How we calculate
Last updated
This page explains how our calculators work and where their figures come from. Every calculator page also has its own formula section, a worked example and a reference table generated by the same code that runs the tool. The construction figures further down are generated from that code too.
How every calculator is checked
- Each calculator has its own calculation engine with automated tests against published values (textbook examples, official worked examples and reference tables).
- Money results use the standard time-value-of-money formulas found in spreadsheets and financial calculators, so a payment or balance matches what a lender's spreadsheet gives for the same inputs.
- Rules of thumb (for example the 30% rent rule or the 50/30/20 budget) are labeled as rules of thumb and can be changed.
- Page text and code are drafted with the help of AI tools and checked through these tests and the sources below. More on how we work.
Where the figures come from
- Tax and income (US): IRS revenue procedures, notices and publications for brackets, standard deductions, credits, contribution limits, mileage rates and depreciation tables; the Social Security Administration for full retirement age and claiming rules. Each page states the tax year.
- UK and other countries: GOV.UK and HMRC for UK rates and allowances; the European Commission for EU VAT rates; national agencies for other country-specific rules.
- Prices and inflation: the US Bureau of Labor Statistics CPI-U series; live currency rates are European Central Bank reference rates, shown with their date.
- Health: published, named equations (for example Mifflin–St Jeor, the US Navy body-fat method, CKD-EPI 2021) and guidance from the CDC, NIH, WHO, ACOG, the National Academies and other health bodies. Health results are estimates, not medical advice.
- Science and units: NIST definitions of units and constants, IUPAC atomic weights, NASA planetary data and National Weather Service formulas.
- Building: typical material densities, bag yields and product sizes (below), with the International Residential Code where a code limit is quoted. Local codes can differ.
Updates and corrections
Each calculator shows the date it was last updated. Year-specific figures are updated when the publisher releases new ones (most US tax figures change each January). If you spot a mistake, tell us and we will correct it.
Building materials: units and conversions
Internally every calculation is done in feet, cubic feet, pounds and US short tons, then converted for display. Metric results use exact conversion factors:
- 1 ft = 0.3048 m (exact); 1 in = 2.54 cm (exact)
- 1 yd³ = 27 ft³ = 0.764555 m³; 1 ft³ = 28.317 L
- 1 lb = 0.45359237 kg (exact); 1 short ton = 2,000 lb = 0.907185 tonnes
Rounding rules
- Things you buy whole (bags, blocks, bars, delivery loads) are always rounded up.
- Ready-mix orders are rounded up to the next ¼ yd³, or the next 0.1 m³ in metric.
- Waste, compaction and settling allowances are added to the volume before converting to weight or bags.
Bulk material densities
Typical loose, dry densities. Moisture, particle size range and fines change real weights, often by 10–20%, and suppliers sell by their own scale weight. Every calculator lets you replace these figures.
| Material | tons / yd³ | tonnes / m³ | Default extra | Default depth |
|---|---|---|---|---|
| Pea gravel (3/8") | 1.4 | 1.66 | 5% | 3 in |
| Crushed stone #57 (3/4"–1") | 1.4 | 1.66 | 5% | 4 in |
| Crusher run / road base (#411, DGA) | 1.5 | 1.78 | 15% | 4 in |
| General gravel (mixed sizes) | 1.4 | 1.66 | 5% | 3 in |
| Sand (dry, loose) | 1.35 | 1.6 | 10% | 1 in |
| River rock 3/4"–1 1/2" | 1.35 | 1.6 | 5% | 2 in |
| River rock 1"–3" | 1.35 | 1.6 | 5% | 3 in |
| Cobbles / beach pebbles 3"–5" | 1.35 | 1.6 | 0% | 5 in |
| Lava rock | 0.55 | 0.65 | 5% | 3 in |
| Decomposed granite (DG) | 1.35 | 1.6 | 15% | 3 in |
| Marble / quartz chips | 1.4 | 1.66 | 5% | 2 in |
| Screened topsoil | 1.1 | 1.31 | 10% | 4 in |
| Fill dirt | 1.2 | 1.42 | 20% | 6 in |
| Garden soil / raised-bed mix | 1 | 1.19 | 10% | 8 in |
| Compost | 0.6 | 0.71 | 5% | 2 in |
| Shredded hardwood mulch | 0.3 | 0.36 | 10% | 3 in |
| Wood chips | 0.25 | 0.3 | 10% | 3 in |
| Pine bark mulch / nuggets | 0.22 | 0.26 | 10% | 3 in |
| Hot-mix asphalt (compacted) | 1.96 | 2.32 | 5% waste | 3 in |
Concrete bag yields
| Bag | Yield |
|---|---|
| 40 lb bag | 0.3 ft³ |
| 50 lb bag | 0.375 ft³ |
| 60 lb bag | 0.45 ft³ |
| 80 lb bag | 0.6 ft³ |
| 20 kg bag | 9.4 L |
| 25 kg bag | 11.7 L |
| 30 kg bag | 14 L |
| 40 kg bag | 18.7 L |
US yields are those printed on standard concrete mix bags (an 80 lb bag makes about 0.60 ft³). Metric bag yields are estimated using the same yield per kilogram; high-strength, rapid-set and lightweight products differ, so check your bag.
