Formula Library

Every formula on this site in one page: the calculation, a worked example, and where each number comes from. Each entry links to its calculator.

Home & yard (12)

Deck Material Calculator

Formula. Number of boards = (deck area in sq ft × 12 ÷ (board width + gap, both in inches)) × (1 + waste %) ÷ board length in feet — always rounded up to a whole board.

Example. A 12 ft × 12 ft deck (144 sq ft) in 5.5-in boards with 1/4-in gaps and 10% waste needs about 301 linear feet of decking — 21 sixteen-foot boards and roughly 496 screws.

• Screw count assumes face-fastening at 2 screws per joist crossing on 16-in joist spacing — standard framing practice, stated and editable on the page.
• Board widths are dressed-lumber actual sizes (a nominal 6-in deck board measures 5.5 in).

Gravel Calculator

Formula. Cubic feet = length × width × (depth in inches ÷ 12); cubic yards = cubic feet ÷ 27; tons = cubic yards × lb-per-cubic-yard ÷ 2,000.

Example. A 12 ft × 20 ft drive topped 4 in deep with crushed stone (about 2,800 lb per yard) takes 80 cubic feet = 2.96 cubic yards = about 4.15 tons.

• Densities are round mid-range values from published aggregate weight tables — the Two Rivers-Ottauquechee Regional Commission yardage chart, for one, puts 3/4-inch dry gravel near 2,565 lb/yd³ and crushed stone near 2,700 (stone type and moisture move both) — editable presets on the page.

Mulch Calculator

Formula. Cubic feet = bed length × width × (depth in inches ÷ 12); bags = cubic feet ÷ bag size, rounded up to a whole bag.

Example. A 10 ft × 12 ft bed mulched 3 in deep holds 30 cubic feet — fifteen 2-cubic-foot bags, or about 1.1 cubic yards in bulk.

• Bag sizes (2 and 3 cubic feet) are the standard US retail mulch bag sizes; bulk mulch is sold by the cubic yard.

Concrete Bag Calculator

Formula. Cubic feet = length × width × (thickness in inches ÷ 12); bags = cubic feet ÷ yield per bag — an 80-lb bag yields 0.60, a 60-lb bag 0.45, a 40-lb bag 0.30 cubic feet — rounded up.

Example. A 4 ft × 4 ft slab poured 4 in thick is 5.33 cubic feet: nine 80-lb bags of concrete mix (or twelve 60-lb, or eighteen 40-lb).

• Bag yields are the manufacturers' printed yield-chart figures — QUIKRETE's Concrete Mix data sheet lists 80 lb = 0.60 and 60 lb = 0.45 cubic feet, and 40 lb = 0.30 follows the same charts — checked October 2026 and editable on the page.

Raised Bed Soil Calculator

Formula. Cubic feet = bed length × width × (depth in inches ÷ 12) × number of beds; bags = cubic feet ÷ bag size, rounded up.

Example. One 4 ft × 8 ft bed filled 12 in deep needs 32 cubic feet of soil — twenty-two 1.5-cu-ft bags; a Mel's Mix splits that into three equal parts of about 10.7 cu ft (compost, peat moss, vermiculite).

• Mel's Mix (equal thirds compost, peat moss, coarse vermiculite) comes from Mel Bartholomew's All New Square Foot Gardening.
• Bag sizes are standard US retail soil bags (1.5 and 3 cubic feet).

Tile Calculator

Formula. Tiles = floor area × 144 ÷ (tile width × tile height, in inches) × (1 + waste %), rounded up; boxes = tiles ÷ tiles-per-box, also rounded up.

Example. A 10 ft × 10 ft floor in 12×24-in tile with 10% waste needs 55 tiles — ten boxes of six, with five tiles spare.

• Waste allowances: 10% is standard for straight-lay patterns, 15%+ for diagonal or herringbone; tiles-per-box varies by manufacturer and is an input.

Drywall Calculator

Formula. Sheets = wall area × (1 + waste) ÷ sheet area (a 4×8 sheet covers 32 sq ft); finishing per sheet runs about 0.32 gal mud, 16 ft of tape, 36 screws.

Example. A 12×12×8-ft room (384 sq ft of wall) in 4×8 sheets at 10% waste takes 14 sheets, about 4.5 gallons of joint compound and 224 ft of tape.

• Finishing quantities per sheet (0.32 gal mud, 16 ft tape, 36 screws) are industry rules of thumb, not any one manufacturer's spec — editable inputs on the page.

Fence Calculator

Formula. Posts = run length ÷ post spacing + 1; pickets = run × 12 ÷ (picket width + gap), rounded up; rails = sections × rails per section.

Example. A 100-ft privacy run at 8-ft post spacing needs 14 posts and 219 pickets from 5.5-in boards butted tight.

