ShopTrig Angle Desk turns everyday shop geometry — roof pitches, compound crown miters, bolt circles, pipe offsets, tapers and cone stretch-outs — into saw-ready numbers with the working shown, so you can check the math before you touch the stock.
Every calculation lives in its own problem bench: a real shop scenario, labelled inputs with sensible defaults, a diagram, the answer, and the tolerance you should be working to. You never have to remember which formula belongs to which job — you pick the job.
Enter rise and run, get the plumb cut, the seat cut, the length factor and the rafter length per 12" of run.
θ = arctan(rise / run) ±0.25°4/12 defaultHip pitch and cheek-cut angle for equal-pitch main and jack roofs, worked from the plan diagonal.
hip run = √(run₁² + run₂²) ±0.25°Spring angle plus wall corner in, miter gauge and blade tilt out — the two numbers you actually set on the saw.
miter = arctan(cos S / tan(C/2)) ±0.5°38° springChord length for your dividers, polar step angle and radius for any hole count on a flange plate.
chord = 2 r sin(π / n) ±0.005" chordCenterline travel and advance for any fitting angle, so the cut list matches the run before you thread anything.
travel = offset / sin θ ±1/8" travelSlope percent and angle against a target maximum, with a clear within target or steep verdict.
% = (rise / run) × 100 ±0.1%Turn a large and small diameter over a length into taper-per-foot, half-angle and included angle for the compound rest.
TPF = (D − d) / L × 12 ±0.001 TPFFlat pattern for a truncated cone: outer and inner radius plus the sector sweep to scribe on the sheet.
s = r θ ±1/16" arcRail pitch, plumb and level cuts from rise and run per tread, plus stringer angle and total run for a riser count.
θ = arctan(rise / run) ±1/16"Miter angle, panel width and glazing width for any regular bay, from a three-sided splay to a full polygon.
miter = 180° / n ±0.25° miterConvert any pitch into degrees and a hypotenuse factor that lines up with the degree scale on your square.
hyp = scale × √(rise² + run²) / run ±0.1°Filter benches by category, or search by keyword — “roof”, “miter”, “bolt circle” — and jump straight to the calculator.
10 categoriesInstant resultsA single number you can’t verify is a number you can’t trust. Every bench shows the headline result, the supporting values, and a step-by-step derivation with the formula, a plain-language explanation and the intermediate value at each stage.
Divide rise by run, then take the arctangent. Intermediate value is shown so you can sanity-check the ratio before it becomes degrees.
Radians converted to the degrees your saw and protractor actually read, rounded to two decimal places.
Multiply by the actual run to get rafter length. The same factor works for stair stringers and pipe travel.
Results are grouped as tagged callouts — ANGLE, MITER, BEVEL, LENGTH, SLOPE, TAPER, MARK — each with a short note telling you exactly where it goes on the stock.
Send a plain-text callout sheet with results and worked steps to anyone on the crew, or print a one-page PDF cut sheet straight from the bench.
Each bench carries a note on where calculators end and craft begins — dry-fit compound miters, add seam allowance after pattern layout, verify birdsmouth depth on the stock.
Every pack states the tolerance it’s designed around — ±0.25° on a plumb cut, ±0.005" on a bolt-circle chord, ±0.001 on taper per foot — so you know when a rounding difference matters.
Save any input combination with a title and notes. The jig you set up last month is one tap away, with the numbers exactly as you left them.
Lengths come back as workable fractions down to sixteenths — 12 5/8", not 12.625 — or as millimetres when you flip the unit switch.
Two tools sit beside the calculators for the part of the job that happens before the cut: planning where marks land, and deciding between options.
Drop ANGLE, BEVEL, LENGTH and MARK tokens onto a virtual board, then drag, scale, rotate and re-stack them until the layout reads clearly. Tap the palette to add a mark and it selects itself automatically, so you can position it immediately.
Run the same problem with different inputs and see the deltas highlighted. Perfect for “does a 6/12 or a 7/12 fit under that soffit”, or for checking whether shaving a degree off a spring angle is worth re-cutting the whole run.
Ten reference formulas grouped by topic — right triangles, circles, tapers, polygons and slopes. Each card gives the expression, what every symbol means, and the shop situations where you’d actually reach for it. There’s a symbol legend too, so an unfamiliar Greek letter never stops you.
a rise · b run · c hypotenuse — rafter length, pipe travel, stair stringer.
The workhorse behind plumb cuts, rail pitch and ramp angle — one ratio, one arctangent.
r radius · n hole count — divider setting for bolt circles and flange layouts.
Behind every cone stretch-out and curved flashing pattern in the app.
The number the compound rest wants — half the included angle, not the full one.
Bay windows, planter boxes, multi-panel frames — anything with equal sides.
