Staircase Calculator

Riser height, tread depth, stringer length and stair angle for a straight residential staircase — with IRC 2021 §R311.7 code compliance check.

Stair geometry

ft
Finished floor to finished floor (vertical).
Standard is more common for residential.
Leave blank to auto-pick the IRC-optimal count.
in
Min 10″ (IRC). Blank = comfort rule (2R + T ≈ 25″).
in
Min 36″ (IRC) clear of handrails.
in
Affects first-riser cut on stringer layout.

Calculation results

Number of risers

—

Riser height

— in

Number of treads

—

Tread depth

— in

Total run

— ft

Stringer length

— ft

Stair angle

— °

2×12 stringers needed

—

Stringer length is the structural hypotenuse from upper landing nose to bottom of bottom riser. Add nosing length and a notch allowance separately when cutting stock.

Informational only. Local code may differ from IRC 2021. For deck stairs, exterior stairs and any commercial/IBC project, verify limits with your AHJ. Handrails are required for any stair with four or more risers.

Understanding the formula

A staircase is a stack of right triangles laid in series. Given a total vertical rise R, the calculator picks the smallest number of risers n such that R / n ≤ 7¾″ (the IRC limit), then derives every other dimension from that choice.

risers = ⌈ total_rise / 7.75 ⌉  ·  riser_height = total_rise / risers
tread_depth = max(10, 17.5 − riser_height)  ·  comfort rule: 2R + T ≈ 25
stringer = √(rise² + run²)  ·  angle = atan(rise / run) × 180/π

Standard vs flush mount

Standard mount: the upper floor itself counts as the top step, so the number of treads is risers − 1. This is the residential default. Flush mount: the last tread is installed at the level of the upper floor, so treads = risers. Flush mount is common when an upper landing or deck surface meets the stair.

Worked example

Total rise of 108 inches (9 ft), standard mount:

  • Risers = ⌈ 108 / 7.75 ⌉ = ⌈ 13.94 ⌉ = 14 risers
  • Riser height = 108 / 14 = 7.71″ (under 7.75″ max — IRC OK)
  • Treads = 14 − 1 = 13 treads (standard mount)
  • Tread depth = max(10, 17.5 − 7.71) = max(10, 9.79) = 10.00″ (IRC minimum)
  • Total run = 13 × 10 = 130.0″ ≈ 10.83 ft
  • Stringer = √(101.29² + 130²) = 164.8″ ≈ 13.73 ft (using stringer height = total_rise − riser_height for standard mount)
  • Angle = atan(101.29 / 130) = 37.9° (comfort range 30 – 37°, at the upper edge)

IRC 2021 §R311.7 quick reference

ParameterIRC limitWhy
Max riser height7¾″ (197 mm)Trip hazard above this
Min tread depth10″ (254 mm)Adult foot length
Min stair width36″ (914 mm)Egress + furniture moves
Min headroom6′-8″ (2,032 mm)Clear walking height
Max riser variation⅜″ (9.5 mm)Uniform tread rhythm prevents falls
Nosing projection¾″ – 1¼″If solid risers; not required with open risers
Handrail height34 – 38″Required when 4 + risers

Common mistakes & tips

  • Measure rise from finished floor to finished floor, not subfloor to subfloor. Flooring thickness changes the total rise and can push a borderline staircase out of compliance.
  • The first and last riser must match. Account for the tread thickness — the bottom riser is cut shorter by one tread thickness so the first step matches the rest.
  • Three stringers minimum. Use 3 stringers up to a 36″ width; 4 stringers from 37″ to 48″. Spacing centre-to-centre should not exceed 16″ under standard 2× tread stock.
  • Notch with care. After the riser/tread cuts are made on a 2×12 stringer, the remaining solid section (throat) must be at least 5″ for residential. Less than that and the stringer needs a sister or LVL upgrade.
  • This calculator covers straight stairs only. Winders, L-shaped, U-shaped and spirals follow the same rise/tread limits but need landings and tread-depth measurements at the walk line — compute each flight separately.

Frequently asked questions

What is the maximum riser height per IRC 2021?
IRC §R311.7.5.1 sets the maximum residential riser height at 7-3/4 inches (197 mm). Going over this is a code violation and a trip hazard. Commercial stairs under IBC §1011.5 are stricter at 7 inches.
How many stairs do I need for an 8-foot ceiling?
A typical 8-foot ceiling has roughly 105-108 inches of total rise (ceiling + joist + flooring). At IRC max 7-3/4″ riser, that needs 14 risers (13 treads with standard mount).
What is the comfort rule for stairs?
The Blondel rule: 2 × riser + tread ≈ 24-25 inches. A 7″ riser pairs comfortably with a 10-11″ tread (2×7+11 = 25). The calculator uses tread = max(10, 17.5 − riser) which approximates this rule while respecting IRC 10″ minimum.
What angle should stairs be?
The IRC effectively limits residential stairs to about 28° – 42°, but the comfort range is 30 – 37°. Below 28° the stair feels like a ramp (too long); above 42° it feels like a ladder.
Standard mount or flush mount — which one do I need?
For residential stairs going up to a finished floor, use standard mount (top floor IS the top step). Flush mount applies when a landing or deck surface meets the stair, and the last tread lands at the upper level instead of one below.
How long should my stringer be?
Stringer length is the hypotenuse: √(rise² + run²). For a 9-ft rise with a 6:12 stair this works out to about 13-14 feet. Buy 2×12 stock at the next standard length above your stringer length plus 12-18″ for end cuts and overhang.
Do I need a handrail?
Yes, on any stair with 4 or more risers (IRC §R311.7.8). Handrail height must be 34 – 38″ measured from the nosing line. At least one continuous handrail per stair flight, on either side.
Can I have stairs without a riser board?
Yes — these are called open-riser stairs. IRC allows them but requires that the opening between treads not pass a 4″ sphere (so toddlers cannot fall through). Open risers are popular for modern designs and reduce material.