Editorial
How these calculators are checked
Every formula on this site lives in a plain TypeScript function, separate from the page. A unit test feeds it a known case — a 1×12×1 board foot, a perfect bowling game, a 6/12 rafter on a 24-foot span, the published 100 kg / 600 kg DOTS score — and the test fails if the result moves. The page cites the same identity the test locks.
Rounding is part of the spec when the trade rounds. Quilt yardage goes up to the next eighth of a yard. IPF GL rounds the body-weight coefficient to six decimal places before multiplying, because that is what the score sheet does. Money is shown in cents; the underlying payment is not rounded until display, and the amortization test checks that 360 payments retire a 6% loan.
Fees are dated, not scraped
Seller rates are constants in the repository, with a last-verified date of 2026-10-17. Etsy, Whatnot, and PayPal were read from the platforms’ own pages. Stripe’s US online card rates are the figures recorded for this batch on the same date:
- Etsy Fees & Payments Policy — $0.20 listing, 6.5% transaction, offsite ads 15% / 12% with a $100 cap.
- Etsy Payments Policy — US processing 3% + $0.25 on the gross order, including shipping and tax.
- Whatnot seller fees — article updated 2026-10-01. US commission tiers and 2.9% + $0.30 processing.
- PayPal merchant fees — page date 2026-10-01, read 2026-10-17. Goods & Services is 2.99% with no fixed fee on that line. Checkout is 3.49% + $0.49. Cards are 2.99% + $0.49. International commercial payments add 1.50%.
- Stripe pricing — US online cards 2.9% + 30¢, international cards +1%, disputes $15. Currency conversion is separate and is not given a percent.
A regulatory operating fee applies to Etsy sellers in some countries and is not modeled; US shops are not charged it. Whatnot’s non-US rate cards differ and are not copied here. If a platform changes a number, the constant, the date, and the test should change together. The page shows the date so a stale rate is obvious.
What “reviewed” means
The checked date on a calculator is the day the formula, the units, and the worked example were walked against the source below. It is not a claim that a person with a trade license signed the page. There is no invented expert byline.
| Calculator | Source of the math |
|---|---|
| Cross stitch | Stitch count ÷ (fabric count ÷ threads per stitch), plus margin on both sides. Counted-thread measurement used by fabric shops. |
| Quilt size | Mattress plus a drop on both sides. Length adds one drop and the pillow tuck. Whole blocks; leftover ÷ 2 is the border. |
| Quilt border | Butted sides match the current length; ends add two border widths. Mitered strips add two border widths plus extra. Cut width adds ½ in. Yardage rounds up to ⅛ yard. |
| Half-square triangles | Two at a time: finished + ⅞ in. Four at a time: finished × √2 + 1¼ in, up to ⅛ in. Eight at a time: 2 × finished + 1¾ in. Geese: width + 1¼ in and height + ⅞ in. |
| Fabric yardage | floor(width ÷ piece) across, ceil(quantity ÷ across) rows, rows × length ÷ 36, up to ⅛ yard. Non-directional cloth keeps the cheaper orientation. |
| Blanket yarn | Area × a planning factor by Craft Yarn Council weight number. Crochet × 1.30. The Council names the weights; the yards per square inch are not a Council figure. |
| Knitting gauge | Cast-on = width × stitches per 4 in ÷ 4. Percent = (yours − pattern) ÷ pattern. |
| Increases and decreases | Flat rows put the remainder at the end. In the round the remainder is split. A decrease consumes two stitches. |
| Quilt backing | Overage added to each side, then the cheaper of the two piecing directions. Yardage rounds up to the next 1/8 yard. |
| Quilt binding | 2 × (width + length) + a join allowance, divided into width-of-fabric strips. |
| Resin | Geometry of the pour, then 128/231 US fl oz per cubic inch. Parts split by the stated volume ratio. |
| Candle | Water weight × specific gravity, then wax = fill ÷ (1 + fragrance load). Armatage Candle Company candle-math equations. |
| Sourdough | Baker’s percentages. Total flour, including flour in the starter, is 100%. |
