Stair Calculator
Enter your floor-to-floor height. Get rise and run dimensions, riser and tread counts, and stringer length instantly — whether you're a DIY stair builder or a working contractor.
Also flags basic IRC code checks (max rise, min run, 2R + R comfort) — verify anything critical with your local building department. Sometimes called a "stairs calculator" or "rise run calculator."
Quick Answer
A stair rise and run calculator (also written "rise run") starts with the total floor-to-floor height. For a standard 9-foot rise (108 inches), the average stair has 15 risers at 7.2 inches each — comfortably within the IRC maximum of 7¾ inches per riser per AWC DCA-6 stair geometry, which restates AWC DCA-6 §3 (restates IRC §R311.7.5). The U.S. residential code limit: 7¾" max rise and 10" min run. Always confirm specific dimensions with your local building department before construction. Enter your stair measurements (total rise, target tread depth) into our stair calculator to get calculated treads and risers count, tread depth, stair stringer length, and a dimensional check against IRC published minimums in seconds. Check current price at Amazon.
What this calculator checks vs. what you must verify locally
Explicit AWC DCA-6 §3 (restates IRC §R311.7) coverage matrix — confirm any unchecked item with your local building department before cutting stringers.
What we check (per AWC DCA-6 §3 (restates IRC §R311.7)):
- Max riser height ≤ 7¾ in (AWC DCA-6 §3 (restates IRC §R311.7.5.1))
- Min tread depth ≥ 10 in (AWC DCA-6 §3 (restates IRC §R311.7.5.2))
- Riser uniformity within ⅜ in across a flight (AWC DCA-6 §3 (restates IRC §R311.7.5.1))
- Total run + total rise math
- 2R + T comfort formula (rule-of-thumb, not code)
What this calculator does NOT check (verify with your local building department):
- Handrail required when ≥ 4 risers (AWC DCA-6 §3 (restates IRC §R311.7.8)) — height, continuity, graspability profile
- Guard required for stairs ≥ 30 in above grade (AWC DCA-6 §3 (restates IRC §R312.1.2))
- Landings at top and bottom; intermediate landing if flight > 12 ft 7 in (AWC DCA-6 §3 (restates IRC §R311.7.6))
- Nosing profile (AWC DCA-6 §3 (restates IRC §R311.7.5.3)) — 0.75–1.25 in projection if riser is ≥ 30 in
- Stair lighting (AWC DCA-6 §3 (restates IRC §R303.7)) — switched at top and bottom
- Winders / spiral / curved stairs (AWC DCA-6 §3 (restates IRC §R311.7.10)) — different geometry rules
- Local IRC amendments; commercial occupancy use (IBC instead of IRC)
Side-Elevation — Stair Rise and Run
- Riser height
- — vertical height of one step
- Stringer
- — diagonal structural support
- Tread depth
- — horizontal depth of one tread
- Tread
- — walking surface
- Nosing
- — overhang past riser below
For quick planning and sanity checks — always verify with your local building code before cutting stringers.
Schematic — not to scale. For quick planning and sanity checks — always verify with your local building code before cutting stringers.
Estimate your Stairs
Start from a preset:
Click any preset to fill the form and recalculate. Each field keeps its own unit — change any row's unit independently.
Your Estimated Stairs
Output units & rounding assumptions
- Linear dimensions (riser height, tread depth, stringer length, plumb/seat cuts) are shown in decimal inches primary, with feet-inches for stringer / total run and centimetres in the muted second line.
- Riser count is rounded to the nearest whole integer (you can't cut half a riser); actual riser height is then back-derived (total rise ÷ riser count) and shown to 2 decimal places. The displayed result is what to cut on every riser in the flight.
- Stringer length is computed exact via the Pythagorean formula and shown rounded to the nearest 0.1″; round up to the next stocked lumber length (12, 14, or 16 ft 2×12) when ordering — the calculator never rounds down.
- Total rise input assumes you measured finished floor to finished floor. If you measured subfloor to subfloor, add finished-floor thickness (~½″ for tile, ~¾″ for hardwood, ~¾″ for carpet+pad) per AWC DCA-6 §3 (restating IRC R311.7.5).
- Stair angle is reported in degrees to 1 decimal place via
atan(rise ÷ run); not used for any IRC check.
- Number of risers
- 15
- Number of treads
- 14
- Riser height
- 7.2" 18.3 cm
- Total run
- 12' 10" 391.2 cm
- Stringer length
- 15' 4-1/16" 467.5 cm
⚠ Exceeds typical 12-14 ft 2x12 retail stock. Verify your supplier carries 16 ft 2x12s OR plan to splice with a connector plate per AWC DCA-6 §3 (restates IRC §R311.7).
- 2×Riser height + Tread depth
- 25.4"
- Stringer height
- 8' 4-13/16" 256 cm
- Stair angle
- 33.21°
- Stringer plumb cut
- 5.95" 15.1 cm
- Stringer seat cut
- 11" 27.9 cm
- Tread thickness
- 1.25" 3.2 cm
- Upper floor thickness
- 10" 25.4 cm
- Min floor opening (IRC 80" headroom)
- 10' 8-5/16" 326 cm
Alternate configurations
For your inputs, these tread counts meet the rise/run dimensional minimums this calculator checks. The highlighted pick sits closest to the 2R+T ergonomic target (~25"). Click a neighbour to try it.
The IRC checks shown here cover dimensional rise/run minimums only. They don't certify the full design — local amendments, structural detailing, and install quality also determine code compliance. Confirm with your local building department before construction.
