Methodology: every formula, constant and source

By Rohit Gaur · Last updated October 11, 2026 · Report a mistake

A calculator is only worth using if you can check it. This page lists the formula behind every shape, the exact value behind every unit, the rounding rules, and the tests that keep them honest. The tables below are generated from the calculator’s own code at build time — nobody retypes a number into this page, so what is published and what runs cannot drift apart.

Formulas

Conversion constants

These are definitions, not measurements: an inch is 25.4 millimetres, exactly, by international agreement. The calculator converts through exact integer ratios rather than through these decimals, so 12 inches is exactly 1 foot and 1 acre is exactly 43,560 square feet with no floating-point dust.

Length

NIST Handbook 44 (2026), Appendix C: General Tables of Units of Measurement · Special Publication 811, Appendix B: Conversion factors · U.S. Survey Foot: Deprecation

Area

NIST Handbook 44 (2026), Appendix C: General Tables of Units of Measurement · Special Publication 811, Appendix B: Conversion factors · U.S. Survey Foot: Deprecation

Volume

Volume units are here because the material estimators use them.

NIST Handbook 44 (2026), Appendix C: General Tables of Units of Measurement · Special Publication 811, Appendix B: Conversion factors · U.S. Survey Foot: Deprecation

The United States survey foot is deliberately absent. NIST retired it on 31 December 2022, and since 1 January 2023 the international foot — exactly 0.3048 metres — is the only foot in use.

Land units of South Asia

These are not definitions the way an inch is. A bigha is whatever a particular state’s land records say it is, and the same word means 14,400 square feet in West Bengal and 9,075 in the bigha-biswa districts of Haryana. So every one below carries the government document it was read from and the date somebody opened it, and the converter makes you pick a region before it answers.

Where a source calls its own figure approximate — Bihar’s glossary on the kattha, Bangladesh’s Ministry of Land on the katha and bigha — the tables here and the converters both say so with a ≈ rather than printing four decimals of false precision.

India

Bangladesh

Three units people ask for are deliberately missing: Rajasthan’s bigha (two jaribs, one source), Pakistan’s marla (225 square feet in Lahore’s planned schemes against 272.25 on the old records, and no government copy of the rules we could open on 21 September 2026), and the Tamil Nadu ground of 2,400 square feet, which is quoted everywhere and stated in no document we could find. A land unit is worth more missing than wrong.

Garden materials: volume, compaction and weight

The mulch, gravel and topsoil calculators share one piece of arithmetic, and it is short:

• Volume is the area times the depth, plus whatever extra you ask for. A cubic yard is 27 cubic feet, so a yard spread an inch deep covers 324 square feet — the figure Clemson’s fact sheet quotes, and a test holds the engine to it. A cubic metre spread 2.5 cm deep covers 40 m².
• A compacted depth is ordered loose. When the depth you give is the finished depth of a base that will be compacted, the order is the loose lift that compacts to it, at the one ratio a source here gives for it (below). A loose cubic yard, or a bag, is taken to cover finished ground at the finished depth: the part that packs down covers nothing.
• Weight is the loose volume times what a cubic foot of it weighs. Tons are US short tons of 2,000 lb; tonnes are 1,000 kg. The weight field starts on a published figure and takes your supplier’s over it; a figure you type is kept in the unit you typed it in, so switching between feet and metres converts it rather than changing what it means.
• Bags are counted whole, rounded up with the same slack as every other count on the site, so 25 litres of mulch in 25 litre bags is one bag. A bag labelled by weight — British gravel comes in 20 kg bags and 800 kg bulk bags — holds that weight of stone, so it is counted as the weight of the job over the weight of the bag, which needs the weight field filled in.

Compacting: a depth given as finished is ordered 1.333 times as deep — the handbook's 8 in loose lift for 6 in finished. It is the only compaction ratio any source here gives, so it is the one used for every compacted depth.

