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🪚 Carpentry, pipe and weld basics

Quick layout math for stairs, rafters, lumber, pipe offsets and slope, and how to read a basic weld symbol. For stair and drainage limits, check your building or plumbing code.

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Stair rise and run

  • Number of risers = total rise ÷ target riser height, rounded up. Actual riser = total rise ÷ number of risers.
  • Number of treads = risers − 1 (when the top floor is the last step). Total run = treads × tread depth.
  • A common comfort check: 2 × riser + tread ≈ 24 to 25 in (610 to 635 mm).
  • Maximum rise, minimum run, headroom and handrails are set by your building code, so check it.

Common rafter length

  • Run = half the span (minus half the ridge board, if there is one). Rise = run × pitch ÷ 12 (pitch as inches of rise per 12 in of run).
  • Rafter line length = √(run² + rise²), or run × √(1 + (pitch/12)²).
  • Add overhang separately, measured along the rafter.

Board feet

  • Board feet = thickness (in) × width (in) × length (ft) ÷ 12
  • One board foot is 1 in × 12 in × 12 in (144 in³).
  • Lumber is usually sold on nominal sizes (for example 2 × 4), so check how your supplier counts.

Rolling offset

  • True offset = √(roll² + set²), where roll is the side-to-side distance and set is the vertical distance.
  • Travel = true offset × fitting multiplier: 45° = 1.414, 60° = 1.155, 22½° = 2.613.
  • Run (advance) = true offset × (1 ÷ tan angle): 45° = 1.000, 60° = 0.577, 22½° = 2.414.
  • Subtract fitting take-off for the cut length.

Pipe grade and slope

  • Fall = run length × slope
  • 1/8 in per ft ≈ 1%; 1/4 in per ft ≈ 2% (2.08%); 1/2 in per ft ≈ 4%.
  • % slope = rise ÷ run × 100.
  • Minimum slopes for drains are set by the plumbing code and depend on pipe size, so check it.

Weld symbol parts

  • Reference line: the horizontal line everything hangs on.
  • Arrow: points to the joint. The side it touches is the arrow side.
  • Weld symbol (fillet triangle, groove shapes and so on): below the reference line means arrow side, and above means other side. On both sides, weld both sides.
  • Size goes to the left of the symbol. Length and pitch go to the right (for example 2-6 means 2 in welds on 6 in centres).
  • Circle at the arrow-to-line joint means weld all around. A flag means field weld.
  • Tail: process, specification or other notes. Leave it off if there's nothing to add.

⚠️ Reference only. Always verify against the manufacturer's specs, your jurisdiction's code and your site's procedures.