Show configurations that meet rise/run dimensional minimums
| Treads | Riser height | Tread depth | 2R+T | IRC check |
|---|
Dimensional Check Results
This compares your dimensional inputs against IRC 2021 rise/run minimums only. It does not certify the full design — local amendments, structural detailing, install quality, and many other IRC provisions also determine code compliance. It is NOT a code-compliance certificate, NOT a building permit application, and NOT a substitute for review by a licensed professional. Confirm with your local building department before construction.
Code checks on this page
✓ This calculator checks
- Max riser height ≤ 7¾″ [calculated] — AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗
- Min tread depth ≥ 10″ [calculated] — AWC DCA-6 §3 (restates IRC §R311.7.5.2) ↗
- Riser uniformity within ⅜″ [calculated — enforced by design: every riser equal] — AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗
- Nosing projection ¾″–1¼″ [guidance only — calculator does not check actual nosing geometry] — AWC DCA-6 §3 (restates IRC §R311.7.5.3) ↗
- 2R + T comfort range (24–25″) [calculated — ergonomic rule, not IRC]
✗ NOT checked here — verify separately
- Headroom ≥ 6′8″ above every tread — AWC DCA-6 §3 (restates IRC §R311.7.2) ↗. The calculator does not know your stairwell ceiling height, so it cannot compute headroom; measure plumb from each tread nosing to the lowest overhead obstruction.
- Stair width ≥ 36″ clear between walls or handrails — AWC DCA-6 §3 (restates IRC §R311.7.1) ↗. Width is not an input.
- Landings + intermediate platforms — AWC DCA-6 §3 (restates IRC §R311.7.6) ↗. Calculator handles a single straight flight only; required intermediate landing if vertical rise > 12′7″.
- Handrail 34–38″ height + 1¼–2″ graspable profile + continuity — AWC DCA-6 §3 (restates IRC §R311.7.8) ↗.
- Guardrail height ≥ 36″ + baluster spacing < 4″ sphere — AWC DCA-6 §3 (restates IRC §R312) ↗.
- Winders, spiral, curved, or alternating-tread stairs — AWC DCA-6 §3 (restates IRC §R311.7.10) ↗ uses different geometry rules; this calculator handles straight runs only.
- Stair lighting switched at top and bottom — AWC DCA-6 §3 (restates IRC §R303.7) ↗.
- Structural framing adequacy + stringer notch depth (minimum 5½″ throat per AWC DCA-6 Fig. 28) + connection hardware.
- Commercial occupancy — IBC applies instead of IRC; rise/run limits and width minimums differ. Use commercial calculator and IBC §1011.
- Local code amendments + jurisdictional overrides (CA Title 24, NYC, state amendments).
Rise/run dimensional checks: 3 of 3 items passed
What was checked · 3 IRC provisions
- Rise within IRC maximum — actual 7.2", standard ≤ 7.75" IRC §R311.7.5.1 ↗
- Rise above IRC minimum — actual 7.2", standard ≥ 4" IRC §R311.7.5.1 ↗
- Run meets IRC minimum — actual 11", standard ≥ 10" IRC §R311.7.5.2 ↗
Not checked by this calculator · 8 other IRC provisions
This calculator verifies dimensional rise/run only. The following IRC requirements must be verified separately with your local building authority:
- Stair width (≥ 36") · IRC §R311.7.1
- Headroom clearance (≥ 6'8") · IRC §R311.7.2
- Handrail height (34–38") and graspability · IRC §R311.7.8
- Rise variation within a flight (≤ 3/8") · IRC §R311.7.5.1
- Nosing projection (3/4"–1 1/4") · IRC §R311.7.5.3
- Landing required every 12' of rise · IRC §R311.7.6
- Guardrail + baluster spacing · IRC §R312
- Local jurisdiction amendments to IRC · IRC §(varies)
Based on International Residential Code (IRC) 2021. Local jurisdictions may adopt different editions or add amendments — always confirm with your local building department before construction.
Build notes — first-step cut adjustment
- 1st step cut depth (bottom stringer)
- 5.95" 15.1 cm
- 1st step walking surface (with tread)
- 7.2" 18.3 cm
Cut the bottom stringer shorter than the others by exactly the tread thickness (1.25"). When you lay the bottom tread on top of that cut, the finished first step matches every other step — no tripping hazard. (Standard mount only; for flush-mount this adjustment is not needed.)
Need a reference? See common rise heights →
📋 Your Build List
78 estimated items — verify before purchasing. Quantities update as you change inputs above.
Affiliate disclosure: CraftedCalcs earns commission on purchases made through the Home Depot and Amazon links below. The commission doesn't change your price. It helps us keep this site free.
- 3 Pressure-treated 2×12 stringer 16' PT lumber Home Depot Amazon
- 14 Oak stair tread 11" × 42" Home Depot Amazon
- 14 1×8 riser board Primed pine, 42" cut-to-fit Home Depot Amazon
- 42 Simpson LSC stair connector Galvanized steel, pre-bent Home Depot Amazon
- 1 Box of 3" structural screws ~100 count per box Home Depot Amazon
Click each item to see its current price at Home Depot. Quantities assume a single flight with the dimensions shown above; adjust if your project has landings, turns, or exposed sides.
What Else You'll Need
Calculator output covers the headline material. This list is the full bill — the fasteners, brackets, sealants, and safety hardware beginners typically forget to buy on the first trip.
Estimate only — not a professional bill of materials. It is NOT professional engineering, architectural, or contracting advice; NOT a code-compliance certificate; NOT a building permit application; and NOT a substitute for review by a licensed professional. Verify every quantity against your actual cut list, site conditions, and local building authority before purchasing. See our full disclaimer for details.