• Post spacing of 6–8 ft and 2–3 rails per section are standard fence-building practice; check local bylaws for height limits and property-line setbacks.

Paint Calculator

Formula. Gallons = (wall area − 20 sq ft per door − 15 sq ft per window) × coats ÷ coverage per gallon (interior latex spreads about 375 sq ft), rounded up to buy.

Example. A 12×14×8-ft room with 2 doors and 2 windows painted in 2 coats needs 1.85 gallons — buy 2.

• Coverage of 350–400 sq ft per gallon is the typical manufacturer spread rate for interior latex; the page default is 375 and editable.

Roof Shingle Calculator

Formula. Squares = footprint area × pitch multiplier × (1 + waste) ÷ 100; bundles = squares × 3 for standard three-tab shingles.

Example. A 30 ft × 40 ft house at 6/12 pitch (multiplier 1.118) with 10% waste is 14.76 squares — 45 bundles.

• Three bundles per square applies to standard three-tab shingles; architectural lines vary — bundles-per-square is an editable input.
• The pitch multiplier is Pythagoras: for 6/12 it is √(6²+12²) ÷ 12 = 1.118.

Paver Calculator

Formula. Pavers = patio area × 144 ÷ (paver width × paver height, in inches) × (1 + waste %), rounded up; polymeric sand runs about one bag per 50 sq ft.

Example. A 12 ft × 16 ft patio of 4×8-in Holland pavers at 5% waste takes 908 pavers plus 4 bags of polymeric sand.

• Polymeric sand coverage of about 50 sq ft per bag is a typical figure — joint width and depth move it; it is an editable input.

Board Foot Calculator (Hardwood Lumber)

Formula. Board feet = thickness (in) × width (in) × length (ft) ÷ 12, times the number of boards; one board foot is 144 cubic inches of wood.

Example. Three 4/4 (1 in) boards, 8 in wide and 8 ft long: each is 1 × 8 × 8 ÷ 12 = 5.33 board feet, so the lot is 16 board feet.

• Board-foot definition (144 cu in), quarter-size designations, nominal/roughsawn measurement and the round-up-to-next-quarter practice verified against Hardwood Industries' board footage page — a working hardwood supplier's own tally rules — fetched and checked October 2026.
• Quarter notation cross-checked against lumber listings in daily trade use; 4/4 surfacing to ~3/4 in is the standard dressed-size relationship.

Fees & seller money (4)

Stripe Fee Calculator

Formula. Fee = charge × 2.9% + $0.30 (US cards), so net = charge − fee; to receive a round net amount, charge = (net + $0.30) ÷ (1 − 0.029).

Example. A $100.00 US card payment costs $3.20 in fees and nets $96.80; charging $103.30 lands exactly $100.00. Canada: 2.9% + CA$0.30 per card charge.

• Canada rates read live from Stripe's Canada pricing page (2.9% + CA$0.30 cards, +0.8% international, +2% currency conversion, pre-authorized debit 1% + CA$0.40 capped at CA$5.00) — checked October 2 and again October 14, 2026.
• US rates read from Stripe's US pricing page on October 14, 2026 (2.9% + $0.30 cards, +1.5% international, +1% currency conversion, ACH 0.8% capped at $5) — editable presets.

PayPal Goods and Services Fee Calculator

Formula. Fee = sale amount × 2.99% for US domestic Goods & Services payments (no fixed fee); card-funded payments add a $0.49 fixed fee. Net = sale − fee.

Example. A $100.00 domestic sale costs $2.99 and you keep $97.01; to keep a clean $100.00 on a card-funded payment, ask for $103.59.

• US rates from PayPal's published US merchant fee schedule, verified October 14, 2026: 2.99% domestic Goods & Services, card-funded 2.99% + $0.49, international adds a 1.50% cross-border fee on top of the domestic rate (4.49% on Goods & Services) plus the $0.49 fixed fee.
• Other countries: PayPal posts a separate fee page per country — type your account's numbers into the custom-rate inputs.

Etsy Fee Calculator

Formula. Fees = $0.20 listing + 6.5% of (item + shipping) + 3% of (item + shipping) + $0.25 US payment processing — plus 12–15% offsite ads when an ad brought the buyer.

Example. A $25 item with $6 shipping carries $3.40 in fees and nets $27.61; on an offsite-ads sale at 15%, fees rise to $8.05 and the net is $22.96.

• Fee table from Etsy's published fees page (etsy.com/legal/fees), checked October 2026: $0.20 listing, 6.5% transaction on item + shipping, US processing 3% + $0.25, offsite ads 12% under $10k/yr (optional) or 15% at $10k+ (mandatory).
• Processing rates differ outside the US — custom rates are inputs on the page.

Mercari Fee Calculator

Formula. Since January 6, 2025: fee = 10% × (item price + buyer-paid shipping); payout = total − fee.

