is rounded up, so arithmetic noise just above a whole number does not add a unit:

G(x) = 0 when x ≤ 0, otherwise the larger of 1 and ROUND(x, 6) rounded up to a whole number

Whole bag count = G(net concrete volume × (1 + concrete waste) ÷ bag yield)

Ready-mix ordered volume (cu yd) = the larger of the minimum order and G(order volume ÷ order increment) × order increment

Ready-mix trucks = G(ready-mix ordered volume ÷ truck capacity)

Bag supply cost = whole bag count × bag unit cost

Ready-mix supply cost = ready-mix ordered volume × unit cost, plus the short-load fee when the ordered volume is below the short-load threshold

The slab rebar takeoff lays bars both ways across each slab's bounding rectangle and counts them as length, in fractions of a line. For a rectangular slab row the rectangle is its Length (W) by its Width (H); for the drawn slab it is the outline's extent along X (W) by its extent along Y (H):

Rebar length before waste (ft) = Σ Quantity × [(H × 12 ÷ transverse spacing + 1) × W + (W × 12 ÷ longitudinal spacing + 1) × H]

Stock bars = G(rebar length before waste × (1 + rebar waste) ÷ stock bar length)

The takeoff is symmetric: exchanging the two sides, or the two spacings, gives the same length, so which side is the length does not change it. The rebar grid route works on the reinforcement plan's clear dimensions, the plan length and width less twice the edge cover:

Longitudinal lines = G(clear width × 12 ÷ transverse spacing) + 1

Transverse lines = G(clear length × 12 ÷ longitudinal spacing) + 1

Rebar length before waste (ft) = longitudinal lines × clear length + transverse lines × clear width

The mesh-sheet route counts sheet columns along the clear length and sheet rows across the clear width, each sheet after the first adding its length (or width) less the overlap; the overhang is rounded to six decimals before it is counted:

Sheet columns = 1 + G(max(0, ROUND(clear length − sheet length, 6)) ÷ (sheet length − overlap))

Sheet rows = 1 + G(max(0, ROUND(clear width − sheet width, 6)) ÷ (sheet width − overlap))

Mesh sheets = sheet columns × sheet rows

The entered-quantity route passes your quantity and unit through. These are quantity relationships, not reinforcement design.

Calculation sequence

1. Check the drawing: one 'Slab from the drawing' row at most, a unit system, complete and consecutive outline and exclusion points, and, when a row uses the drawing, an outline of at least three points that encloses an area and leaves a net area after its exclusions.
2. Check the routes, the inputs the chosen routes use, and all ten element rows.
3. Measure the drawing: its gross area, each exclusion's area and the net area, and its bounding rectangle; convert a Metric drawing's net area and rectangle to square feet and feet.
4. Compute each included row's gross and net volume, then the net concrete volume, the concrete before waste and the waste-adjusted order volume.
5. Compute the bag count and cost and the ready-mix order, trucks and cost for the supply route, the supply-route result and the ready-mix threshold answer.
6. Compute the reinforcement quantity for the reinforcement route, and the placement-temperature note.
7. Return the status. A NOT VALID verdict replaces every figure but the drawing's areas.

Outputs and interpretation

• Concrete before waste (cu yd): the net concrete of every included row; the headline figure.
• Waste-adjusted order volume (cu yd) and net concrete volume (cu ft): the concrete after and before the one waste factor.
• Drawn slab concrete (cu yd): the 'Slab from the drawing' row's net concrete before waste; 0 when no row uses the drawing.
• Active concrete element count: the included rows.
• Drawing use: whether an included row pours the drawing.
• Whole bag count and bag supply cost: 0 under the Ready mix supply route.
• Ready-mix ordered volume, ready-mix truck count and ready-mix supply cost: the trucks are counted from the rounded ready-mix order, and all three are 0 under the Bags supply route.
• Supply-route result: a forced route reads as chosen. Under the comparison it reads Bags when the bag count is within the bag handling limit and the bag cost is no more than the ready-mix cost, and Ready mix otherwise.
• Above the ready-mix threshold: a volume fact, separate from the supply-route result. It is evaluated under every supply route and reads Yes when the waste-adjusted order volume is above the threshold, compared to six decimals, No at or below it, and Not evaluated when the threshold is blank.
• Reinforcement quantity and its unit: stock bars under the rebar grid or the slab rebar takeoff, mesh sheets, your entered quantity and unit, or 0 and Not estimated.
• Rebar length before waste (ft): the rebar grid's bars or the takeoff's length; 0 under mesh sheets, an entered quantity or no estimate.
• Longitudinal or sheet-column count and transverse or sheet-row count: the rebar grid's lines or the mesh layout's columns and rows; 0 under every other route, the slab rebar takeoff included, which measures length.
• Placement-temperature note: whether the entered placement temperature is below the cold review threshold, above the hot one, or within the band; Not evaluated when the note is skipped.
• From the drawing: the net slab area, the gross area inside the outline and each exclusion's area, in the drawing's unit. They are measured whether or not a row uses the drawing.

The chart compares the bag and ready-mix supply costs from the same results; it adds no calculation.

