Steel Stair Calculator: Rise, Run and Stringer Layout

To lay out a steel stair, divide the total rise by the maximum allowed riser height and round up to get the number of risers, divide the total rise by that number to get the actual riser height, then multiply the number of treads (one fewer than the risers in a straight flight) by the run to get the total run. The stringer angle and length, the headroom and any landings follow from those three numbers. In Ontario, Part 9 of the 2024 Building Code limits risers to 200 mm in houses and 180 mm on public stairs, with minimum runs of 255 mm and 280 mm.

Below is the calculation step by step, with worked examples. A calculator gets you a layout to discuss; the final geometry is fixed on the shop drawings after a site measure.

The numbers you need first

Measure, or get from the drawings:

1. Total rise: vertical distance from the finished floor at the bottom to the finished floor at the top. Use finished surfaces, not subfloor or slab. A 20 mm floor finish missed at one end turns into a bad first or last step.
2. Available run: horizontal space for the stair, plus any landing.
3. Floor structure thickness at the top opening (joists or slab plus finishes), for the headroom check.
4. Stair width you want.
5. Stair type: private (within a house or serving one dwelling) or public (most other stairs in Part 9 buildings).

Code limits that drive the calculation

From the 2024 Ontario Building Code, Division B, Table 9.8.4.1.:

Other limits that come into the calculation:

• Tread depth must be at least the run and no more than the run plus 25 mm (Sentence 9.8.4.2.(2)). That limits nosing overhang.
• Uniformity: risers within 5 mm of each other between adjacent steps and 10 mm across the flight, and the same for runs (Article 9.8.4.4.).
• Maximum flight height: 3.7 m vertically without a landing (Article 9.8.3.3.).
• Headroom: at least 1,950 mm over stairs serving a single dwelling unit or a house with a secondary suite, and 2,050 mm elsewhere (Article 9.8.2.2.).
• Width: at least 860 mm for stairs within a dwelling unit and 900 mm for public stairs in residential buildings (Article 9.8.2.1.).

These are Part 9 values. Larger buildings designed under Part 3 follow Section 3.4, and their stairs are set by the architect. Our article on Ontario Building Code rules for steel stairs covers the rest, including winders, spirals and open risers.

The formulas

The headroom distance is how far back from the top of the stair, measured horizontally, the edge of the floor opening has to be for the required clear height. It assumes a flat ceiling at the underside of the floor structure.

Worked example 1: a straight basement stair

A house with a total rise of 2,720 mm, private stair, floor structure above 300 mm thick including finishes.

1. Risers: 2,720 ÷ 200 = 13.6, round up to 14 risers.
2. Riser height: 2,720 ÷ 14 = 194.3 mm, within the 125 mm to 200 mm range.
3. Treads: 14 - 1 = 13 treads.
4. Run: pick a value between 255 mm and 355 mm; take 260 mm.
5. Total run: 13 × 260 = 3,380 mm.
6. Angle: arctan (194.3 ÷ 260) = about 36.8 degrees.
7. Nosing line length: 3,380 ÷ cos 36.8° = about 4,220 mm.
8. Headroom: (1,950 + 300) × 260 ÷ 194.3 = about 3,010 mm. The floor opening has to extend at least that far back from the top of the stair.

If the room can't fit 3,380 mm of run, a shorter run (down to 255 mm) or a turn with a landing or winders are the options. If 3,010 mm of opening isn't available, the floor framing or the stair layout has to change, which is a conversation for the designer.

Worked example 2: a stair with a landing

A public stair in a small Part 9 residential building, total rise 4,200 mm, 900 mm wide, straight run with a mid-landing.

1. Risers: 4,200 ÷ 180 = 23.3, round up to 24 risers.
2. Riser height: 4,200 ÷ 24 = 175 mm.
3. Landing needed? Yes. 4,200 mm is more than the 3.7 m maximum for one flight. Split into two flights of 12 risers each, so each flight rises 2,100 mm.
4. Treads per flight: 12 - 1 = 11 treads, because the landing acts as the top step of the lower flight.
5. Run: at least 280 mm for a public stair; take 280 mm. Each flight runs 11 × 280 = 3,080 mm.
6. Landing length: landings must be at least as wide and long as the stair, but a straight-through landing need not be longer than the lesser of the required stair width or 1,100 mm (Article 9.8.6.3.). Here that is 900 mm.
7. Total run: 3,080 + 900 + 3,080 = 7,060 mm.
8. Angle: arctan (175 ÷ 280) = about 32 degrees.

Keep the same riser height in both flights. The code's uniformity limits apply within each flight, but a change in step height at a landing still catches people out.

Steel stair details that change the numbers

A calculator works in nosing-to-nosing dimensions. A steel stair adds a few practical points:

• Tread thickness. Rise is measured nosing to nosing, so every tread must be the same thickness. If steel pans will hold 40 mm of concrete or a wood tread sits on a steel angle, the shop allows for it in the stringer layout. See types of steel stair treads.
• Top and bottom risers. The first riser runs from the finished floor to the first tread; the last from the top tread to the finished floor above. These are the two that go wrong when floor finishes change.
• Stringer depth. A deep plate or channel stringer has to fit under the stair and clear the floor at the bottom. Our guide to steel stair stringer sizes covers common sections.
• Top connection. The stringer's cut length depends on how it attaches: hung off a header with plates, sitting on a ledger or landing on a beam. The nosing line length is a starting point, not a cut list.
• Width and stringers. Stringers and handrail brackets can project only a limited distance into the required width, so the overall width between walls is often wider than the required stair width.
• Tread count and width. For a "steel stair tread calculator": the number of treads is risers - 1 per flight, and the tread length is the clear width between stringers.

From calculator to shop drawings

A calculation like this gets you a layout that fits the code and the room. Before steel is cut, a fabricator measures the actual opening and floors, then draws the stair with every riser, tread, stringer and connection dimensioned. That drawing, approved by you and your designer, is what the shop builds from. Our post on how steel stairs are fabricated walks through what happens next.

Getting a steel stair laid out and built

We fabricate custom steel stairs, railings and landings to your drawings, with in-house shop drawings and CWB certified shop welding, and deliver across the GTA and Ontario. Send us your floor heights and opening size, or your architectural drawings, and we'll work the layout into a quote. Request a quote or see our fabrication services.