Staircase Calculator

Staircase Calculator

Plan risers, treads, total run, slope, and stringer length from total rise and your preferred step sizes — with simple code checks.

Practical Guide

Staircase Calculator: Accurate Rise, Run, and Stringer Layout

Use this step-by-step guide to turn floor-to-floor height into a safe, code-aligned stair: choose riser and tread targets, get step count, run, angle, and stringer length, then sanity-check with examples and variations.

8–10 min read Updated November 10, 2025

Quick Start

  1. 1 Enter floor-to-floor height (total rise). If you only have floor-to-finished-floor, include subfloor and finish thicknesses.
  2. 2 Pick a target riser height (often 7–7.75 in / 178–197 mm residential; verify your local code). The calculator rounds to an integer step count.
  3. 3 Choose tread depth (going) (often 10–11 in / 254–279 mm) and nosing as applicable; the tool returns total run, slope, and stringer length.
  4. 4 Add landings/turns and re-check headroom. Adjust riser/tread targets to meet space and code.
  5. 5 Export the results and use the example steps below to verify by hand.

Tip: If space is tight, try slightly smaller risers and deeper treads to reduce slope and increase comfort.

Watch-out: Many jurisdictions require minimum tread depth, maximum riser, consistent riser variation (e.g., ≤3/8 in), minimum headroom (often 6′-8″ / 2032 mm), and guard/handrail rules. Always check local code before building.

Core Equations (used by the calculator)

Let \(R_\text{total}\) be total rise, \(h\) target riser, \(d\) tread depth (going), and \(N\) number of risers/steps.

A
Step count: \[ N = \left\lceil \dfrac{R_\text{total}}{h} \right\rceil \]
B
Exact riser: \[ h_\text{exact} = \dfrac{R_\text{total}}{N} \]
C
Total run (straight stair): \[ \text{Run}_\text{total} = (N-1)\,d \] (top floor serves as the final “tread”).
D
Slope/angle: \[ \theta = \arctan\!\left( \dfrac{h_\text{exact}}{d} \right) \]
E
Stringer length (planar): \[ L = \sqrt{R_\text{total}^2 + \text{Run}_\text{total}^2} \]

Variables & Symbols

  • \(R_\text{total}\) — floor-to-floor vertical rise.
  • \(h\) — target riser height (per step); \(h_\text{exact}\) — adjusted riser after rounding.
  • \(d\) — tread depth (going), measured horizontally; may be affected by nosing.
  • \(N\) — number of risers; for straight stairs the number of treads is \(N-1\).
  • \(\theta\) — stair angle; comfort is typically 30°–37° for residential.
  • \(L\) — stringer length along the slope line.

Approaches to Sizing

Method A — Known Rise, Target Riser

Most common for new stairs. You know floor-to-floor; you prefer a riser height (e.g., 7-1/2″).

  • Fast and code-friendly.
  • Straightforward rounding to even risers.
  • Easy to adjust for finish thicknesses.
  • May push total run beyond available space.
  • Requires iteration if headroom is tight.
N = ceil(\(R_\text{total} / h\)); then \(h_\text{exact} = R_\text{total}/N\).

Method B — Known Space, Target Tread

Best when you have a fixed shaft or hallway length and must fit the stair inside.

  • Prevents overruns into doors or corridors.
  • Good for remodels with hard constraints.
  • Can force steeper stairs if run is limited.
  • May require a landing/turn to comply with headroom.
\(\text{Run}_\text{total} \leq \text{Space}\); choose \(d\), then check \(\theta\) and code.

What Moves the Number

Total rise (floor-to-floor)

The larger the rise, the more risers; subtle changes from finish buildup can affect count and exact riser height.

Target tread depth

Deeper treads create longer run and lower angle (more comfortable). Shallow treads shorten run but steepen the stair.

Headroom

Low headroom pushes longer runs or different layouts (L/U with landing). Always confirm early.

Local code limits

Max riser, min tread, nosing, variation limits, and minimum landing sizes can force adjustments.

Landings & turns

Each landing resets headroom geometry and adds length. Winders change going; many codes restrict them.

Stringer stock & construction

2×12 stringers are common for wood stairs; notch depth, hanger types, and finish thicknesses alter layout.

Worked Examples

Example 1 — US (Imperial) Straight Stair

  • Total rise \(R_\text{total}\): 108 in (9 ft) floor-to-floor including finishes
  • Target riser \(h\): 7.5 in
  • Tread depth \(d\): 10.25 in (accounting for a 1 in nosing)
  • Objective: step count, exact riser, total run, angle, stringer length
1
Step count: \[ N=\left\lceil \dfrac{108}{7.5} \right\rceil = \lceil 14.4 \rceil = \mathbf{15} \]
2
Exact riser: \[ h_\text{exact}=\dfrac{108}{15}= \mathbf{7.2\ \text{in}} \]
3
Total run: \( (N-1)\,d = 14 \times 10.25 = \mathbf{143.5\ \text{in}}\) (11′-11.5″)
4
Angle: \[ \theta=\arctan\!\left(\dfrac{7.2}{10.25}\right) \approx \mathbf{35.1^\circ} \]
5
Stringer: \[ L=\sqrt{108^2+143.5^2}\approx \mathbf{179.4\ \text{in}} \ (14′-11.4″) \]

Rounding to 15 risers keeps comfort (≈35°) and typical code ranges. If the available run is shorter, consider an L-shaped layout with a landing.