Example. A $50 item with $8 buyer-paid shipping owes $5.80 in fees — the seller is paid $52.20.

• Mercari's fee change effective January 6, 2025, from Mercari's Help Center fees article: flat 10% seller fee on item + buyer-paid shipping (pre-2025 listings kept 10% + 2.9% + $0.30 — the page has both modes).

Pool care (3)

Pool Salt Calculator

Formula. Pounds of salt = pool gallons × 8.345 × (target ppm − current ppm) ÷ 1,000,000.

Example. Taking a fresh 10,000-gallon pool to 3,200 ppm needs about 267 lb of salt — seven 40-lb bags.

• Pool water weighs 8.345 lb per gallon — the constant all pool-dosing math rests on.
• Target range 3,000–3,400 ppm is the salt-chlorinator industry standard; confirm against your unit's manual.

Pool Liquid Bleach Calculator

Formula. One gallon of 10% bleach per 10,000 gallons of pool water raises free chlorine about 9.5 ppm — scale the dose to your target rise and pool volume.

Example. Raising a 15,000-gallon pool by 4 ppm with 10% bleach takes 0.63 gallon — about 81 fluid ounces.

• Dosing follows the plain-bleach method used across the pool-service industry — the same arithmetic as TroubleFreePool's PoolMath, which the source now maintains as its pool-care app (the original web calculator at troublefreepool.com/calc.html still runs but is marked legacy and no longer updated).
• Chlorine strengths: plain household bleach 5–8.25%, pool-store liquid chlorine 10–12.5% — the strength input covers all of them.

Pool Volume Calculator (Rectangular, Round & Oval)

Formula. Gallons = surface area (sq ft) × average depth (ft) × 7.48; the area is L × W for a rectangle, π × radius² for a round pool, and π × (L ÷ 2) × (W ÷ 2) for an oval.

Example. A 32 × 16 ft rectangular pool with a 3 ft shallow end and 8 ft deep end averages 5.5 ft: 32 × 16 × 5.5 × 7.48 = 21,064 gallons.

• Shape formulas and the 7.48 gal/cu ft constant verified against The Pool Nerd's pool volume reference, fetched and checked October 2026.
• Water weight 8.345 lb/gallon is the same constant our salt dosing math rests on; dosing practice follows TroubleFreePool's Pool Math, the community dosing calculator since 2007.
• Worked examples on this page are computed by the page's own tested math, not copied from any chart.

Gaming (3)

Twitch Bits to USD Converter

Formula. US dollars paid to the streamer = Bits × $0.01 — Twitch's fixed payout rate of one cent per Bit.

Example. 10,000 Bits = $100.00 to the streamer; a viewer buying 1,000 Bits pays $14.00 using two 500-Bit packs, the cheapest combination.

• Streamer payout: Twitch pays a fixed $0.01 per Bit cheered — stable for years, per Twitch's cheering guide on help.twitch.tv.
• US web pack prices checked against multiple independent sources, October 2026 (the live authority is the Bits purchase dialog itself); the price table on the page is editable if Twitch reprices.

eDPI Calculator

Formula. eDPI = mouse DPI × in-game sensitivity; cm per 360 = 360 ÷ (DPI × yaw × sensitivity) × 2.54.

Example. 800 DPI at sensitivity 2 in CS2 is an eDPI of 1600 and a 25.98 cm/360; the identical feel in Valorant (yaw 0.022 vs 0.07) is sensitivity 0.6286.

• Yaw values are the games' standard rotation-per-count constants: CS2/CS:GO 0.022, Valorant 0.07, Overwatch 2 0.0066; a custom yaw input covers anything else.

Sensitivity Converter

Formula. Same feel across games: new sensitivity = old sensitivity × old yaw ÷ new yaw (CS2 0.022, Valorant 0.07, Overwatch 2 0.0066).

Example. CS2 sensitivity 2 equals Valorant 0.6286 — both turn exactly 25.98 cm per full 360 at the same DPI.

• Yaw values are the games' standard rotation-per-count constants: CS2/CS:GO 0.022, Valorant 0.07, Overwatch 2 0.0066.
• Conversion preserves cm per 360 — the physical distance of a full turn, the cross-game comparison standard.

Work & time (3)

Timecard Calculator with Lunch Break

Formula. Decimal hours = hours + minutes ÷ 60; the weekly total sums each day's (clock-out − clock-in − unpaid break).

Example. Five 9-to-5 days with a 30-minute lunch is 37 h 30 m on the timesheet — 37.50 decimal hours for payroll.

• The decimal conversion is exact arithmetic (minutes ÷ 60).
• Overtime at 1.5× after 40 hours follows the standard US FLSA workweek; other jurisdictions differ — the overtime toggle covers both.

