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Methodology

This page lists the formulas the calculators use and where each reference value comes from. It is generated from the same records the calculators read, so what you see here is what is calculated.

A reference value is offered only when two sources publish it. Where two sources give different figures, the range is shown, the value used is stated, and the calculator lets you replace it. A starting value for waste is not a reference value: it is a number to change, and each one says below what it rests on.

Formulas

Areas and volumes are plain geometry. No manufacturer or trade association publishes a formula for the volume of a cylinder or of a flight of steps, so none is cited: the formulas are written out here and in each calculator's breakdown instead.

Fence: runs and gates are entered in order, runs by their length and gates by their width. Sections = run ÷ post spacing, rounded up; posts = sections + 1 per run and 2 per gate, less one post for each place where two of them meet (in order: every join; closed loop: one more; separate: none). Pickets = run or gate width ÷ (picket width + gap − overlap), rounded up, per run and per gate. Rails = panels × rails per section. Post length = fence height ÷ (1 − 1/3): a third of the post in the ground, the rule Quikrete and Sakrete both print. Gates are listed as a count of hinge and latch sets; the hardware itself is not chosen. Concrete per post = π × (hole diameter ÷ 2)² × hole depth, the hole as dug, without taking off the post, so it is a little high. Bags = posts × concrete per post × (1 + waste) ÷ the yield of one bag, rounded up. Post spacing, gates, hole size, gap, overlap and rails are the user's entries; the picket styles only fill in a starting gap and overlap.

Deck: each area is a rectangle, its length along the boards. Rows = (width + gap) ÷ (board width + gap), rounded up, the last row ripped to fit. Joists = length ÷ joist spacing, rounded up, + 1. A row no longer than a board is cut from one board, and rows per board = board length ÷ row length, rounded down, so boards = rows ÷ rows per board, rounded up. A longer row joins end to end over a joist: each board is used up to the last joist it reaches, (board length ÷ spacing, rounded down) × spacing; boards per row = row length ÷ that, rounded up; butt joints = rows × (boards per row − 1). Boards to buy = boards × (1 + waste), rounded up; offcuts of long rows are not reused and no saw cut is taken off. Crossings = rows × joists; fasteners = crossings × fasteners per crossing + butt joints × extra per joint; boxes = fasteners ÷ per box, rounded up. Board width, gap, joist spacing, board length and fastening are the user's entries: the gap and joist spacing come from the board maker's instructions, and the site sizes no joists, beams or footings. Each item with a price costs its count × its price.

Roofing: each roof plane is entered by its plan footprint, and the planes are added. Slope factor = √(1 + (rise ÷ 12)²) for a pitch of rise in 12, plain geometry (Pythagoras); it matches the IKO estimating table, 1.031 at 3/12 to 1.414 at 12/12. A pitch entered in degrees becomes rise in 12 as 12 × tan(angle), and one entered as a rise over a run as 12 × rise ÷ run. Pitches from 2/12 are offered, the lowest the GAF and Owens Corning instructions allow; below 4/12 and above 21/12 a note repeats their low-slope and steep-slope requirements. Roof surface = plan area × slope factor. Squares = roof surface ÷ 100 sq ft. Shingle bundles = squares × (1 + waste) × bundles per square, rounded up. Starter strip and hip and ridge bundles = the length to cover ÷ the length one bundle covers, rounded up; drip edge pieces = the eaves and rakes ÷ the piece length, rounded up. Underlayment rolls = roof surface × (1 + waste) ÷ (roll length × (roll width − overlap)), rounded up. Nails = squares × (1 + waste) × shingles per square × nails per shingle, rounded up; boxes = nails ÷ nails per box, rounded up. Each item with a price costs its count × its price, and the estimated cost is their sum.

Rebar grid: in each direction, bars = (side − 2 × edge clearance) ÷ spacing, rounded down, + 1, and each bar spans the other side − 2 × edge clearance. A bar longer than the stock length is made of pieces that overlap by the lap: splices per bar = (bar − lap) ÷ (stock length − lap), rounded up, − 1. Total length = bars × (bar + splices × lap), both directions and all areas added. Bars to buy = total length ÷ stock length, rounded up, which assumes the offcuts are used in other runs and adds nothing for cutting loss. Weight = bars to buy × stock length × the bar's weight per foot. Ties = bars one way × bars the other way, one per crossing, for each area. Spacing, edge clearance and lap are the user's entries; the site has no values of its own for them.