Example 2 — Metric with Space Constraint

  • Total rise \(R_\text{total}\): 2.85 m
  • Available run (max): 3.8 m inside a corridor
  • Target tread \(d\): 270 mm
  • Trial riser \(h\): 175 mm (typical residential)
1
Step count: \(N=\lceil 2850/175 \rceil = \lceil 16.29 \rceil = \mathbf{17}\)
2
Exact riser: \(h_\text{exact}=2850/17 = \mathbf{167.6\ \text{mm}}\)
3
Total run: \((17-1)\times 270 = \mathbf{4.32\ \text{m}}\) → exceeds 3.8 m
4
Adjust layout: Use an L-stair with a landing splitting into two flights of 8 risers each (8 treads per flight). Each flight run ≈ \(8\times 270 = \mathbf{2.16\ \text{m}}\) → fits.
5
Angle check (each flight): \(\theta = \arctan(167.6/270) \approx \mathbf{31.8^\circ}\), comfortable.

With constrained run, landings maintain comfort and headroom. Re-check landing width against your code.

Stair Types & Variations

Layout changes geometry, headroom, and labor. Use the table to anticipate impacts before you cut stringers.

VariationWhen to UseDesign ImplicationsImpact
Straight runSimple spans with clear headroomLongest continuous run; easy layout; guard/handrail straightforwardLowest cost; requires longest footprint
L-shaped (quarter turn)Fit inside corners; manage headroomLanding required; divides rise; two stringer setsModerate cost; better fit in tight plans
U-shaped (half turn)Very tight footprint; mid-landingTwo landings or one large; careful headroom at turnMore labor; compact plan
Winders (pie treads)Turning without a full landingGoing varies; codes often restrict dimensionsComplex cuts; check code carefully
Exterior stepsDecks, porchesDurable materials, slip resistance, drainageWeatherproofing; larger nosing often avoided
  • Include finish build-ups (treads, nosing, floor finishes) in rise and going.
  • Keep riser variation minimal (often ≤ 3/8″ or 10 mm difference allowed—verify locally).
  • Confirm headroom along the entire path, not just at one cross-section.
  • Lay out from a consistent baseline (finished floor at top or bottom) and stick to it.

Materials, Layout & Practical Checks

Selection & Materials

  • Stringers: Many residential wood stairs use 2×12 SPF or southern pine. Check notch depth and span (use hangers/ledger as required).
  • Treads & Risers: Solid wood, engineered, or plywood with finish nosing. Exterior: composite/treated lumber with anti-slip.
  • Fasteners: Structural screws or nails per manufacturer; corrosion-resistant outdoors.
  • Guards & Rails: Follow post spacing, graspability, and height rules per local code.

Layout & Installation Tips

  • Strike a story pole (mark all risers) to catch tolerance drift before cutting.
  • Lay out stringers with a framing square and stair gauges; test on scrap.
  • Account for finish thicknesses: top/bottom adjustments keep first/last risers consistent.
  • Pre-dry-fit landing and guard posts to avoid interference with tread overhangs.

Sanity Checks

  • Does the calculator’s angle fall in the comfortable 30°–37° range?
  • Is total run compatible with headroom and clearances at doors/landings?
  • Are first and last risers equal after flooring is installed?

This article provides planning math and best practices; final design and construction must meet your jurisdiction’s code and manufacturer instructions.

Frequently Asked Questions

How do I know how many steps I need?
Divide floor-to-floor rise by your target riser height and round up to a whole number of risers: \(N=\lceil R_\text{total}/h\rceil\). Then recompute exact riser height \(h_\text{exact}=R_\text{total}/N\) and confirm it’s within your code limits.
What is a comfortable stair angle?
Most residential stairs feel comfortable around 30°–37°. You can compute angle with \(\theta=\arctan(h_\text{exact}/d)\). If it’s steeper, increase tread depth or add a landing.
Do I include the top tread in total run?
For straight stair calculations, the top floor acts as the final tread, so total run uses \(N-1\) treads. Layout details can vary; keep your baseline consistent.
How do nosings affect tread depth?
Code tread depth is typically measured horizontally from nosing to nosing. If you have a large nosing, the effective going can differ from the tread stock depth. Align your measurement method with your code definition.
What if my headroom doesn’t clear?
Use a landing and split into two flights, reduce riser height and increase tread depth (longer run), or re-route under a higher ceiling area. Confirm headroom at every point along the walking line.
Is there a quick materials takeoff rule?
A typical straight stair has three stringers for residential width; treads ≈ \(N-1\); risers ≈ \(N-1\). Add nosing, adhesive, fasteners, and guard/rail components per the design.

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