Minutes to Decimal Hours Converter

Formula. Decimal hours = hours + minutes ÷ 60.

Example. 7:45 = 7.75 decimal hours; the payroll quarter-hour anchors are :15 = 0.25, :30 = 0.50, :45 = 0.75.

• Exact arithmetic, no estimates; the quarter-hour anchors are the standard payroll convention.

Prorated Rent Calculator

Formula. Prorated rent = monthly rent ÷ days in that month × days occupied (the move-in day counts as occupied).

Example. Moving in on the 10th of a 30-day month at $1,500/month: $1,500 ÷ 30 × 21 days = $1,050.00.

• Two legitimate methods exist — actual days in the month vs the fixed 30-day "banker's month"; your lease wording decides which applies, and the calculator does both.

Garage (2)

Tire Size Calculator

Formula. Overall diameter (inches) = wheel diameter + 2 × (section width in mm × aspect ratio ÷ 100 ÷ 25.4); revolutions per mile ≈ 63,360 ÷ (diameter × 3.1416).

Example. A 225/65R17 tire stands 28.52 in tall; upsizing to 235/65R17 adds 1.79% rolling diameter, so the speedometer reads 60 mph at a true 61.07.

• Markings follow the standard tire-size convention: aspect ratio is sidewall height as a percentage of section width; 25.4 mm = 1 inch, exact.

Nm to ft-lbs Torque Converter

Formula. 1 N·m = 0.7375621 ft-lb — multiply newton-metres by 0.7376 for foot-pounds, divide to go back.

Example. 100 N·m = 73.76 ft-lb (= 885.07 in-lb); 250 ft-lb = 338.95 N·m.

• Exact definitions: 1 lbf = 4.4482216152605 N and 1 ft = 0.3048 m, so the conversion factor is arithmetic — it cannot drift.

Craft & home brew (3)

Epoxy Resin Calculator

Formula. Gallons = (area in square inches × thickness in inches) ÷ 231 — then split by the mix ratio and add your waste allowance.

Example. A 24 in × 36 in tabletop sealed at 1/8 in with 10% extra needs about 0.51 gallons total: at a 1:1 mix that is 0.26 gal resin + 0.26 gal hardener.

• 231 cubic inches = 1 US gallon, exact.
• Mix ratios follow manufacturer labels (1:1 and 2:1 are the common tabletop ratios); the ratio inputs are editable.

Candle Wax Calculator

Formula. Wax (oz by weight) = jars × jar fluid ounces × fill % × wax density (soy ≈ 0.86); fragrance oil = wax weight × fragrance load %.

Example. Six 8-oz jars filled to 90% take 38.76 oz (2.42 lb) of soy wax plus 2.33 oz of fragrance oil at a 6% load.

• Soy wax density of about 0.86 g/mL (wax weighs less than water per volume) and a 6–10% fragrance load are typical craft-industry figures — editable inputs.

ABV Calculator (OG & FG)

Formula. ABV = (original gravity − final gravity) × 131.25.

Example. A beer fermenting from OG 1.050 down to FG 1.010 finishes at (1.050 − 1.010) × 131.25 = 5.25% alcohol by volume.

• ABV = (OG − FG) × 131.25 is the standard homebrewing formula; the page also shows the alternate gravity formula, which reads higher on big beers.

Canadian tax (1)

Reverse HST Calculator (Ontario & All Provinces)

Formula. HST inside a total = total × rate ÷ (100 + rate); the before-tax price = total ÷ (1 + rate as a decimal).

Example. An Ontario receipt totalling $113.00 contains exactly $13.00 of HST (13%) and $100.00 of goods.

• All Canadian rates verified against the CRA's published GST/HST rate pages, October 2026.
• Nova Scotia dropped from 15% to 14% effective April 1, 2025 — receipts before that date use 15%.

Pets (1)

Dog Food Calculator

Formula. Daily calories = 70 × (weight in kg)^0.75 × life-stage factor (1.6 for a neutered adult dog).

Example. A 22-lb (about 10 kg) neutered adult: 70 × 10^0.75 × 1.6 ≈ 629 kcal a day — about 1.68 cups of a 375-kcal-per-cup food.

• RER = 70 × kg^0.75 and the life-stage factors are the standard veterinary nutrition equations — the same method as Ohio State Veterinary Medical Center's nutrition calculator.
• Calorie arithmetic only — a veterinarian sets an individual dog's real plan.

How to read this page

Each block above is lifted from the calculator it links to — the same formula sentence, the same worked example, the same source list shown on that page. Nothing here is maintained separately; regenerate the page and these entries follow the calculators. Source links open the authority a rate or constant was verified against; entries with no link state their basis in words instead (typical published figures, standard practice), exactly as their calculator pages do.

Last reviewed: October 2026. Spotted a stale number? info@orbitalfour.com.