Concrete shapes
- Slab or footing: length × width × thickness. Thickened edges add a perimeter strip of (edge width) × (edge depth − slab thickness), with corners counted once.
- Round slab, column or tube: π × r² × height.
- Bell footing: volume of a truncated cone, π × h ÷ 3 × (r₁² + r₁r₂ + r₂²).
- Steps: solid steps poured against grade; step i is run × (i × rise) × width, plus an optional top platform.
- Post holes: hole cylinder minus the post's cross-section (actual lumber sizes), over the depth above the gravel layer.
Concrete block
| Block | Nominal face incl. joint | Approx. core volume |
|---|---|---|
| 4×8×16 in | 16 × 8 in | 0.1 ft³ |
| 6×8×16 in | 16 × 8 in | 0.17 ft³ |
| 8×8×16 in (standard) | 16 × 8 in | 0.25 ft³ |
| 10×8×16 in | 16 × 8 in | 0.33 ft³ |
| 12×8×16 in | 16 × 8 in | 0.4 ft³ |
| 440×215 mm (UK, solid) | 450 × 225 mm | Solid |
| 390×190×140 mm (15.01) | 400 × 200 mm | 4.7 L |
| 390×190×190 mm (20.01) | 400 × 200 mm | 7 L |
Blocks = net wall area ÷ nominal face area × (1 + waste). Core volumes are approximations (hollow units are roughly half void) and vary by manufacturer. Grout is estimated as the share of cores filled × core volume per block.
Rebar
| Bar | Diameter | Weight |
|---|---|---|
| #3 (3/8") | 0.375 in | 0.376 lb/ft |
| #4 (1/2") | 0.5 in | 0.668 lb/ft |
| #5 (5/8") | 0.625 in | 1.043 lb/ft |
| #6 (3/4") | 0.75 in | 1.502 lb/ft |
| #7 (7/8") | 0.875 in | 2.044 lb/ft |
| #8 (1") | 1 in | 2.67 lb/ft |
| 10M (Canada) | 11.3 mm | 0.785 kg/m |
| 15M (Canada) | 16 mm | 1.57 kg/m |
| 20M (Canada) | 19.5 mm | 2.355 kg/m |
| 8 mm bar | 8 mm | 0.395 kg/m |
| 10 mm bar | 10 mm | 0.617 kg/m |
| 12 mm bar | 12 mm | 0.889 kg/m |
| 16 mm bar | 16 mm | 1.58 kg/m |
| 20 mm bar | 20 mm | 2.469 kg/m |
US unit weights follow ASTM A615. Canadian M bars use CSA G30.18 nominal weights, and generic metric bars use d² ÷ 162 kg/m. Bars each way = ⌊(span − 2 × edge clearance) ÷ spacing⌋ + 1. Runs longer than a stock bar are spliced with the lap length you enter (40 bar diameters by default, a common rule of thumb).
Tile, grout and thinset
- Tiles: area ÷ ((tile length + joint) × (tile width + joint)) × (1 + waste), rounded up. Default waste by layout: straight 10%, offset 10%, diagonal 15%, herringbone 20%.
- Grout: joint volume per unit area = joint width × tile thickness × (length + width) ÷ (length × width); powder weight = volume × grout density (default 100 lb/ft³ ≈ 1.6 kg/L) + 10%. In metric this equals kg/m² = (A + B) ÷ (A × B) × C × D × 1.6, with sizes in mm. The grout bag's coverage chart takes priority.