Structural
- Qty: 2 stringers for widths ≤ 36"; 3 for wider · 2×12 pressure-treated (exterior) or straight-grain 2×12 (interior). Order length = stringer length × 1.05 to allow waste. AWC DCA-6 Fig. 28 requires 5.5 in minimum throat after notch cuts.
- Qty: 1 per stringer · Simpson LSC or equivalent joist hanger — secures stringer to top header per AWC DCA-6 §3 stair connection prescriptive guidance.
- Qty: 14 treads (example run) · 5/4 deck boards OR solid 1"–1¼" hardwood (oak, maple) for interior. Min 10 in tread depth per AWC DCA-6 §3 stair geometry.
- Qty: 15 risers (example run) · ½" or ⅝" paint-grade for closed-riser stairs. Skip for open stairs. Max 7-3/4 in riser height per AWC DCA-6 §3 stair geometry.
Fasteners
- Qty: ~4 per tread per stringer · 2½" or 3" deck screws (exterior) or #10×2½" wood screws (interior). Pre-drill to prevent splits.
- Qty: ~6 per riser · Finish nails or 2" trim-head screws. Only if using risers.
- Qty: 1 tube per 4–5 treads · Liquid Nails or PL Premium on tread-to-stringer contact — prevents squeaks.
- Qty: Per bracket spec · 1½" Simpson SD screws for LSC brackets (galvanized for exterior).
Safety + Code
- Qty: Length of stringer × 1.1 · 1½"–2" round (IRC §R311.7.8 ↗ graspable, restated in AWC DCA-6 §3 handrail provisions). Continuous top-to-bottom for any flight of 4+ risers.
- Qty: Every ~48" of run + 1 at top + 1 at bottom · Rated 200 lb minimum. Metal or powder-coated. See AWC DCA-6 §3 handrail provisions for residential bracket spacing guidance.
- Required if stair is > 30" above grade (IRC §R312 ↗, restated in AWC DCA-6 §3 guard requirements). 36" residential height, balusters spaced < 4" apart.
- Adhesive strips or rubber inserts for exterior/high-traffic stairs.
Finish
- Exterior: penetrating oil (Cabot, Ready Seal). Interior: 2–3 coats oil-based poly.
- Paint-grade primer + 2 coats latex for closed-riser paint finish.
- If finishing over bare wood — order 10% more than tread count for stair carpet pattern match.
Affiliate disclosure: CraftedCalcs earns commission on purchases made through the Home Depot and Amazon links above. The commission doesn't change your price. It helps us keep this site free.
15 items across 4 categories. Quantities assume standard residential practice — adjust up for longer spans, complex geometry, or pro-grade specification.
The Math
# Worked example: 108" total rise, 7" target riser, 11" tread depth
# (the 9-ft floor preset shown above)
risers = round(total_rise ÷ target_rise) = round(108 ÷ 7) = 15
actual_rise = total_rise ÷ risers = 108 ÷ 15 = 7.20"
treads = risers − 1 = 15 − 1 = 14
total_run = treads × tread_depth = 14 × 11" = 154" = 12'10"
# 2R + T ergonomic check (rule-of-thumb, target 24–26"):
2R + T = 2 × actual_rise + tread_depth = 2(7.20) + 11 = 25.40" ✓
# Stringer geometry — standard mount (deck face = top tread):
stringer_span = total_rise − actual_rise = 108 − 7.20 = 100.80"
stringer_length = √(stringer_span² + total_run²)
= √(100.80² + 154²) = √(10,161 + 23,716) ≈ 184.1" = 15'4"
stair_angle = atan(actual_rise ÷ tread_depth) = atan(7.20 ÷ 11) ≈ 33.2°
# Stringer geometry — flush mount (stringer top flush with deck):
stringer_span = total_rise = 108"
stringer_length = √(total_rise² + total_run²)
= √(108² + 154²) = √(11,664 + 23,716) ≈ 188.1" = 15'8"
stair_angle = atan(total_rise ÷ total_run) = atan(108 ÷ 154) ≈ 35.0° Five derived numbers — riser count, actual rise per step, tread count, total run, and stringer length — fall out of two inputs (total rise + target rise) and one tread depth. The riser count rounds because you can't cut half a riser; the actual rise is back-derived so every step in the flight is identical (within the 3/8 in uniformity limit of IRC R311.7.5.1). The stringer is the diagonal support board and follows the Pythagorean theorem, but which triangle to solve depends on how the stringer attaches: in standard mount the deck face IS the top tread, so the stringer spans from the lower floor to the second-to-last tread (total_rise − one rise); in flush mount the stringer top sits level with the deck, so the triangle uses the full total rise. The 2R+T ergonomic rule has been used since Nicolas-François Blondel documented it in 1672 — it matches the natural human stride and lands in 24–26 in for the most comfortable rise/tread pairings (per AWC DCA-6 §3, restating IRC R311.7.5).
Source: AWC DCA-6 §3 (restating IRC R311.7.5) + standard residential carpentry practice
How This Calculator Estimates
Three numbers drive every staircase: total rise (how tall — from finished floor to finished floor), rise (vertical height of one step), and run (horizontal depth of one tread). Get these right, and everything else — number of steps, stringer length, landing position — falls out of the math.
The calculator rounds the number of risers to the nearest whole number, then recalculates the actual rise per step so every step in the flight is equal. Per IRC 2021 R311.7.5.1, the tallest and shortest riser in a flight can differ by no more than 3/8 inch. A flight with uneven steps is a trip hazard and typically does not meet this IRC limit — confirm with your local building department, since jurisdictions may apply different editions or amendments.