Four tables you’d otherwise be squinting at on a faded shop poster: decimal-inch conversions, common tap-drill sizes in both imperial and metric, slope-to-percent mapping, and speed-square quick marks.
| Fraction | Decimal |
|---|---|
| 1/16" | 0.0625 |
| 1/8" | 0.1250 |
| 1/4" | 0.2500 |
| 3/8" | 0.3750 |
| 1/2" | 0.5000 |
| 3/4" | 0.7500 |
| Thread | Drill |
|---|---|
| 1/4-20 | #7 (0.201") |
| 5/16-18 | F (0.257") |
| 3/8-16 | 5/16" |
| 1/2-13 | 27/64" |
| M8×1.25 | 6.8 mm |
| M12×1.75 | 10.2 mm |
| Pitch | Common |
|---|---|
| 3/12 | ~14.0° |
| 4/12 | ~18.4° |
| 6/12 | ~26.6° |
| 8/12 | ~33.7° |
| 10/12 | ~39.8° |
| 12/12 | 45.0° |
Sites lose signal. Gloves are dirty. Light changes from the truck bed to the basement. The app is designed around all three.
All benches, formulas, tables and saved setups live on the device. The app works in a basement, on a roof, or in a steel building with no bars.
One switch changes every bench at once. Fractional inches to sixteenths, or millimetres to one decimal.
A high-contrast dark theme for dim interiors and a paper-white light theme for bright sites, or just follow the system setting.
A compact widget keeps your current pitch and its degree equivalent on the home screen — no need to open anything mid-cut.
An optional daily notification with a short, practical geometry reminder. Off by default, and one tap to turn off for good.
Every bench opens pre-filled with a realistic scenario, so you can change one number and read the answer instead of typing a full setup.
The last bench you opened is at the top of the home screen. Come back after a phone call and you’re still on the same job.
No sign-up, no profile, no ad network. Your saved setups and layout boards stay on your device.
ShopTrig Angle Desk is a layout-math tool for education and the trades. It is not a code compliance check, a structural engineering calculation, or a substitute for a stamped drawing.
Questions, bug reports, a formula that doesn’t match your handbook, or a problem bench you wish existed — write to us. Support is handled directly by the developer, and every message is read by a person.
To get a useful answer on the first reply, please include your device model, your Android version, the app version, the bench you were on and the exact inputs you entered. If a result looks wrong, the numbers you expected and where they came from — a handbook, a jobsite measurement or another calculator — help enormously.
No. ShopTrig Angle Desk is offline-first. Every problem bench, formula card, reference table, saved setup and layout board is stored on your device and computed locally. You can use it in a basement, inside a steel structure, or anywhere with no signal at all. The only optional network-adjacent feature is nothing more than the system share sheet, which uses whichever app you choose to send a callout sheet with.
Yes. Open Settings and flip the display units switch — the change applies to every bench at once, not just the one you’re on. In imperial mode, lengths are given as workable fractions down to sixteenths (for example 12 5/8"), and in metric mode as millimetres to one decimal place. Angles are always shown in degrees to two decimal places, since that is what saws, protractors and bevel gauges read.
Compound miter numbers are extremely sensitive to the spring angle of the moulding, and printed saw charts almost always assume a standard 38° or 45° spring with a perfect 90° corner. Real walls are rarely a true 90°, and moulding profiles vary between suppliers. Measure your actual spring angle and your actual corner angle, enter both, and always dry-fit a pair of offcuts before committing full lengths. If the difference is still larger than about half a degree after that, please email us your inputs and expected values.
Yes. On any bench, tap Save dimension setup to store the current inputs under a title with your own notes. Saved setups appear in your favourites and reopen the bench with everything exactly as you left it, which is ideal for a recurring jig, a standard roof pitch on a housing development, or a shop fixture you rebuild every season. Saved setups are stored locally on the device.
The results are layout mathematics and are intended for education and trade work. They are not a code compliance check and not an engineering calculation. Ramp slope results, for example, tell you the percentage and angle you’ve actually got — they do not certify accessibility compliance, and riser/tread uniformity is governed by your local building code. For structural members and anything inspected, treat the app as a fast, accurate layout aid and verify the final cut against a physical square or protractor and against the approved drawings.
Every bench can produce a callout sheet. Sharing sends a plain-text summary containing the headline result, supporting values, all tagged callouts with their notes, and the numbered worked steps — readable in any messaging or email app. Printing generates a one-page PDF cut sheet through the standard Android print dialog, so you can send it to a shop printer, save it as a PDF, or forward it to the crew.
Yes, at any time. Open Settings and switch off Daily shop tip — the reminder stops immediately and nothing else in the app changes. You can also revoke the notification permission from the Android system settings for the app. The tip is a small optional extra and the app is fully functional with it disabled.
None. There is no account, no sign-in, no profile and no analytics or advertising network. Your saved setups, layout boards, unit preference and theme choice live in local storage on your device and are never uploaded anywhere. If you contact support by email, we only see what you choose to write in that email.