Stair calculations, drawings & design standards
Use Stair Calculator to compare straight, L, U and spiral layouts, study parking ramp profiles and export preliminary drawings. This guide explains the geometry and the assumptions behind each result.
How to calculate stair risers, tread depth and total run
Start with the finished floor-to-floor height H, a whole number of risers N and the desired horizontal tread depth T. The riser height R is H divided by N. A single straight flight has N risers and N−1 treads because the final rise reaches the upper floor.
For a height of 3,300 mm, 19 risers and 280 mm treads, R is approximately 173.68 mm, the total run is 5,040 mm and the pitch is approximately 31.8°. Dimensions are calculated internally in millimetres; changing to inches converts the display using 25.4 mm per inch.
The straight-flight run formula does not describe the footprint of a turned or spiral stair. Select the layout, flight width, landing or winder configuration and plan envelope in the calculator. Read the actual plan dimensions rather than treating the developed walking-path length as a rectangular footprint.
R = H / N · straight run = (N − 1) × T · pitch = atan(R / T)
Blondel formula: a check of stair comfort
The Blondel formula combines two riser heights with one tread depth: 2R + T. The calculator uses 600–640 mm as its comfort reference and labels 620–630 mm ideal. These are preliminary ergonomic references, not a substitute for the building regulations that apply to a particular project.
In the 19-riser example above, 2R + T is approximately 627.37 mm. The supplementary formulas R + T ≈ 450 mm and T − R ≈ 120 mm provide additional proportion checks. Increasing tread depth usually reduces pitch but increases the required plan length.
For winders and spirals, the app evaluates walking-line tread depth using the stated two-thirds-width convention. Local rules may prescribe a different walking line and narrow-end requirements, so these layouts need separate verification.
Blondel: 2R + T · comfort reference: 600–640 mm
Headroom, landings and the floor opening
Enter the upper slab thickness and the horizontal opening-edge position measured from the bottom of the stair. For a straight flight, the app estimates clearance under a horizontal soffit using a conservative nosing-line model. Its general headroom reference is 2,000 mm; the IRC profile uses 2,032 mm.
Beams, overlapping flights and local obstructions can reduce actual clearance. L/U headroom is marked unverified rather than receiving a passing result from the straight-flight formula. Spiral checks estimate clearance between complete turns, while the upper floor opening still needs project review.
Optional Vietnamese traditional step count
The Vietnamese interface includes the Sinh–Lão–Bệnh–Tử cycle. Counting the risers, including the final rise to the upper floor, counts of 4n + 1 end in Sinh (Birth): for example 17, 21 and 25. The preference is optional and is hidden in the English calculator interface.
A traditional count is evaluated separately from comfort and dimensional limits. At 3,300 mm with 21 risers, R is approximately 157.14 mm. A 280 mm tread gives a Blondel value of 594.29 mm, outside the app’s reference; a 300 mm tread raises it to 614.29 mm and requires a 6,000 mm straight run. Check the available space before adopting that change.
IRC, TCVN and Eurocode: what is checked?
The 2021 IRC profile checks selected dimensions for ordinary residential stairs: riser ≤196.85 mm, rectangular tread ≥254 mm, clear width ≥914.4 mm, headroom ≥2,032 mm and handrail height 863.6–965.2 mm. Passing these modeled dimensions does not verify nosings, landing provisions, guards, handrail projections, fire or egress requirements, special stair exceptions or local amendments.
TCVN and Eurocode selections are project templates. Enter the applicable document, edition, building use and dimensional limits. Eurocodes address structural design; national regulations also govern stair geometry. A project profile without the four core limits cannot produce an automatic optimization recommendation.
TCVN 2737:2023 concerns loads, actions and their combinations in structural design. It does not supply the Blondel comfort range. Designing a reinforced-concrete stair requires loads, material properties, support conditions and appropriate structural checks beyond the app’s geometry and preliminary BOQ.
Concrete, steel and timber quantities; drawing export
Select the material in the BOQ panel below the drawing. Concrete quantities combine the modeled sloping waist, step wedges, landings and separately entered beams. Waist thickness is measured normal to the sloping surface. Reinforcement mass is an editable kg/m³ budgeting estimate, not a reinforcement design or bar-bending schedule.
Steel and timber modes count modeled tread/landing panels and straight flight stringers. Enter the chosen steel section mass or timber section sizes, panel thickness, extra beams and waste allowance. Curved support members are not inferred for winders or spirals. Quantities exclude unmodeled supports, rails, fixings, finishes and foundations.
Use Export BOQ CSV above the drawing to download net quantities and quantities with allowance. BOQ units remain m³, m², m, kg and pieces when drawing units change. Piece allowances round up. Export Blueprint offers SVG, PNG and editable 2D DXF in real millimetres; these are preliminary drawings, not a DWG or BIM model.
- Set height, layout, tread depth and plan limits.
- Review comfort, headroom and the selected project limits.
- Choose material assumptions and inspect the BOQ.
- Export CSV or the drawing from the buttons above the blueprint.
Parking ramp slope and anti-scrape transitions
Parking ramp grade is vertical drop divided by horizontal run, multiplied by 100. The calculator can solve for the main grade from an available run, or for the required run from a desired main grade. Each transition contributes its own length and drop.
The default top and bottom transitions are each 2,000 mm at 8%. For a 3,000 mm drop and a 22,000 mm total horizontal run, these transitions leave an 18,000 mm main segment at approximately 14.89%. The app warns above its 15% main-grade reference, above 17%, and when transition lengths or grades exceed the stated references.
Without transitions, grades above 13% trigger a low-clearance vehicle scrape warning. These geometric references do not simulate a particular vehicle’s wheelbase, overhangs or ground clearance. This module is for parking ramps; it is not a wheelchair-accessibility compliance check.
Grade (%) = vertical drop / horizontal run × 100