| Board foot | (thickness in × width in × length ft) / 12. A 1×12×1 is one board foot. |
| Board and batten | n boards and n−1 gaps fitted to the wall, gap recomputed so the courses fill the width. |
| Rafter | Pythagorean common rafter. Run is half the span minus half the ridge thickness. |
| Stair stringer | ceil(rise ÷ max riser) equal risers, one fewer tread, hypotenuse of rise and run. IRC R311.7.5 riser and tread limits. Throat is stock minus the perpendicular notch. |
| Gravel, mulch, soil, stone | Shape × depth, ÷ 27 for yards. Ordering densities in tons per cubic yard, with waste and, for soil, a settle factor. Bag counts round up. |
| Cubic yard | 27 cubic feet. Rectangle, circle, triangle, or a known area. |
| Concrete | Same volume. Bags from Quikrete Concrete Mix 1101: 0.30 / 0.45 / 0.60 cu ft. Weight at 150 lb/ft³. Solid steps use n(n+1)/2. |
| Asphalt | Compacted 145 lb/ft³. Tons = cubic feet × 145 / 2,000. Depth is finished thickness. |
| Stair | Equal risers, one fewer tread per flight. IRC R311.7.3 flight rise 151 in. R311.7.6 landing 36 in. Cross-linked to the stringer cut. |
| Roof pitch | Pitch per 12, degrees = arctan(slope), percent = slope × 100, multiplier = √(1 + slope²). |
| Roofing | Footprint × the pitch multiplier. One square is 100 ft². Bundles, underlayment, drip edge, and hip-and-ridge cap round up. Waste is a percent you set. |
| Room BTU | ENERGY STAR room-air-conditioner chart, then sun ±10%, +600 BTU per person past two, +4,000 for a kitchen, round down to 1,000. Ceiling and insulation multipliers are this site’s, not ENERGY STAR. Not a Manual J. |
| AC tonnage | Planning cooling BTU/ft² by DOE climate zone × area × ceiling/8 × insulation, ÷ 12,000. The zone rates are not a DOE table. Not a Manual J. |
| Duct size | Altshul–Tsal friction factor and Darcy–Weisbach at ASHRAE standard air. Huebscher equivalent diameter. Checked within 2% of a 710 CFM, 12 in, 0.10 in. wg chart. |
| Mini split | Same room estimate as the BTU page. Heads round up to catalog sizes. The outdoor unit rounds up from the sum of the unrounded loads. |
| Off-grid solar | Daily Wh ÷ (peak sun hours × (1 − system loss)). Battery Ah from autonomy, voltage, DoD, and inverter efficiency. Controller amps × 1.25. |
| Battery runtime | Battery amps = watts ÷ (volts × inverter efficiency). Peukert t = H ((C·DoD) / (I·H))^k. k = 1 skips the extra reduction. |
| kWh | watts × hours × days ÷ 1,000, times a rate you enter. |
| Density altitude | Moist density from the ballistic atmosphere model, inverted on the ISA troposphere. Humidity is the virtual-temperature term. Compared with the FAA 120-foot rule of thumb. |
| Recessed lighting | Spacing ≈ ceiling height. Lumens = foot-candles × area. Foot-candle targets are published residential summaries, not the IES selector. |
| Box fill | NEC 2023 314.16(B) allowances and Table 314.16(A) volumes. Grounds count once, clamps once, each yoke twice. Not a statement that the box is safe. |
| Watts, amps, volts | P = V × I × PF, or √3 × V × I × PF for three phase. VA leaves the power factor out. |
| Tire size | Nominal diameter and width from the molded size. Revs per mile = 63,360 / (π × diameter). Actual speed = indicated × new diameter / old diameter. |
| Displacement | (π/4) × bore² × stroke × cylinders. 16.387064 cm³ per cubic inch. |
| Specific gravity | Hall 1995 hydrometer cubic as a ratio of correction factors. Brix inversion of the ASBC-style conversion. Terrill 2011 refractometer cubic, shared with the ABV page. |
| Ballistic | Point-mass G1/G7, BRL Cd(Mach), |a| = ρ π g Cd v² / (1152 BC). Checked against a Shooter’s Calculator G7 chart. No reloading data. |
| Gear ratio | Nominal tire diameter. RPM = mph × axle × gear × 63360 / (60 π diameter). |
| Compression ratio | (swept + chamber) / chamber. Chamber includes gasket, deck, and a signed piston volume. Dynamic stroke at IVC. |
| Wheel offset | Backspace = (width + 1 in) / 2 + ET/25.4. Poke and inner clearance are the differences. |
| Wire size | NEC 2023 Table 310.16, 75°C column, plus 240.4(D) and the Chapter 9 voltage-drop K method. 3% is advisory. |