Planning a stair with a landing between flights? See the stairs with landing calculator — covers AWC DCA-6 §3 (restates IRC §R311.7.6) ↗ landing dimensions, L-shape vs U-shape design, and a split-flight worked example.
Stair math — full worked example
The default 9-foot (108") example in the calculator above — 7" target riser, 11" treads — walks through every formula. Here is each step, so the math behind any staircase becomes clear:
- Riser count. Divide total rise by target riser height and round to the nearest whole number:
108 ÷ 7 = 15.43 → 15 risers. Fractional risers are impossible to build; rounding is always required. - Actual rise per step. Back-derive from the rounded count:
108 ÷ 15 = 7.2"per step. The target was 7", but 7.2" is what to cut — every riser in the flight must be this height so the variation stays within the ⅜" limit. - Tread count. Always one less than the riser count:
15 − 1 = 14 treads. The upper floor or deck surface acts as the final tread, so only 14 physical tread boards are needed. - Total run. How far the staircase projects horizontally:
14 × 11" = 154"(12 ft 10"). This is the floor footprint to plan around before framing the opening. - 2R+T ergonomic check.
2(7.2) + 11 = 25.4"— lands in the 24–26" comfort zone. Nicolas-François Blondel documented this proportion in 1672 as a match for the natural human stride when climbing. A result outside 24–26" often means stairs feel steep or overly shallow even when every IRC dimension passes. - Stringer length. Pythagorean theorem on the rise-run triangle:
√(108² + 154²) = √(11,664 + 23,716) = √35,380 ≈ 188.1"(15 ft 8"). Order a 16-foot 2×12 and trim to fit — a 14-footer does not reach. - Stair angle.
atan(7.2 ÷ 11) ≈ 33.2°. The typical residential range is 30–37°. Stairs steeper than 40° commonly fail residential inspection; shallower than 20° is impractical for most floor-to-floor heights.
Change the target riser in the calculator above to 6.5" or 7.75" and every downstream value — actual rise, total run, stringer length, ergonomic check — updates instantly.
How to choose your target riser height (6.5"–7.75")
Code lets you build anything from a 4" riser to 7¾" (per AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗), but the comfort band most carpenters target is 6.5"–7.5". The 2R+T rule is the reason: pair any rise in that band with a 10–11" tread and the sum lands in the 24–26" ergonomic range that matches a natural walking gait. Use this table to pick a target before you enter inputs above:
| Target rise | Pairs with tread | 2R + T | Best for |
|---|---|---|---|
| 6.5" | 11" | 24.0 | Aging-in-place; shallow walk feel; longer total run (needs more horizontal footprint) |
| 7.0" | 11" | 25.0 | The classic "7-11" — best general-purpose interior stair; matches the typical residential gait |
| 7.5" | 10" | 25.0 | Compact stair where horizontal run is constrained; still inside the 24–26 comfort band |
| 7.75" | 10" | 25.5 | Code maximum — short rise = steepest acceptable stair; common for tight basement or deck stairs |
Rule of thumb: if you have the horizontal run, target 7" for comfort. If your floor plan is tight, step up toward 7.5–7.75" — never above 7¾" per AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗ (restated in AWC DCA-6 §3 stair geometry). For exterior deck stairs the 7" target is also customary because outdoor stairs are descended in the dark, in rain, and often by users carrying loads — the shallower step gives more recovery room. Always confirm with your local building department before committing.
IRC 2021 dimensional requirements — quick reference
The International Residential Code (IRC) 2021 sets the dimensional minimums for residential stairs. This table is a static reference; the Dimensional Check Results panel in the calculator above shows pass/fail for your specific rise and run against the rise/run provisions.
| Requirement | IRC 2021 section | Value |
|---|---|---|
| Maximum riser height | AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗ | 7¾" |
| Minimum riser height | AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗ | 4" |
| Riser-height uniformity (max variation) | AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗ | ⅜" within one flight |
| Minimum tread depth | AWC DCA-6 §3 (restates IRC §R311.7.5.2) ↗ | 10" |
| Nosing projection (closed-riser stairs) | AWC DCA-6 §3 (restates IRC §R311.7.5.3) ↗ | ¾" – 1¼" |
| Minimum headroom | AWC DCA-6 §3 (restates IRC §R311.7.2) ↗ | 6 ft 8 in |
| Minimum stair width | AWC DCA-6 §3 (restates IRC §R311.7.1) ↗ | 36" |
| Handrail — when required | AWC DCA-6 §3 (restates IRC §R311.7.8) ↗ | ≥ 4 risers; height 34–38" above nosing |
| Guardrail — when required | AWC DCA-6 §3 (restates IRC §R312) ↗ | ≥ 30" drop; ≥ 36" height; < 4" baluster spacing |
What this calculator checks: riser height (max and min per AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗), riser-height uniformity (⅜" rule), tread depth (AWC DCA-6 §3 (restates IRC §R311.7.5.2) ↗), and the 2R+T ergonomic ratio. The Dimensional Check Results panel shows each item individually.
What this calculator does not check: headroom clearance (AWC DCA-6 §3 (restates IRC §R311.7.2) ↗), stair width (AWC DCA-6 §3 (restates IRC §R311.7.1) ↗), nosing dimensions, handrail graspability, guardrail baluster spacing, structural framing adequacy, or local code amendments. Verify those provisions separately with your local building authority and a licensed professional before construction.
IRC 2021 is the model code. Local jurisdictions may adopt different editions (IRC 2018, IRC 2015) or apply overlays such as California Title 24, the NYC Building Code, or state-specific amendments. Always confirm the edition in force in your jurisdiction with your local building department.