The cubic yard calculator is the same arithmetic over several sections: each is a rectangle (length × width), a circle (π × half its width squared), a triangle (half its base × its height) or an area already known, times its own depth; the sections are added with compensated summation, and the extra, the weight and the bags are worked out on the total.

Sod has no depth. The sod calculator orders the lawn’s area plus the extra, counts pieces and pallets as whole things with the same slack as every other count, and weighs the order at the University of Tennessee’s figure — about a ton for a pallet of about 50 square yards — which is a figure for planning a delivery, not a scale: wet sod weighs more.

Building: pavers, concrete, the roof, the deck, insulation and siding

• Pavers are counted by the space each one takes with its joint. A paver L long and W wide with a joint J takes (L + J) × (W + J), so an area needs the area over that, plus the extra — 5 per cent, or 10 where a lot is cut, as Oregon State’s installation guide gives them. The base is the area times its compacted depth, ordered loose at the ratio Penn State’s road handbook lays it (8 inches loose for 6 finished) and weighed at the gravel page’s figure; the dig is the base, the bedding sand and the paver’s thickness together. The joint, the base depths and the inch of sand are ICPI’s (Tech Spec 2).
• Concrete is worked out pour by pour: a slab, footing or wall is length × width × depth; a round hole or column π × (half its width)² × its depth; a slab of known area, the area times its thickness; and n solid steps are width × rise × run × n(n + 1) ÷ 2, because each tread stands on every rise below it. Pours are added with compensated summation, the allowance goes on the total — 4 to 10 per cent, as the National Ready Mixed Concrete Association advises — and bags are the total over one bag’s yield as its maker prints it.
• A roof’s area is its plan area times √(1 + (rise ÷ 12)²), which is exact for a footprint of any shape as long as every slope has the same pitch. On a rectangle the edges follow: a gable has a ridge as long as the roof, two eaves and four rakes each half the width times the slope factor; a hip has a ridge the length less the width, eaves all round and four hips each √(2 + (rise ÷ 12)²) times half the width. The ice barrier reaches from the eave’s edge to 24 inches inside the walls, measured up the slope, and at least 36 inches from 8 in 12 (IRC R905.1.2); on a hip roof each strip is a trapezoid whose ends the hips cut off at 45°. Bundles are counted from the coverage Owens Corning prints, 98.4 square feet to a square.
• A deck is ⌈(width + gap) ÷ (board + gap)⌉ rows — one fewer when no more than a gap is left over, and a warning when the last row is short of a board by more than half a gap, since the TDCA’s code asks for no board to be cut along its length. A row no longer than a board is cut from one, as many to a board as fit; a longer one is whole boards joined over joists — as much of each board as reaches its last joist — and an end piece, as many end pieces to a board as fit. Joists are ⌈length ÷ spacing⌉ + 1, and screws two in every board at every joist, as both Trex and the TDCA ask.
• Blown insulation is counted from the chart on the bag. A chart gives each R-value a minimum number of bags per 1,000 square feet and a maximum area per bag, and its rounding can set the two a bag apart; the page keeps to both, so the count is ⌈max(area ÷ coverage, area × bags per 1,000 ÷ 1,000)⌉, with the chart’s minimum depth beside it — Owens Corning and Greenfiber each say the R-value needs the bags and the depth together. A target between two rows takes the next row up. Depth markers are ⌈area ÷ 300 sq ft⌉, as the IRC asks (N1101.10.1.1). Batts are counted by the framing they sit between: each covers its length times the spacing.
• Siding is walls at length × height and gable ends at ½ × width × height, less what the maker’s own method takes off for openings: the vinyl makers (the Vinyl Siding Institute and CertainTeed) count windows and doors in and take half of a large opening off, then add 10 per cent; James Hardie counts the walls less every opening and leaves waste out. A piece covers its length times its exposure. Starter strip runs along the base, J-channel round every opening and up every rake, and a corner post down each corner, spliced with the institute’s 3/4 in lap when the wall is taller than a post. House wrap covers the gross wall, at (9 ft − 6 in) × (150 ft − 12 in) a roll after DuPont’s laps.