| ABV | (OG − FG) × 131.25, the alternate gravity formula, and Terrill’s 2011 refractometer cubic. |
| Conduit fill | NEC Chapter 9 Table 1 fill (53% / 31% / 40%, 60% for a nipple ≤ 24 in). Table 4 and Table 5 areas. Note 7 rounds a same-size count up at 0.8. |
| Voltage drop | 2 K I L / cmil single phase, √3 K I L / cmil three phase. K = 12.9 copper, 21.2 aluminum. Circular mils from Chapter 9 Table 8. 3% and 5% are informational notes. |
| RPE | Reactive Training Systems chart (Mike Tuchscherer). 5 reps at RPE 8 = 81.1% of 1RM. |
| DOTS, Wilks, IPF GL | Published polynomials and the IPF GL coefficient sheet (1 May 2020). GL coefficient rounded to 6 decimals. |
| Bowling | Ten-pin rules: strike adds the next two rolls, spare adds the next one, tenth frame may have fill balls. |
| Arrow | AMO front-of-center. Easton kinetic energy: grains × fps² / 450,240. Speed scales from the IBO 70 lb / 30 in / 350 gr condition. |
| Ski length | Retailer landmark chart: beginner chin to nose, intermediate nose to forehead, advanced head height and above. Not a DIN setting. |
| Snowboard length | All-mountain chin to nose, park 2 in shorter, powder longer. Wide board at a US men’s boot of 11 or larger. |
| Bullet energy | grains × fps² / 450,437. Momentum = grains × fps / 225,218. Joules = ft·lbf × 1.35582. Not the arrow page’s 450,240. |
| Crosswind | FAA crosswind geometry. Component = wind × sin(angle). Headwind = wind × cos(angle). |
| Mortgage | Standard fixed-rate annuity. M = P r (1+r)^n / ((1+r)^n − 1). |
| BMI | kg/m², or lb/in² × 703 (CDC). WHO adult cutoffs. Not a diagnosis. |
| Etsy | Listing 0.20 USD, transaction 6.5%, processing from the Etsy Payments table. Verified 2026-10-17. |
| Whatnot | US tier card effective 2026-09-21. Processing 2.9% + $0.30. Help article updated 2026-10-01. Verified 2026-10-17. |
| PayPal | Checkout 3.49% + $0.49. Goods & Services 2.99% and no fixed fee. Cards 2.99% + $0.49. International +1.50 points. Page date 2026-10-01. Verified 2026-10-17. |
| Stripe | US online cards 2.9% + $0.30. International cards +1 point. Dispute $15, optional. Recorded 2026-10-17. Currency conversion is not priced. |
| Steel weight | Volume in cubic inches × (0.0254)³ × density in kg/m³. Densities are room-temperature typicals: steel 7850, 304 stainless 8000, 6061 aluminum 2700, generic brass 8500, copper 8960, Grade 2 titanium 4510. A mill certificate wins. |
| Speeds and feeds | RPM = SFM × 12 / (π × diameter). Feed = RPM × chipload × teeth. Starting SFM and chipload are this site’s, clamped for mill and drill. The tool manufacturer’s chart wins. |
| 3D print cost | Grams × spool price / spool grams, plus watts/1000 × hours × rate, plus a machine rate × hours. Price = cost × (1 + markup). |
| Pool volume | Rectangle, circle, or ellipse times average depth. Kidney is the bounding box × a factor that starts at 0.85. Gallons = ft³ × 7.48052. |
| Pool salt | Pounds = gallons × ppm gap × 8.34 / 1,000,000. Bags round up. The label and the chlorinator manual win. No mixing instructions. |
| Aquarium | Rectangle, cylinder, or regular hexagon (3√3/2 × side²). Bow-front adds a parabolic segment, (2/3) × chord × bow. Gallons = in³ / 231. Fresh water at 8.34 lb/gal. |
| Rebar | Bars = floor(span / spacing) + 1 from both edges. Splices = ceil((span − stock) / (stock − lap)). Weight from ASTM A615 nominal lb/ft. #4 is 0.668. |
| Concrete block | Area × 1.125 blocks per square foot on a 16 × 8 in module. Mortar from the 3/8 in joint. Grout defaults to 0.195 ft³ for both cores of one block. Planning figures. |
| Tile | ceil(area × (1 + waste) / tile area). Waste starts at 10% straight, 15% diagonal, 20% herringbone. Grout volume is the joint prism. Bag coverage is editable. |
| Drywall | Sheets from net area and waste. Tape is the grid of seams. Mud defaults to 1 gal per 100 ft². Screws default to 32 a sheet. The bucket and the fastening schedule win. |
| Fence | Posts = ceil(length / spacing) + 1. Pickets = floor((inches + gap) / (picket + gap)) on the length that is not a gate. Concrete is the hole minus the post, using Quikrete bag yields. |
