Construction & Trades

Expected diagonal of a right corner, or scale a 3-4-5 triangle. Optional measured diagonal reports error.

Arc length, chord, and sagitta from radius plus central angle, chord, or sagitta.

Complement between a bevel measured from the face and the same bevel measured from square.

Same equal-spacing layout as stud count, worded for joists, rafters, and blocking.

Cut length and angle from horizontal and vertical offsets. Same right-triangle hypotenuse as FRAM-05.

Member length and slope from horizontal and vertical layout offsets. Uses the right-triangle solver.

Equal leftover on each end when centering a feature in an overall length.

Midpoint of a span, or equal side offsets for a centered feature.

Radius, diameter, circumference, and area from any one of the four.

Geometric common-rafter length from horizontal run and pitch (rise per 12). Optional overhang adds to run. No ridge or birdsmouth deduction.

Flat-on-table crown/saw settings from included wall corner and spring angle (from the wall). Not nested/upright settings.

Divide a length into equal spaces, or space N item centerlines. Do not mix “5 items” with “5 spaces.”

Equal piece length from stock, piece count, and explicit kerf. Do not assume a blade kerf.

Grade = rise/run, slope angle, and run:rise ratio from a horizontal distance and Δelevation.

Symmetric two-piece miter: each piece is half the included joint angle. 90° corner → 45° per piece.

Offset a station along P1→P2 by a signed perpendicular distance. Left is positive when walking P1 to P2.

Planar shoelace area and perimeter from ordered local easting/northing vertices.

Prism volume V = A × h. Screening earthwork, not a TIN/end-area engine.

Diagonal from width × height, or the difference between two measured diagonals.

Solve a right triangle from two of leg A, leg B, hypotenuse, and angle A (opposite A).

Simple gable/shed surface area = footprint × √(1 + grade²). Pitch 6:12 is grade 0.5. No waste factor.

Equal clear openings with N shelf boards. Opening count is N + 1.

Actual riser, total run, angle, and stringer slope from total rise, riser count, and tread. Treads default to risers − 1.

Integer riser candidates around total rise / target rise. Returns floor, ceil, and the closer actual riser.

Stringer slope length from the same rise/run geometry as STAIRS-01. Not a birdsmouth or stock template.

Equal-spacing stud layout: spaces = ceil(L / S), count = spaces + 1. Optional opening is subtracted from length, not a king/jack schedule.

Triangle area from three measured side lengths (Heron).