The Tack Box · Stairs

Stair stringer calculator for steel stairs

Put in the total rise and get the risers, treads, stringer length and angle, with a riser cut list you can read off a tape. Every rule is checked against the 2024 IRC or IBC with its section number. Built for shops that build steel stairs and for students learning layout.

Updated November 2026

Quick answer

A 9 foot rise (108") takes 14 risers (6 at 7-3/4", 8 at 7-11/16") and 13 treads per the 2024 IRC, which caps a riser at 7-3/4". At the 10" minimum tread that is 10'-10" of run, a 14'-8-13/16" stringer and a 37.6° stair. Under the IBC the same rise takes 16 risers at 6-3/4" and 15 treads at 11".

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How the stair math works

Count risers first. Divide the total rise by the code's max riser and round up, and every riser comes out at or under the limit. A straight flight has one fewer tread than risers, because the top step is the upper floor.

risers = ⌈total rise ÷ max riser⌉
riser height = total rise ÷ risers
treads = risers − 1
total run = treads × tread
stringer = risers × √(riser² + tread²)
angle = atan(riser ÷ tread)

Worked example: a 9 foot rise under the IRC

  1. Risers: 108 ÷ 7.75 = 13.94, rounded up to 14.
  2. Riser height: 108 ÷ 14 = 7.714", about 7-11/16". On the tape that is 6 at 7-3/4" and 8 at 7-11/16".
  3. Treads: 14 − 1 = 13, each 10", the IRC minimum (R318.7.5.2).
  4. Total run: 13 × 10 = 130", or 10'-10".
  5. Stringer: 14 × √(7.714² + 10²) = 14 × 12.630 = 176.82", or 14'-8-13/16".
  6. Angle: atan(7.714 ÷ 10) = 37.6°.

Why the cut list splits the risers: rounding every riser to the nearest sixteenth stacks up over a flight, and the last riser can end up more than the 3/8" the code allows between the tallest and shortest. The calculator rounds the total rise once and spreads the sixteenths, so no two risers differ by more than one sixteenth and they add back to the total.

Open risers, the usual plate or grating stair, have their own rule. The IRC lets an open riser pass up to a 4" sphere once the walking surface is more than 30" above the floor or grade below (R318.7.5.1). A full 7-3/4" riser doesn't meet that, so most open steel stairs get a riser bar. The IBC wants solid risers (1011.5.5.3) except on stairs not required to meet 1009.3, and in I-3 and in F, H and S areas not open to the public. With solid risers on a tread under 11", the IRC wants a 3/4" to 1-1/4" nosing (R318.7.5.3).

If the open side drops more than 30", it needs a guard. The railing picket spacing calculator lays out the pickets for the stair side and weighs the steel, and the welding quote calculator puts the whole stair on one page for the customer.

Stair code: IRC vs IBC (2024)

The IRC covers one- and two-family houses and townhouses. The IBC covers commercial, industrial and multifamily common areas. These are the model codes, with section numbers from the 2024 editions.

  • Max riser height
    IRC 7-3/4" · R318.7.5.1
    IBC 7" · 1011.5.2
  • Min riser height
    IRC None set
    IBC 4" · 1011.5.2
  • Min tread depth
    IRC 10" · R318.7.5.2
    IBC 11" · 1011.5.2
  • Largest minus smallest riser or tread
    IRC 3/8" · R318.7.5.1, R318.7.5.2
    IBC 3/8" · 1011.5.4
  • Min headroom
    IRC 6'-8" · R318.7.2
    IBC 6'-8" · 1011.3
  • Max rise of one flight
    IRC 12'-7" · R318.7.3
    IBC 12'-0" · 1011.8
  • Nosing projection
    IRC 3/4" to 1-1/4", none needed at 11"+ tread · R318.7.5.3
    IBC 1-1/4" max · 1011.5.5, 1011.5.5.1
  • Open risers
    IRC 4" sphere where over 30" up · R318.7.5.1
    IBC Solid required, with exceptions · 1011.5.5.3
  • Handrail required
    IRC 4 or more risers, one side · R318.7.8
    IBC Every flight, both sides · 1011.11
  • Handrail height
    IRC 34" to 38" · R320.2
    IBC 34" to 38" · 1014.2
The fine print on these rules
  • IRC 2024 R318.7.5.1: Measured between the leading edges of adjacent treads.
  • IRC 2024 R318.7.5.2: Measured horizontally between the nosings of adjacent treads.
  • IRC 2024 R318.7.5.1, R318.7.5.2: Largest riser (or tread) in a flight minus the smallest.
  • IRC 2024 R318.7.2: 6'-8", measured plumb from the sloped line through the nosings.
  • IRC 2024 R318.7.3: 12'-7" between floor levels or landings.
  • IRC 2024 R320.2: Measured plumb from the sloped plane through the nosings.
  • IRC 2024 R318.7.8: At least one side of each flight with four or more risers.
  • IRC 2024 R318.7.5.1: Openings in open risers must not let a 4" sphere through where the walking surface is more than 30" above the floor or grade below.
  • IBC 2024 1011.5.2: Inside R-3 and R-2 dwelling units the IBC allows 7-3/4" (1011.5.2, exception for dwelling units); use IRC for those.
  • IBC 2024 1011.5.2: Inside R-3 and R-2 dwelling units the IBC allows 10" (1011.5.2, exception for dwelling units).
  • IBC 2024 1011.5.4: Largest riser (or tread) in a flight minus the smallest.
  • IBC 2024 1011.3: Measured plumb from the line through the nosings.
  • IBC 2024 1011.8: 12' between floor levels or landings.
  • IBC 2024 1014.2: Measured from the line through the nosings; uniform.
  • IBC 2024 1011.11: Handrails on each side of every flight.
  • IBC 2024 1011.5.5.3: Risers must be solid, unless one of the exceptions below applies.
  • IBC 2024 1011.5.5.3, exception for stairs not required to meet 1009.3: Open risers are allowed on a stair that doesn't have to meet 1009.3 (accessible means of egress), if the opening stops a 4" sphere.
  • IBC 2024 1011.5.5.3, exception for I-3 and for F, H and S areas not open to the public: Open risers are allowed in Group I-3, and in Group F, H and S areas the public can't get to, with no limit on the opening.
  • IRC 2024 R318.7.5.3: Solid risers need a 3/4" to 1-1/4" nosing unless the tread is 11" or deeper. Edge radius no more than 9/16".