Validation and status logic

The status is the first of these that applies, in this order:

• NOT VALID: use one 'Slab from the drawing' row; its Quantity repeats the same slab
• NOT VALID: choose US or Metric
• NOT VALID: 'Slab from the drawing' needs an outline of at least three points, drawn on the calculator's web page
• 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 slab outline encloses no area
• NOT VALID: the exclusions leave no slab area
• NOT VALID: correct the supply, reinforcement, temperature, scalar, or complete concrete-element inputs
• CHECK: forced bag supply exceeds the entered handling limit
• CHECK: entered placement temperature is outside the user review band
• CHECK: the drawn slab does not fill its bounding rectangle or has exclusions, so its rebar, laid across that whole rectangle, can be more than the bars it needs
• OK

The first item applies when two or more included rows use the drawing; one row's Quantity already repeats the same slab. The third, and the two after the consecutive-rows item, apply only when an included row uses the drawing. The point items apply whether or not a row uses the drawing: an unused drawing must still be complete. The element-input item covers a route outside its list, an input of an active route outside its domain or relationship (such as a reinforcement plan no larger than twice its edge cover, a mesh overlap not smaller than the sheet, or a cold review threshold not below the hot one), a negative ready-mix threshold, any of the ten element rows incomplete or out of its domain, a void deduction not smaller than its included row's gross volume, two rows with the same label, and no included row.

A NOT VALID verdict replaces the figures: every result number reads 0, the drawing's areas excepted, and every text result reads NOT VALID after one of the drawing items and Not available after the element-input item.

The first CHECK applies only under the forced Bags route. The second applies when the temperature note is evaluated and the entered placement temperature is below the cold review threshold or above the hot one. The third applies under the slab rebar takeoff when a row uses the drawing and the drawn slab's gross area, compared to six decimals, is less than its bounding rectangle (an L or a T, or a rectangle not drawn square to the grid) or it has an exclusion. A CHECK keeps every figure.

Assumptions and limitations

Trust boundary. On this page the drawing tool keeps the slab outline a simple polygon and each exclusion inside it and apart from the others, and the spreadsheet trusts it: it does not check containment or overlap. The drawing is used only by a 'Slab from the drawing' row. Over MCP the drawing is not offered, and a request is computed from the typed element rows alone. A direct call to this page's calculation endpoint that sends a drawing must meet the drawing tool's guarantees: overlapping exclusions would give a wrong net area and a wrong drawn slab volume with an OK status.

• The slab rebar takeoff lays bars across the whole bounding rectangle of each slab. For an L- or T-shaped drawn slab, or one with exclusions, that is more bar than the slab needs, which is what the third CHECK says. Rectangular slab rows are always rectangles.
• Solid stairs are counted as solid blocks down to grade, not as a sloped waist slab.
• Void deductions are total cubic feet for each row.
• One waste factor applies to all the concrete, and one to all the rebar.
• The typed inputs are in US units only; only the drawing can be in metres, and its conversion is exact.
• The bag yields of the worked examples are a manufacturer's published figures for one mix; the yield is an input, and the bag count varies inversely with it before it is rounded up to whole bags.
• The shipped defaults are illustrative.
• Structural adequacy, the concrete mix, the reinforcement design, excavation, formwork, subgrade, frost protection, placement and curing are not determined. A licensed engineer and a qualified concrete professional must set the project's requirements.

Restrictions and non-computing states

Each numeric control offers a working range chosen for usable entry, which is not always the limit this calculator enforces; a value outside that limit is rejected with a message rather than quietly accepted. The calculator additionally enforces allowed choices, active-field types, complete fixed-grid rows, and conditional or cross-field rules before computing.

Unsupported route values, incomplete element rows, out-of-domain inputs, relational failures, an incomplete or gapped drawing, and a drawn slab with no area are non-computing states. Inputs that do not apply to the chosen routes remain in the values sent to the calculator but do not affect the results.

Errors and warnings

A rejected entry means the submitted state failed the published input rules. Workbook NOT VALID identifies an invalid active domain, an unusable drawing or unsupported derived arithmetic. Workbook CHECK retains a finite result while flagging a planning condition that needs review. OK means only that the delivered workbook logic closed within the entered assumptions; it is not code compliance, professional approval, or a safety guarantee.

• NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically - National Institute of Standards and Technology. The exact factors the workbook uses: foot 3.048E-01 m and square foot 9.290304E-02 m² (both exact), with cubic foot and cubic yard.
• QUIKRETE Concrete Mix product data sheet, No. 1101 - manufacturer data: a 60 lb bag yields about 0.45 ft³ and an 80 lb bag about 0.60 ft³, the two bag yields of the worked examples.
• OSHA 1926 Subpart Q, Concrete and Masonry Construction - Occupational Safety and Health Administration: the federal safety standard for concrete construction work.

Licensing conclusion: no proprietary, supplier-price, code or mix table is embedded. The bag yield is an editable input; its default (0.60 cu ft) and the 0.45 cu ft of two worked examples are the manufacturer's published values; the volume, step-prism and takeoff arithmetic is geometry.