Rounding

• Every calculation runs at full double precision. Rounding happens once, on the way to the screen.
• Areas and lengths are shown to two decimals, unit conversions to four, and a measurement you typed is echoed back with up to six.
• Unit conversion uses an exact integer ratio rather than two decimal factors, so 12 inches is exactly 1 foot and 1 acre is exactly 43,560 square feet.
• Waste, price and tax are applied to the unrounded area, so a rounded number is never multiplied by another rounded number.
• Room totals are added with compensated summation, so a 1,200 sq ft great room and a 6.25 sq ft cupboard still add up exactly.
• Anything sold in whole units — boxes, tiles, rolls, sheets, lengths of trim, pails, bags, pavers, deck boards, shingle bundles — is rounded up after the waste is added, never down. A count a hair above a whole number from floating-point noise is taken as that number, so 12 ft of trim in 4 ft lengths is 3 pieces, not 4.
• Paint in US units is rounded up to the next quart and shown as gallons and quarts. On a metric page it is packed into the tin sizes you stock: the least paint that covers the job, then the fewest tins.
• Materials cut from a roll are cut before they are counted: carpet is laid in whole roll widths, a wallpaper drop is rounded up to whole pattern repeats, and a roll gives only whole drops. The count follows the cuts, not the area.

How the maths is tested

Every formula has unit tests with fixed, checkable cases: a 12 × 12 room is 144 square feet, a 3-4-5 triangle is 6 square units, a 20 × 10 room with an 8 × 4 corner taken out is 168.

On top of those, property tests run each formula against thousands of random inputs and check statements that must hold for every one of them:

• an area is never negative and never NaN, whatever the input;
• scaling a room by k scales its area by k²;
• converting a length to another unit and back returns the original;
• the drawing agrees with the answer — the outline drawn on screen is measured with the polygon formula, and its area must equal the area the calculator reports.

That last one is the reason the diagrams can be trusted as drawings rather than decoration: a room that draws differently from the way it calculates fails the build.

Measuring a whole house (ANSI Z765)

The house calculator follows ANSI Z765, the square-footage method Fannie Mae has required for appraisals with effective dates from 1 April 2022. These are the rules it applies, and where each was read:

Where these came from, and what is missing. The official copy of ANSI Z765-2021 (Home Innovation Research Labs, USD 25) has not been bought. The rules above were read in Fannie Mae’s Selling Guide B4-1.3-05, which requires the standard and restates parts of it, and in a published slide deck from an Appraisal Institute chapter that reproduces the standard’s own wording, including its section numbering for rounding and reporting (PDF, opened 22 September 2026). A copy of the standard hosted by an MLS was found but is an encrypted PDF, and we did not try to open it. Since 11 October 2026 the rules have also been checked against Fannie Mae’s ANSI FAQ (September 2025) and the standard’s free public draft of February 2020, which Home Innovation says the 2021 edition changed mainly in its commentary; the house square footage guide lists every source.

Until the official copy is read, treat this page as what it is: a careful implementation of a standard we have read about rather than read. An appraisal that has to cite the standard should be checked against the standard.

What this calculator does not do yet

• The official text of ANSI Z765. The house calculator above is built from sources that restate the standard, not from the standard itself. That is the next thing to fix on this page.
• Other national standards. Germany’s Wohnflächenverordnung and France’s Loi Carrez decide living area differently again — a balcony usually at a quarter of its area and at most half, a minimum height of 1.80 m — and each needs its own mode rather than an approximation of one. They are planned with those languages.
• What holds a deck or a roof up. The deck and roof pages count what goes on the frame, not the frame: joist, beam and rafter sizes, posts and footings come from span tables and the building code where you build, and are for your plans.
• Land units outside South Asia. Tsubo, ping, dunam and the rest need per-region values with the government document each was read from, the way the South Asian units above do.

Corrections

If a number here is wrong, that is a bug and it will be fixed. Write to contact@sqftmath.com with the page and the measurement you used, and the correction will be dated when it ships.