Questions welders keep asking about stairs

How many stairs for a 9 foot rise?

Count risers, not treads. The 2024 IRC caps a riser at 7-3/4" (R318.7.5.1), so a 9 foot rise (108") takes 108 ÷ 7.75 = 13.94, rounded up to 14 risers of 7.714". On the tape that is 6 at 7-3/4" and 8 at 7-11/16". That is 13 treads, because the top step is the upper floor. Under the IBC the max riser is 7", so the same rise takes 16 risers at 6-3/4" and 15 treads.

What is the maximum riser height for residential stairs?

7-3/4" under the 2024 IRC (R318.7.5.1), measured between the leading edges of the treads. Treads have to be at least 10" (R318.7.5.2), and the tallest riser in a flight can't be more than 3/8" taller than the shortest, same for treads. On an open-riser stair more than 30" up, the opening has to stop a 4" sphere (R318.7.5.1), so a bare 7-3/4" open riser fails. The calculator starts with a riser bar leaving 3-1/2", which passes. Commercial stairs under the IBC are 7" max and 4" min, with treads at least 11" (1011.5.2).

IRC or IBC: which stair code do I use?

The IRC covers one- and two-family houses and townhouses. The IBC covers the rest: commercial, industrial and multifamily common areas. The IBC is stricter: risers 7" max against 7-3/4", treads 11" min against 10", guards 42" high against 36", handrails on both sides of every flight instead of one side once a flight has 4 risers, and solid risers unless an exception applies (1011.5.5.3). Inside R-3 and R-2 dwelling units the IBC allows 7-3/4" (1011.5.2, exception for dwelling units); use IRC for those. The building department has the final say on which one applies.

How do you calculate stair stringer length?

Multiply the number of risers by one step along the pitch line, √(riser² + tread²). For the 9 foot IRC stair that is 14 × √(7.714² + 10²) = 14 × 12.630 = 176.82", or 14'-8-13/16". That is the nosing line from the lower floor to the edge of the upper floor. A channel or plate stringer is longer by whatever its depth and end cuts add, so lay it out on the steel before you cut.

What angle should a stair be?

The code sets the riser and the tread, and the angle falls out of them. The 9 foot IRC stair at 7.714" risers and 10" treads comes out at 37.6°. The IBC version, with 6-3/4" risers and 11" treads, is 31.5°. A shorter riser or a deeper tread lays the stair down and takes more floor.

When does a stair need a handrail and a guard?

Under the IRC, a flight with 4 or more risers needs a handrail on at least one side (R318.7.8), 34" to 38" high from the nosing line (R320.2). The IBC wants handrails on both sides of every flight (1011.11), at the same height (1014.2). A guard goes on any open side that drops more than 30" (R321.1.1, 1015.2): at least 34" high on an IRC stair and 42" under the IBC.

How much headroom does a stair need?

6'-8" under both codes (R318.7.2, 1011.3), measured plumb from the sloped line through the nosings up to the lowest thing overhead. Check headroom in the calculator to test yours.

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This calculator lays out the stair. Bead Board is for the job around it. Your steel prices stay saved, so the quote for the stringers, treads and rail is a few taps, and the hours go on the job as you build it.

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