What does AWC DCA-6 §3 (restating IRC R311.7.5.1) say about riser height?
AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗ sets three requirements for riser height in residential stairs:
- Maximum riser height: 7-3/4 inches (196 mm). Each individual riser in a flight must not exceed 7-3/4 inches, measured vertically between the leading edges (nosings) of two consecutive treads. This is the most-cited IRC stair dimension — often phrased as "maximum riser height 7-3/4 inches" in permit drawings and inspection reports.
- Maximum variation within a flight: 3/8 inch (9.5 mm). The tallest riser and the shortest riser within the same flight cannot differ by more than 3/8 inch. Non-uniform risers are a documented trip hazard and a common inspection point. This calculator enforces equal risers by design — dividing total rise by the number of risers to produce uniform actual riser height.
- Riser geometry: essentially vertical. Risers must be essentially vertical, or may slope inward from the underside of the nosing according to the code's geometry limits (see IRC Figure R311.7.5.1).
Quick check: This calculator flags your actual riser height (total rise ÷ number of risers) against the 7-3/4" maximum in the Dimensional Check Results panel. Enter your total rise above to see whether your stair meets AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗.
Source: AWC DCA-6 §3 — Stair Geometry (restating IRC R311.7.5.1) ↗. Local jurisdictions may apply different IRC editions or amendments — always confirm with your local building department.
What does AWC DCA-6 §3 (restating IRC R311.7.5.2) say about tread depth?
AWC DCA-6 §3 (restates IRC §R311.7.5.2) ↗ sets three requirements for tread depth (called "run" informally in trade usage, but "tread depth" in the IRC):
- Minimum tread depth: 10 inches (254 mm). Each tread must have a minimum depth of 10 inches, measured horizontally between the vertical planes formed by the nosings of two adjacent treads, perpendicular to the leading edge. In practice, 11 inches is a widely used residential tread depth — it pairs with a 7-inch riser height in the "7-11 rule" for comfortable walking.
- Maximum tread variation within a flight: 3/8 inch (9.5 mm). The deepest tread and the shallowest tread within one flight cannot differ by more than 3/8 inch, matching the riser-uniformity rule in AWC DCA-6 §3 (restates IRC §R311.7.5.1) ↗.
- Nosing exception at 11 inches or more. Where a tread is at least 11 inches deep, a projecting nosing is not required by the IRC. Open-riser stairs may omit nosings entirely when the opening between treads will not permit passage of a 4-inch sphere — see AWC DCA-6 §3 (restates IRC §R311.7.5.3) ↗.
Source: AWC DCA-6 §3 — Stair Geometry (restating IRC R311.7.5.2) ↗. Local jurisdictions may apply different IRC editions or amendments — always confirm with your local building department.
What does AWC DCA-6 §3 (restating IRC R311.7.5.3) say about nosing projection?
AWC DCA-6 §3 (restates IRC §R311.7.5.3) ↗ governs the projection, uniformity, and geometry of stair nosings — the horizontal overhang of the tread beyond the face of the riser below it:
- Nosing projection: 3/4 inch to 1-1/4 inches (19–32 mm). On closed-riser stairs with treads shallower than 11 inches, the nosing must project not less than 3/4 inch and not more than 1-1/4 inches beyond the riser below. This range gives your foot a clear landing edge — enough overhang to be useful, not so much that it becomes a toe-catch hazard.
- Nosing uniformity: within 3/8 inch across a flight. The largest and smallest nosing projections within a single flight must not differ by more than 3/8 inch. Inconsistent nosing depths disrupt the visual rhythm of the stair and can cause missteps, especially on descent.
- Beveled leading edge permitted. The IRC also sets limits on bevel angle and leading-edge radius (see IRC R311.7.5.3, restated in AWC DCA-6 §3 stair geometry); confirm the current limits with your local building department for the edition adopted in your jurisdiction.
Source: AWC DCA-6 §3 — Stair Geometry (restating IRC R311.7.5.3) ↗. Local jurisdictions may apply different IRC editions or amendments — always confirm with your local building department.
AWC DCA-6 §3 (restating IRC R311.7.5) Quick Reference card
Single-glance summary of the three IRC 2021 provisions this page covers. Use this card when drafting permit drawings or reviewing an inspector's punchlist.
IRC 2021 R311.7.5 — Stair Dimensions at a Glance
R311.7.5.1 — Riser Height
Max: 7-3/4 in (196 mm)
Uniformity within one flight: ≤ 3/8 in variation
R311.7.5.2 — Tread Depth
Min: 10 in (254 mm)
Nosing optional when tread ≥ 11 in
R311.7.5.3 — Nosing
3/4 in – 1-1/4 in (19–32 mm)
Applies to closed-riser stairs with treads < 11 in
Source: AWC DCA-6 §3 — Stair Geometry (restating IRC R311.7.5) ↗. Confirm the IRC edition adopted in your jurisdiction with your local building department — local amendments may differ.
Planning stairs between two floors with a landing? See the stairs with landing calculator — covers AWC DCA-6 §3 (restates IRC §R311.7.6) ↗ landing dimensions, L-shape vs U-shape layouts, and split-flight design.
Inputs explained
- Total rise: measure from the finished floor at the bottom to the finished floor at the top. Include carpet, tile, or hardwood thickness. Common residential values: 96 (8 ft), 108 (9 ft), 120 (10 ft).
- Rise: the per-step vertical. 7 inches is the residential comfort standard. Per IRC 2021 R311.7.5.1, the maximum is 7¾"; stairs designed right at that limit often feel steep. Local jurisdictions may apply different editions or amendments — confirm with your building department.
