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Stair Stringer / Step Calculator

Punch in the total floor-to-floor rise, your preferred riser height and your tread depth (going). The calculator rounds the riser count, recomputes the actual riser height, total horizontal run, stringer length and pitch, then checks the geometry against three widely cited codes — IRC (US residential), IBC (US commercial) and UK Approved Document K (private dwellings) — including the long-standing 2R + T walking-line rule of thumb. Useful for renovators, owners and design students iterating on riser/tread combinations.

Risers required

15 steps

14 treads

Actual riser height

180.0 mm

640 mm · 2R + T

Total horizontal run

3920 mm

≈ 3.92 m

Stringer length (hypotenuse)

4760 mm

≈ 4.76 m

Pitch angle

34.6 °

≈ 69%

Code compliance (IRC (US residential))

  • ✓

    Riser height

  • ✓

    Tread depth

  • ✓

    2R + T

  • ✓

    Pitch

For preliminary sizing only — verify against the latest local building code (Hong Kong follows an IBC-style ~175 mm riser cap) and your detailed shop drawings before ordering material.

Formula

N_risers = round(total rise / target riser) | actual riser = total rise / N_risers | total run = (N_risers − 1) × tread | stringer = √(total rise² + total run²) | pitch = atan(total rise / total run) | walking-line = 2 × actual riser + tread

Frequently asked

Why does the tool round my riser height?

Every code and every safety best-practice insists on equal-height risers throughout a flight — your brain builds a step rhythm from the first two risers and a mid-flight mismatch of even 5 mm causes trips and missed steps. The calculator rounds total rise ÷ target riser to the nearest whole number, then divides total rise by that count again so every riser shares the same actual height (no 5- or 10-mm "remainder" at the top). If you really want exactly 180 mm risers but the tool returns 183.3 mm, either (a) tweak total rise by removing/adding underlayment so the division comes out clean, or (b) accept it — carpenters typically shim out small discrepancies during stringer cut-out.

What is "2R + T" and why does it fail even when riser and tread are both within the code limits?

"2R + T" is the Blondel walking-line formula (1675): an adult's natural step covers ~600–660 mm horizontally, and each stair tread asks you to lift a leg AND advance a foot, so 2 × riser + tread should approximate your stride. Above the window (e.g. 700 mm+) feels lunging; below it (e.g. 500 mm−) you trip on your own toe-cap. A 200 mm riser + 280 mm tread design has fine riser and fine tread individually, but 2R + T = 680 mm, well past IRC's 610–635 mm convention, so descending feels "jumpy." The walking-line check is the early-warning that the proportions are off even if each axis passes. Easy fix: drop the riser a bit and deepen the tread.

Is the stringer length the same as the timber I need to order?

The stringer length output is the clean hypotenuse (√(rise² + run²)). Order longer than that: add 100–200 mm at the top and bottom for cuts/connections, the nosing overhang at every tread (if any), and a safety margin for the metal hangers or notch cut-outs. Carpenters usually add ~10–15% to the hypotenuse when buying solid lumber. So a 4,760 mm computed stringer is typically ordered as 5,300–5,500 mm of 2×12 / 38 × 286 mm stock. For LVL (laminated veneer lumber) stringers, use the supplier's nominal length (often 4.9 m, 5.5 m, 6.1 m).

Which code should I pick for a Hong Kong residential interior stair?

The Hong Kong Buildings Department's Building (Planning) Regulations §7.3 govern interior stairs and align most closely with the IBC (US commercial) approach — typical limits are riser ≤ 175 mm, tread ≥ 225 mm, clear width ≥ 900 mm. Pick "IBC" here for the most conservative, BD-aligned check. If the stair is in your own village house, never used as a fire-escape, and not part of a sale plan, you can use "IRC" for a comfort-only sanity check. For European-style designs, "UK Part K" applies. Always have a Registered Authorised Person (RAP) or Registered Structural Engineer (RSE) verify against the latest BD circular before submitting drawings.

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