- Thinset: bags = area ÷ coverage per bag. Typical coverage per 50 lb bag: 1/4 × 1/4 in notch ≈ 95 ft², 1/4 × 3/8 in ≈ 65 ft², 1/2 × 1/2 in ≈ 45 ft² (20 kg bags pro rata). Check the bag.
Drywall and flooring
- Drywall sheets: (wall area + optional ceiling − doors and windows) × (1 + waste, default 10%) ÷ sheet area, rounded up, with walls and ceiling rounded separately.
- Joint compound, tape and screws (rules of thumb): about 9.4 gal of compound and 370 ft of tape per 1,000 ft² of board (0.38 L and 1.2 m per m²); about 32 screws per 4 × 8 ft sheet on walls and 40 on ceilings, scaled by sheet size. All are editable because finish level and technique vary.
- Flooring: area to buy = room area × (1 + layout waste: straight 10%, diagonal and herringbone 15%); boxes = area to buy ÷ coverage per box (printed on the box). Baseboard = room perimeter − doorways.
Pavers and retaining walls
- Pavers: area ÷ paver face area × (1 + pattern waste: running bond 5%, herringbone 10%, circular 15%). Base = (area + perimeter × overhang) × compacted depth × (1 + 15%) of crusher run; bedding sand = area × depth + 10%; polymeric sand = area ÷ coverage per bag (varies widely; check the bag).
- Retaining walls: courses = ⌈exposed height ÷ block height⌉ + buried courses; blocks = wall length ÷ block length × courses × (1 + waste). Base = length × trench width × depth + 15% compaction; drainage stone = length × zone width × wall height + 5%. Walls above about 3–4 ft (1–1.2 m) often need engineering, reinforcement or a permit.
Fences and decks
- Fences: for one continuous run, sections = ⌈(length − gates) ÷ post spacing⌉ + corners and posts = sections + 1 + gates (a run that closes on itself needs one fewer). Pickets = ⌈net length ÷ (picket width + gap)⌉ × (1 + waste). Chain-link fittings use common rules of thumb (for example about one tension band per foot of height) and are labeled as such.
- Decks: board rows = ⌈deck length ÷ (board width + gap)⌉; boards = rows × ⌈width ÷ board length⌉ × (1 + waste); joists = ⌈width ÷ spacing⌉ + 1; posts and footings = ⌈width ÷ post spacing⌉ + 1 with footing concrete from the form-tube formula; screws = 2 per board per joist. The deck calculator counts materials only; joist, beam and footing sizes must come from your local code or plans.
Lawns: sod and grass seed
- Sod: pieces = lawn area × (1 + waste) ÷ piece area; pallets = the same area ÷ the pallet coverage you enter (pallet sizes vary by farm). Piece sizes offered: 16 × 24 in slab (2.67 ft²), 18 × 24 in slab (3 ft²), 2 × 5 ft roll (10 ft²), 1 m² roll, 0.5 m² roll.
- Seed: pounds = area ÷ 1,000 × rate in lb per 1,000 ft² (1 lb per 1,000 ft² ≈ 4.88 g/m²). Default rates are the middle of the typical ranges below; overseeding uses roughly half. The rate on the seed bag takes priority.
| Grass | New lawn (lb / 1,000 ft²) | Overseeding |
|---|---|---|
| Kentucky bluegrass | 2–3 | 1–1.5 |
| Tall fescue | 6–8 | 3–4 |
| Perennial ryegrass | 6–8 | 3–4 |
| Fine fescue | 3–5 | 2–3 |
| Sun and shade mix (cool-season blend) | 4–6 | 2–3 |
| Bermudagrass (hulled) | 1–2 | 0.5–1 |
| Zoysia | 1–2 | 0.5–1 |
| Centipede grass | 0.25–0.5 | 0.25 |
Mulch
Mulch uses the same volume method as gravel and soil (area × depth, plus a settling allowance), but the headline result is volume because mulch is sold by the cubic yard or bag. Its weight varies a lot with moisture, so the weight shown is only an estimate.
What the calculators don't do
The calculators estimate quantities and costs. They don't design structures. Slab thickness, footing size, rebar size and spacing, and wall reinforcement for anything structural must come from your plans, an engineer or your local building code. See our terms and disclaimer.
Found a problem?
If a figure looks wrong for your area or product, please tell us. We review every correction.