| Truss | Top chord uses the pitch multiplier. King post, four-panel Fink, and four-panel Howe member lists are fixed on the page. Board lengths only. No load check. |
| Tank volume | Vertical cylinder, rectangular prism, or the circular segment for a horizontal cylinder. Dipstick at tenths of the diameter. |
| Pipe volume | π(ID/2)² × length. Steel IDs from published ASME B36.10 Schedule 40 and 80. Copper from published ASTM B88 walls. PEX SDR-9 wall = OD/9. |
| Friction loss | Hazen–Williams 0.2083 (100/C)^1.852 Q^1.852 / d^4.8655, checked within 2% of a Spears 1/2 in, 1 gpm row at that row’s velocity-implied ID. Darcy–Weisbach with Swamee–Jain. 3 in Schedule 40 at 100 gpm and ε 0.00015 ft is 2.41 ft/100 ft, within 5% of a 2.5 ft steel chart. Fittings are equivalent length, not a Crane table. |
| Ohm’s law | Any two of V, I, R, and P. V = IR and P = VI. 12 V at 0.5 A is 24 Ω and 6 W. |
| Resistor network | Series sum. Parallel is the reciprocal of the conductance sum. 100 Ω ∥ 100 Ω is 50 Ω. |
| Wavelength | λ = v/f. Radio uses c = 299,792,458 m/s times a velocity factor. Sound uses 331.3 √(1 + T/273.15) m/s. |
| Resistor color code | 4-band is two digits, a multiplier, and a tolerance. 5-band adds a digit. 6-band adds ppm/°C. E12, E24, and E96 are IEC 60063. Red-violet-orange-gold is 27 kΩ ±5%. |
| Voltage divider | Vout = Vin R2/(R1+R2). A load replaces R2 with R2 ∥ RL. The E-series pair search is this site’s, from 100 Ω to 1 MΩ. 12 V to 3.3 V on E24 is 24 kΩ over 9.1 kΩ. |
| RC and LC filter | fc = 1/(2πRC). LC resonance f0 = 1/(2π√(LC)). Series band-pass Q = (1/R)√(L/C). Bode magnitude is tabulated, not only drawn. 1 kΩ and 1 µF is 159.155 Hz. 10 µH and 100 pF is 5.032921 MHz. |
| RC time constant | τ = RC. Charge Vs(1−e^(−t/τ)). Discharge Vs e^(−t/τ). 10 kΩ and 100 µF is 1 s. At one tau from 5 V, charge is 3.161 V and discharge is 1.839 V. |
| LED resistor | R = (Vs − n Vf)/I. The suggested part is the next E24 value at or above that resistance. 9 V, 2 V, 20 mA is 350 Ω, then 360 Ω. |
| 555 timer | Astable uses ln(2), not the rounded 1.44. Monostable uses the TI LM555 constant 1.1. 1 kΩ, 10 kΩ, 10 nF is 6,870 Hz at 52.38% duty. |
| Dipole length | Half-wave is (c × VF / 2f) × end effect. Default end effect 0.95. The 468/f rule is the rounded feet form. 14.1 MHz is 10.099 m, 33.13 ft. Ham buttons are band centers. |
| Impedance | XL = 2πfL, XC = 1/(2πfC). Series magnitude is the hypotenuse. Parallel magnitude is 1/|Y|. 1 kHz, 10 mH, 1 µF, 100 Ω series is 138.85 Ω at −43.93°. |
| Free-space path loss | 20 log10(d) + 20 log10(f) + 20 log10(4π/c). The 32.44 form is the rounded shortcut. 2.4 GHz over 1 km is 100.052 dB. Mid-path Fresnel radius is ½√(λD). |
| Coax loss | LMR-400/240/600 use the Times Microwave k1√f + k2 f formula, within 0.05 dB of the rounded datasheet cells (LMR-400 is 1.537 vs 1.5 at 150 MHz). RG-58, RG-8X, and RG-213 are the Belden 8259, 9258, and 8267 tables. Listed cells are exact. Gaps are log-log interpolation. |
| Microstrip | IPC-2141 Hammerstad wide/narrow pair, zero thickness, no mask. εr 4.4, h 1.6 mm, W 3.0 mm is 50.82 Ω, within 0.1 Ω of a published 50.8 Ω. The 50 Ω width is 3.083 mm, within 1% of about 3.06 mm. |
| SWR | |Γ| = (SWR−1)/(SWR+1). Return loss −20 log10|Γ|. Mismatch loss −10 log10(1−|Γ|²). SWR 1.5 is |Γ| 0.2, 13.979 dB return loss, and 4 W reflected from 100 W. |
| Subwoofer box | Gross internal is (W−2t)(H−2t)(D−2t), with an extra t off the depth for a double baffle. 1 ft³ = 1,728 in³ = 28.3168 L. Sealed box is Small 1972: Vb = Vas/((Qtc/Qts)²−1), Fc = Fs·Qtc/Qts. Ported start is Keele QB3, JAES 1981. Port length is c²Sp/(4π²Fb²Vb) − kd, c = 343 m/s, k = 0.732 or 0.85. A starting point, not a WinISD model. |
| Projector throw | Width = diagonal × a / √(a²+b²). Throw distance = throw ratio × width. Foot-lamberts = lumens × gain / area(ft²). Nits = fL × 3.426. About 14 fL is SMPTE ST 431-1. About 16 fL is SMPTE 196M. The spec sheet wins, including where the distance is measured. |
Old questions
The previous site’s FAQ URL redirects here. If a result disagrees with a cited source, the source wins and the function should change.