- Run: the per-step horizontal (a.k.a. tread depth in IRC language). Per IRC 2021 R311.7.5.2, the residential minimum is 10". 11" is common for residential; commercial and public stair codes often specify 12". Confirm the edition in force in your jurisdiction.
What the outputs mean
Stringer length is the diagonal — order your stringer lumber at this length plus a few inches for attachment. A standard 16-foot 2x12 covers most 9-foot residential stairs. 2×Riser height + Tread depth is the ergonomic check; if this number falls outside 24–26 inches, the stairs may feel awkward even when the dimensions stay within IRC minimums.
Choosing stringer lumber — size and treatment
The calculator gives you the stringer length; the table below guides the board size and treatment. Most residential stairs use 2×12 regardless of flight height — the deeper board leaves more material at the notch cuts (the "throat"), which is the structural weak point of a cut stringer. A 2×10 can work on very short flights (≤6 risers) in space-constrained interior applications, but the shallower board leaves less throat depth after notching and is uncommon in practice.
| Application | Board size | Min stringers | Treatment |
|---|---|---|---|
| Interior, stair width ≤ 36" | 2×12 | 2 | Kiln-dried (SPF or Douglas Fir) |
| Interior, stair width 36–48" | 2×12 | 3 | Kiln-dried (SPF or Douglas Fir) |
| Exterior / deck stair, above grade | 2×12 | 2–3 | Pressure-treated UC3B (above-ground) |
| Exterior, bottom cut at or near grade / concrete | 2×12 | — | Pressure-treated UC4A or higher |
Stringer count and treatment per standard residential carpentry practice and the AWPA Use Category system (UC3B = above-ground exposed; UC4A = ground contact). Stair width > 48" typically requires additional intermediate stringers. Structural adequacy depends on specific span, load, and notch depth — verify with your local building authority and a licensed contractor before cutting. See our full disclaimer.
Standard mount vs. flush mount — and why it changes the stringer math
Under the hood there are two physical ways a stringer attaches at the top, and the formulas differ between them. Toggle the mount type in Advanced mode if your build uses flush mount.
- Standard mount (default): the deck or upper-floor surface itself is the top tread. The stringer board spans from the lower floor up to the second-to-last tread and hangs beneath the upper-floor framing via a joist-hanger connector. Stringer board height = total rise − one rise. This is the common residential convention and matches how most carpenters cut a 2x12 against a framing square.
- Flush mount: the top of the stringer is cut level with the upper-floor surface; the first tread board then sits on top of the stringer at deck height. The stringer spans the full total rise. Flush mount adds one extra tread of horizontal footprint and is often chosen when ground-slope or appearance allows.
Our formulas branch automatically on the mount type you pick. The stringer length we report is the minimum length of 2x12 you need for the physical board itself — order a bit longer to allow for cuts and attachment flats. The stair angle we report is the actual slope of the stringer board, which in standard mount equals the per-step slope atan(rise ÷ run) and in flush mount is the overall diagonal atan(total rise ÷ total run).
Comparison — Standard vs. Flush-Mount Stringer
Formula convention follows standard residential carpentry practice and AWC DCA-6 §3 (restates IRC §R311.7.5) ↗. Pythagorean geometry traces to classical trigonometry; Blondel's 2R+T ergonomic rule dates to 1672.
Planning alongside other framing
Stairs are usually planned alongside the framing they connect to. For deck stairs, the same AWC DCA-6 §3 (restates IRC §R311.7) ↗ rise-and-run rules apply to the stringer cuts, and the upper landing typically attaches to a joist that needs to be sized per our deck joist calculator (AWC DCA-6 (restates IRC §R507.5) ↗ span tables). For interior or porch stairs that land on a concrete pad at the bottom, our concrete slab calculator sizes the landing pad — typical residential stair landings use a 4-inch slab at minimum the width of the stairs plus 12 inches per AWC DCA-6 §3 (restates IRC §R311.7.6) ↗ walking-surface guidance.
Related answer pages
For multi-flight stairs with intermediate landings, see Stairs with a landing calculator — covers the AWC DCA-6 §3 (restates IRC §R311.7.3) ↗ 12-foot flight cutoff, AWC DCA-6 §3 (restates IRC §R311.7.6) ↗ landing dimensional minimums, L-shape vs U-shape design tradeoffs, and a split-flight worked example using this calculator.
Common Mistakes
The seven errors that most often surface during inspection or produce awkward stairs.
Measuring finished vs subfloor
Uneven top or bottom riser
Forgetting the nosing
Ignoring proportion and scale
Overlooking light and visibility
Choosing style over practicality
Inadequate safety hardware
Standard Stair Rise and Run — Quick Reference Chart
Pre-calculated using the divide-by-7 method, rounded to the nearest whole riser. All values are ≤ 7¾" IRC maximum. Enter your specific height in the calculator above for estimated dimensions.
| Total Rise | Risers | Rise per Step | Treads |
|---|---|---|---|
| 84" (7 ft) | 12 | 7.00" | 11 |
| 96" (8 ft) | 14 | 6.86" | 13 |
| 102" | 15 | 6.80" | 14 |
| 108" (9 ft) | 15 | 7.20" | 14 |
| 114" | 16 | 7.13" | 15 |
| 120" (10 ft) | 17 | 7.06" | 16 |
| 132" (11 ft) | 19 | 6.95" | 18 |
| 144" (12 ft) | 21 | 6.86" | 20 |
All values use the divide-by-7 method, rounded to the nearest whole riser, ≤ 7¾" IRC maximum. ← Custom rise height? Use the calculator
Stair Terminology
14 terms — every one is a standard stair-code definition or a calculator input.