Steps are counted as one solid block with no landing: the first step is one rise high, the second two, and so on, which adds up to steps × (steps + 1) ÷ 2 rises. Quikrete's instructions for concrete steps note that filling the inside of the form with rubble reduces the mix needed, so the solid figure is an upper estimate.

A post hole is counted as a plain cylinder. A post standing in the hole takes up some of that space, so the figure is slightly high for a hole with a post in it.

Calculations run in meters and kilograms and are not rounded along the way. Only the numbers shown are rounded. A bag count that lands on a whole number is not pushed up to the next bag.

Units

Unit conversions are definitions: 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 cu yd = 27 cu ft, 1 US short ton = 2,000 lb = 907.18474 kg. Tons on this site are US short tons.

Both documents are published by NIST, which defines these units for the United States.

Concrete: standard concrete mix

BagVolumeSources
40 lb0.30 cu ftQuikrete Concrete Mix; Sakrete High Strength Concrete Mix
60 lb0.45 cu ftQuikrete Concrete Mix; Sakrete High Strength Concrete Mix
80 lb0.60 cu ftQuikrete Concrete Mix; Sakrete High Strength Concrete Mix

These values are for standard concrete mix. Only bag sizes that two sources publish are offered. The volume printed on the bag is the number to trust: if it differs from the one above, go by the bag.

Weight to haul: 2.02 tons per cu yd (150 lb per cu ft) for normal-weight concrete; sources give 140 to 155 lb per cu ft. Bags are weighed by the weight on the bag; this density is used for a bulk order. Sources: FHWA; Ohio University.

Starting value for waste: 10%. Starts at 10%, the top of the 4% to 10% that NRMCA, the ready-mix industry association, says to order over the plan dimensions. That is one source, so treat 10% as a starting value and change it to suit the job.

Sizing a post hole

Sources

Deck boards: composite and PVC deck boards from Trex, TimberTech and Fiberon, and 5/4 × 6 treated wood decking

Board width the field starts at: 5.5 in. Sources: Trex; TimberTech; Fiberon; ProWood.

Each maker chip fills in that maker's own instructions for its own boards, as a starting point to check against the guide for the board you buy. They are not reference values for other boards.

Starting value for waste: 0%. Starts at 0%: no board maker gives one figure. The count already buys a whole board for every row; add a few percent for boards you reject and cuts that go wrong.

Sources

Fence parts: fence panels, chain-link line posts and wood pickets sold at US retailers

Picket width offered: 5.5 in. Sources: The Home Depot; Lowe's.

Sources

Gravel, crushed stone and sand: bulk aggregate sold by the ton

Material typeValue usedSources giveConditionSources
Gravel or crushed stone, loose1.35 tons per cu yd1.30 to 1.42 tons per cu ydLoose and dry in one source; the other does not state the conditionNew Mexico EMNRD; CIWMB (now CalRecycle)
Clean crushed stone, 3/8 to 3/4 in1.30 tons per cu yd1.20 to 1.41 tons per cu ydDry; loose in one source, rodded in the otherRhode Island DOT; CIWMB (now CalRecycle)
Dense-graded base, compacted1.90 tons per cu yd1.85 to 1.95 tons per cu ydCompacted in placeWSDOT Design Manual M 22-01.23; Ohio DOT
Sand, loose and dry1.20 tons per cu yd1.20 to 1.45 tons per cu yd1.20 is loose dry sand and is the value used; the source of 1.45 does not state the conditionNew Mexico EMNRD; CIWMB (now CalRecycle)
Pea gravel, loose1.35 tons per cu yd1.30 to 1.35 tons per cu ydLoose and dry in a 50 lb bag of 0.5 cu ft in one source, 100 lb per cu ft; worked out from the area one ton covers 3 in deep in the other, which does not state the conditionQuikrete; Do it Best; Front Range Material (Colorado)
#57 stone (3/4 in crushed stone)1.34 tons per cu yd1.25 to 1.40 tons per cu ydPlaced, as a state DOT converts its quantities, in one source; the other gives 1.25 for rock and about 1.40 worked out from the area one ton of 3/4 in rock covers 3 in deep, without stating the conditionTennessee DOT; Front Range Material (Colorado)
Crusher run or road base, loose1.45 tons per cu yd1.25 to 1.48 tons per cu ydLoose and dry as measured in the truck in one source, 1.43 to 1.48; the other gives 1.25 for base course without stating the conditionWSDOT Design Manual M 22-01.23; New Mexico EMNRD

The two sources of each type give different figures. The value used lies inside their range: the dry figure where one source states the condition and an allowance for damp material is offered, otherwise close to the middle, on a 0.05 step. The calculator lets you replace it. Weight depends on the rock and on how wet the material is; a supplier's figure for the material you are buying beats any of these. Types for which two sources could not be found are not offered.

