How these calculators work
Every construction calculator on this site follows the same path: convert entered lengths into metres, run the formula in SI units, convert the result into the display units, and round once at render. Conversion factors come from units.json. Densities, bag yields, paint coverage rates and stair limits come from materials.json. Nothing in that chain invents a round number to make the working look neat.
SI first, then display units
Hand calculators often multiply feet by inches without converting, then wonder why the cubic yards look wrong. The engines avoid that class of error by normalising early.
input length → metres
input area → square metres
input volume → cubic metres
compute
output → ft, yd, m, ft³, yd³, m³, lb, tons as requiredIEEE-754 floating-point precision is kept through the chain. Display rounding happens once. That is why 27 cubic feet remains exactly one cubic yard on the way back out, instead of drifting to 26.99 after a round trip through a rounded intermediate.
Imperial strings such as 7' 3-1/2" parse into a single metre value before any formula sees them. Mixed units on one form (length in feet, thickness in inches) are therefore safe: each field converts on its own.
Conversion constants that never change
| Constant | Value | Where it appears |
|---|---|---|
| Cubic feet per cubic yard | 27 | Concrete, cubic yards, material volumes |
| Inches per foot | 12 | Every thickness entered in inches |
| Square feet covered by 1 yd³ at 1 in depth | 324 | Cubic Yards coverage table |
| Square feet per square yard | 9 | Area conversions |
| Square feet per acre | 43,560 | Large site areas |
| Metres per foot | 0.3048 | All imperial length input |
| Centimetres per inch | 2.54 | Fractional inch to metric |
The 324 figure is not a mystery constant. One cubic yard is 27 ft³. Spread one inch deep, that volume becomes 27 × 12 = 324 ft² of coverage. At 2 inches the coverage halves to 162 ft²; at 3 inches it is 108 ft². The Cubic Yards Calculator owns that explanation so gravel and mulch pages can point to it instead of rewriting it.
Densities and bag yields
Bulk materials are sold by the yard or by the ton. Volume alone is not enough for a truck order when the quarry prices by weight. Densities in materials.json are typical loose bulk figures, for example:
| Material | Example density |
|---|---|
| Concrete (cured / ordered) | 4,050 lb/yd³ (about 2,400 kg/m³) |
| Pea gravel | 2,565 lb/yd³ |
| Dense graded aggregate / ABC | 3,374 lb/yd³ |
| Hardwood mulch | 600 lb/yd³ |
| Screened topsoil | 2,000 lb/yd³ |
The file opens with an explicit caveat: bulk densities vary by supplier, moisture and compaction. Confirm the density on the delivery ticket before treating tonnage as final. When a calculator offers a custom density field, that field is there so the ticket value can replace the table default.
Concrete bag yields are also table-driven:
| Bag | Yield | Bags per yd³ |
|---|---|---|
| 40 lb | 0.30 ft³ | 90 |
| 50 lb | 0.375 ft³ | 72 |
| 60 lb | 0.45 ft³ | 60 |
| 80 lb | 0.60 ft³ | 45 |
Paint coverage rates (smooth drywall 400 ft²/gal, textured 350, wood siding 275, brick 200, stucco 175) and door/window deductions (21 ft² and 15 ft²) live in the same materials file so the Paint Calculator and this page cannot disagree.
Waste, compaction and settling
Geometric volume answers "how much space is there." Ordering volume answers "how much should arrive on the truck." Those are different numbers for most bulk jobs.
| Allowance | Typical default | Meaning |
|---|---|---|
| Waste / overage | 5-10% | Spillage, edge forms, uneven subgrade |
| Compaction (gravel, road base) | 15-20% base | Loose yards needed to finish at compacted depth |
| Settling (topsoil) | about 15% | Grade drop after watering and traffic |
The fields stay separate on purpose. Combining them into one hidden "fudge factor" makes the working impossible to audit. Each calculator shows geometric volume and ordering volume side by side when an allowance is active.
What the working panel shows
"Show the working" prints the substituted steps: converted dimensions, intermediate area or volume, density multiplication, and the waste factor. That panel is the same arithmetic the engine used, rounded only for reading.
If a published worked example on a locked page disagrees with the live tool, the engine is wrong and should be fixed; the content is treated as a fixture.
Live recalculation uses a short debounce (about 150 ms) so typing does not thrash the result panel. Share links serialise the current inputs into the query string; the canonical URL stays on the clean path without those parameters.
Limits worth stating
- Stair riser and tread figures (maximum riser 7.75 in, minimum tread 10 in, and related limits) are general guidance stored for reference, not a citation of your local building code.
- Tank fill depth in a horizontal cylinder is non-linear; a half-full reading by stick is not half the gallons.
- Square footage for appraisal or listing purposes follows standards such as ANSI Z765 for finished living area. The Square Footage Calculator measures geometric area for construction and material takeoffs; it does not replace an appraiser's sketch.
- No page invents reviews, star ratings or user counts.
Frequently asked questions
Why convert to metres first?
Metres first prevents mixed-unit mistakes and keeps one code path for imperial and metric input. Display units are a presentation choice after the math finishes.
Can the densities be wrong for my supplier?
Yes. Moisture alone can move gravel and topsoil weight noticeably. Replace the default with the ticket density whenever it is available.
Why is waste not included automatically on every page?
Some jobs need geometric volume only (tank capacity, room volume). Where waste or compaction is common practice, the field defaults on and stays editable so the assumption is never hidden.
Where do the paint door and window deductions come from?
They are stored as 21 ft² per door and 15 ft² per window in the materials table, matching common estimating practice for a 3×7 door and a roughly 3×5 window. Unusual openings should be measured and entered as custom deductions when the tool allows.
Summary
Construction results on this site come from SI-normalised inputs, published conversion constants, and material tables with stated caveats. Densities are typical, not guaranteed. Waste and compaction stay visible. The working panel shows the same steps the engine ran, so any figure on the page can be checked with a pencil.