Riser height
IRC §R311.7.5.1 ↗ · Max 7¾" for residential; min 4".
Tread depth
IRC §R311.7.5.2 ↗ · Minimum 10" in residential construction.
Total Rise
IRC §R311.7.5.1 ↗ · IRC R311.7.5.1 limits riser-to-riser variation in any flight to 3/8" — accurate total-rise measurement is the foundation of meeting that limit.
Total Run
Tread
IRC §R311.7.5.2 ↗ · Tread depth and surface requirements are specified alongside run.
Nosing
IRC §R311.7.5.3 ↗ · Allowed projection: ¾" to 1 1/4".
Stringer
IRC §R311.7.5 ↗ · The IRC specifies tread + riser requirements that together govern stringer cut geometry.
Headroom
IRC §R311.7.2 ↗ · Minimum 6'8" (80") above the nosing line. A common point of inspection scrutiny.
Stair Width
IRC §R311.7.1 ↗ · Minimum 36" clear width for residential stairs.
Handrail
IRC §R311.7.8 ↗ · Height 34–38" above nosings; graspable diameter 1¼" to 2" (round) or equivalent.
Guardrail
IRC §R312 ↗ · Height 36" residential, 42" commercial. Baluster gaps < 4".
Landing
IRC §R311.7.6 ↗ · Minimum 36" in the direction of travel; matches the stair width otherwise.
Winder
IRC §R311.7.5.2.1 ↗ · Narrow end minimum 6"; at 12" from the narrow end, tread must be at least 10" deep.
Mount Type
AWC DCA-6 Fig. 28 ↗ · Affects step count and top-riser height — gets this wrong and your top step is uneven.
Frequently Asked Questions
How do I calculate how many stairs I need?
Divide your total rise (floor-to-floor height in inches) by the rise you want per step (typically 7 inches for comfortable stairs, within the 7-3/4 in max per AWC DCA-6 §3 stair geometry). Round to the nearest whole number. That's your number of risers. The number of treads is always one less than the number of risers, because the top floor acts as the final tread.
For a 108" (9 ft) total rise: 108 ÷ 7 = 15.4, rounded to 15 risers per the same AWC DCA-6 §3 riser limits. That gives you 14 treads and a comfortable 7.2" step — confirm with your local building department before construction.
What is the 7-11 rule for stairs?
The 7-11 rule sets stair proportions by pairing a 7-inch riser with an 11-inch tread (consistent with AWC DCA-6 §3 stair geometry). This ratio (also expressible as "2 × rise + run ≈ 25") produces a walking rhythm that matches the natural human gait — climbing feels steady rather than steep, and descending feels secure rather than cramped. A 7" rise with an 11" run gives 2(7) + 11 = 25, landing squarely in the ergonomic sweet spot of 24-26 inches — verify with your local building department for any flight with non-standard rise/run.
The rule is not in the IRC as a hard requirement, but it underlies why IRC §R311.7.5.2 ↗ mandates minimum 10" treads and IRC §R311.7.5.1 ↗ caps risers at 7¾" (restated in AWC DCA-6 §3 stair geometry). Stairs that deviate — say, 8" rise with 9" run (2(8)+9=25, same "math" but much steeper) — feel awkward despite the arithmetic. Keep rise at 7" and run at 11" whenever layout allows; it's why it became a rule.
What is the standard rise and run for stairs?
Per IRC 2021 (IRC §R311.7.5 ↗, restated in AWC DCA-6 §3 stair geometry): maximum rise is 7¾ inches, minimum is 4 inches. Minimum run (tread depth) is 10 inches. Local jurisdictions may apply different editions or amendments — confirm with your local building department. The ergonomic "rule of 25": 2 × rise + run should equal 24–25 inches for comfortable walking. A 7" rise with an 11" run gives 2(7) + 11 = 25 — the sweet spot (per the same AWC DCA-6 §3 dimensional minimums).
How do you calculate stair stringer length?
Use the Pythagorean theorem: stair stringer length = √(total rise² + total run²). For a 108" rise and 154" total run: √(108² + 154²) = √(11,664 + 23,716) = √35,380 ≈ 188.1 inches, or roughly 15 feet 8 inches (verify with your local building department for spans this long). Add a few inches for attachment at top and bottom — most carpenters round up and trim. Standard 2×12 lumber comes in 8-, 10-, 12-, 14-, 16-, and 20-foot lengths; for any stringer over 14 feet, plan to splice or order custom-cut lumber from a yard that stocks 16-foot 2×12 stock in your area (notch geometry per AWC DCA-6 Fig. 28).
What is the maximum rise allowed by code?
Per IRC 2021 IRC §R311.7.5.1 ↗ (restated in AWC DCA-6 §3), the maximum rise for residential stairs is 7¾ inches. Commercial stairs are typically limited to 7 inches max. Exceeding the max rise typically results in inspection failure under jurisdictions that adopt the IRC 2021 — local jurisdictions may apply different editions or amendments. Beyond the code question, an over-spec rise is a documented trip hazard. The IRC also limits rise variation between steps to 3/8 inch (the largest and smallest riser can differ by no more than that). Confirm requirements with your local building department before construction.
Do I need a handrail on stairs?
Per IRC 2021 IRC §R311.7.8 ↗ (restated in AWC DCA-6 §3 handrail provisions), a handrail is required on any stairway with four or more risers. Local jurisdictions may apply additional or different requirements — verify with your local building department. The handrail must be 34–38 inches above the nosing, be graspable (1¼–2 inches in diameter for round) per AWC DCA-6 §3 graspability dimensions, and run continuously from top to bottom. A guardrail (IRC §R312 ↗; 36" residential, 42" commercial) is required wherever the floor level is 30" or more above the surface below — confirm with your local building department for exact dimensions.