Sand is damp: the calculator can add 20% to the reference value, which gives 1.44 tons per cu yd. It is switched off by default and is not applied to a density you type in. The allowance rests on one source: the CIWMB table says to increase the weight of loose dry sand by 20% if it is damp and by 30% if it is wet or compacted. The 1.45 that NM EMNRD gives without stating a condition is consistent with the damp figure. Sources: CIWMB (now CalRecycle).

Starting value for waste: 10%. Starts at 10%. The only published figure we found is in a Washington State highway design manual, which adds 10% when material is stockpiled. It is one source and it is about road work, so change it to suit the job.

Sources

Mulch: bagged wood and bark mulch

BagVolumeSources
1.5 cu ft1.50 cu ftScotts Nature Scapes Color Enhanced Mulch; Do it Best; True Value
2 cu ft2.00 cu ftScotts Nature Scapes Color Enhanced Mulch; Patuxent Nursery
3 cu ft3.00 cu ftUnity Church Hill Nursery; The Gardens Nursery

These values are for bagged wood and bark mulch. Only bag sizes that two sources publish are offered. The volume printed on the bag is the number to trust: if it differs from the one above, go by the bag.

Starting value for waste: 0%. Starts at 0%. We found no authoritative figure for how much extra mulch to buy, so none is added. Enter your own percentage if you want a margin.

Recommended mulch depth

Sources

Rebar: standard deformed reinforcing bars, nominal weight

Bar sizeWeightSources
#30.376 lb/ftNucor; CRSI
#40.668 lb/ftNucor; CRSI
#51.043 lb/ftNucor; CRSI
#61.502 lb/ftNucor; CRSI

Starting stock bar length: 20 ft. Starts at 20 ft: Nucor lists 20 ft among its cut lengths and The Home Depot sells #4 bar in 20 ft lengths. Shorter bars are sold too; type the length your supplier sells.

Sources

Roofing shingles: asphalt shingles sold in bundles, counted by the roofing square

One roofing square: 100 sq ft of roof surface. Sources: Owens Corning; NRCA Roofing and Waterproofing Manual.

Starting bundles per square: 3. Starts at 3: the count Owens Corning, TAMKO and GAF publish for their standard 3-tab and architectural shingles. Some products differ, such as GAF Woodland at 4 a square. The count on the wrapper or data sheet of your shingle is the one to use. Sources: Owens Corning; TAMKO; GAF; Owens Corning; TAMKO.

Starting nails per shingle: 4. Starts at 4: the standard pattern in the Owens Corning and GAF instructions. Both call for 6 a shingle on slopes steeper than 21/12 (60°), and some products, wind ratings and local codes call for 6 as well. The installation instructions of your shingle give the count to use. Sources: Owens Corning; GAF.

Shingle slope limits, rise in 12: lowest 2/12, low-slope rules below 4/12, steep-slope rules above 21/12. Sources: GAF; Owens Corning.

Drip edge piece offered: 10 ft. Sources: Gibraltar Building Products; Englert.

Starting value for waste: 10%. Starts at 10%. GAF recommends adding 10–15% for trim allowance and waste, and more for valleys, dormers and complex roofs. One source and an estimating recommendation, not a rule: change it to suit your roof.

Sources

Topsoil: bagged topsoil

BagVolumeSources
0.75 cu ft0.75 cu ftScotts Premium Topsoil; Blain's Farm & Fleet
1 cu ft1.00 cu ftHemlock Hardware; Mahoney's Garden Center; Tierra Supply Co.

These values are for bagged topsoil. Only bag sizes that two sources publish are offered. The volume printed on the bag is the number to trust: if it differs from the one above, go by the bag.

Weight to haul: 1.05 tons per cu yd (77.8 lb per cu ft) for loose, dry topsoil; sources give 59.3 to 77.8 lb per cu ft. A starting value you can change. The two tables give different figures, so this is a starting value, the higher of the two. Wet soil weighs more: CIWMB gives 1.5 tons per cu yd for excavated, wet earth. Use your supplier's figure if you have one, or empty the field to leave the weight out. Sources: New Mexico EMNRD; CIWMB (now CalRecycle).

Starting value for waste: 0%. Starts at 0%. No authoritative source we found says how much extra topsoil to allow, so none is added. Enter a percentage of your own if you want spare.

What bulk topsoil weighs

Sources

Calculators