How much does a stair stringer weigh?
Stringer weight depends on lumber grade, species, and treatment chemistry — for a typical 2x12 pressure-treated pine stringer running about 16 feet (a 9-foot staircase, sized per AWC DCA-6 Fig. 28), expect a heavy lift requiring two people — verify the manufacturer's weight rating with your local lumber yard. Check the tag at the lumber yard for the specific weight rating, or weigh on-site if precision matters. Most residential stairs use 2 or 3 stringers — a middle stringer is typically added if treads span more than 36 inches per AWC DCA-6 Fig. 28 (16 in o.c. max stringer spacing). LVL (laminated veneer lumber) stringers are lighter and straighter but more expensive — verify with your local building department for any non-standard stringer material.
Can I DIY stair construction?
This calculator helps you plan the design. The build itself involves load-bearing structural decisions that depend on your local code, the specific framing context, and inspection requirements that vary by jurisdiction. For any structural, load-bearing, or code-critical work — and for commercial stairs, stairs with landings or turns, or curved/spiral stairs — consult a licensed contractor and your local building authority before construction. Rejection after construction is expensive; consult your local building inspector before starting if you have any doubt. CraftedCalcs is not a substitute for professional advice; see our disclaimer for the full scope of claims.
What is the ideal riser height for residential stairs?
The ideal riser height for residential stairs is between 7 and 7¾ inches. Most building codes set a maximum of 7¾ inches (IRC §R311.7.5.1 ↗, restated in AWC DCA-6 §3 stair geometry) and a minimum of 4 inches. The 7-inch target pairs naturally with an 11-inch tread — the "7-11 rule" — for stairs that meet dimensional minimums and feel comfortable. Confirm requirements with your local building authority before construction.
What is a good angle for stairs?
A comfortable stair angle is between 30 and 35 degrees. This range produces a walking rhythm matching the natural human gait — easy to climb and safe to descend. Stairs steeper than 40° typically fail residential code inspection. The standard 7" rise with 11" run gives approximately 32°.
How do I measure total rise for stairs?
Measure the vertical distance from the top of the finished floor at the bottom to the top of the finished floor at the top, in inches. If flooring is not yet installed, measure subfloor-to-subfloor and add your flooring thickness (typically ½–1 inch for hardwood or tile). Even a small error in total rise throws off every riser height in the staircase.
Can riser heights vary within the same staircase?
No — all risers in a single staircase must be uniform in height. IRC §R311.7.5.1 ↗ (restated in AWC DCA-6 §3 stair geometry) allows a maximum variation of only ⅜ inch between the tallest and shortest riser. Non-uniform risers are a documented trip hazard and a common point of inspection scrutiny. See our disclaimer for the full scope of safety-related claims.
How many stringers do I need for stairs?
Most residential stairs need two stringers (one on each side) for widths up to 36 inches. Add a third center stringer for widths between 36 and 48 inches per AWC DCA-6 Fig. 28 (16 in o.c. max stringer spacing). Stairs wider than 48 inches typically require additional stringers at regular intervals. Always check your local building code — commercial stairs often require more stringers than residential.
What is nosing on stairs?
Nosing is the horizontal overhang of the tread beyond the riser face below it. IRC §R311.7.5.3 ↗ (restated in AWC DCA-6 §3 stair geometry) requires nosing of ¾–1¼ inches for stairs with solid risers. Nosing improves safety by giving your foot a clear landing edge and reduces trip hazards. It must be uniform across all treads and slip-resistant.
How do I account for finished flooring thickness in rise calculations?
Measure your total rise from finished floor to finished floor — this automatically includes flooring thickness on both ends. If the top floor flooring is not yet installed, add its thickness to your subfloor measurement (carpet + pad ≈ ¾", hardwood ≈ ¾", tile ≈ ½"). The bottom riser is the one most commonly cut incorrectly when flooring thickness is ignored.
How is this stairs calculator different from a stair stringer calculator?
This stairs calculator focuses on rise and run geometry — it takes your floor-to-floor height and target tread depth, then outputs riser count, tread count, actual riser height, and stringer length. A stair stringer calculator goes one step further: it uses the stringer length from this tool plus your lumber size (2×12 is standard) to check notch geometry, throat depth (AWC DCA-6 Fig. 28 minimum 5.5 inches), and whether the board length is commercially available. For stringer-specific sizing and notch layout, use the stair stringer calculator after you finalize your rise and run here.
Troubleshooting Tips
Common install/post-install issues and how to fix them. Click any item to expand.
My inspector failed the stairs — the riser heights aren't consistent. What went wrong and can I fix it?
The stringer is cracked after only a few months — is that a structural problem?
The whole staircase feels wobbly or bounces when I walk on it — is that dangerous?
My stairs failed the handrail inspection — the rail is the wrong height or missing. What's required?
The stairs have no guardrail on the open side and there's a big drop — does that meet code?
My stairs squeak and creak badly — was this installed wrong?
There's a visible gap between my riser and the tread — is that a problem?
The top riser is shorter than all the others — my foot catches on it every time. What happened?
The stair treads feel slippery, especially in socks — is there a code requirement for grip?
My staircase doesn't have enough headroom — I keep hitting my head. What's the minimum?
There's a small gap where the bottom of the stringer meets the floor — should I caulk it?
The paint on my risers is chipping after just a few months — what paint or primer should I use?
My wood treads are darkening unevenly — some spots look stained. Is this a manufacturing defect?
Related Calculators
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