Stair Calculator
From total rise and preferred riser height, automatically size safe stairs per Korean Building Code Enforcement Decree Article 48 and the Blondel formula.
Result
Enter total rise and preferred riser height.
What this tool does
The stair calculator computes step count, actual riser height, tread depth, stair length, angle, and Blondel value from total rise (floor-to-floor height) and preferred riser. It simultaneously checks the Korean Building Act Enforcement Decree Article 48 limits (residential: riser ≤ 200 mm, tread ≥ 240 mm; public: riser ≤ 180 mm, tread ≥ 280 mm) and the ergonomic Blondel formula (2R + T = 600–640 mm), displaying warnings when values fall outside safe ranges. Providing the optional total run enables measured tread instead of the Blondel-recommended default.
Who uses this
- New timber-frame homes: draft stair layout (step count, riser, tread) once floor-to-floor height is fixed
- Renovation: re-plan stair division when ceiling height changes
- Compact housing / loft stairs: verify tread depth and pitch angle meet safety criteria in limited horizontal space
- Pre-permit check: spot riser/tread violations before drawing submission
- Deck and exterior stairs: calculate slope angle and stringer length for outdoor construction
How to Use (4 Steps)
- 1Enter total rise in mm — the floor-to-floor structural height including finish materials. Example: 2,700 mm between level 1 and level 2.
- 2Enter preferred riser height. Residential stairs typically target 170–200 mm. The tool rounds to the nearest whole step count and divides evenly.
- 3(Optional) Enter total run if you know the horizontal stair footprint. Leave blank to get the Blondel-formula tread recommendation (T = 620 − 2R).
- 4Choose use type (Residential / Public). The building-code thresholds change accordingly. Review the Blondel pass/fail indicator and any riser or tread warnings in the results.
Formulas & Standards
Step count = round(total rise ÷ preferred riser) [min 2] Actual riser (R) = total rise ÷ step count Tread depth (T): With total run → T = total run ÷ (step count − 1) Without total run → T = 620 − 2 × R (Blondel recommendation) Stair length = √(total rise² + (T × (step count − 1))²) Pitch angle = atan(R ÷ T) [degrees] Blondel value = 2R + T → 600–640 mm is ergonomically safe Korean Building Act Enforcement Decree Art. 48: Residential: R ≤ 200 mm, T ≥ 240 mm, width ≥ 750 mm Public: R ≤ 180 mm, T ≥ 280 mm, width ≥ 1,200 mm Headroom: ≥ 2,100 mm (both types)
Examples
Example 1: Total rise 2,700 mm, preferred riser 175 mm
Step count = round(2700 ÷ 175) = 15. Actual R = 2700 ÷ 15 = 180 mm. T = 620 − 2×180 = 260 mm (Blondel). Blondel = 2×180 + 260 = 620 mm → pass. Angle = atan(180÷260) = 34.7°. Stair length = √(2700² + (260×14)²) ≈ 4,534 mm.
Example 2: Total rise 3,000 mm, total run 3,640 mm
Preferred R 180 mm → step count = round(3000÷180) = 17. Actual R = 3000÷17 ≈ 176.5 mm. T = 3640÷(17−1) = 227.5 mm. Blondel = 2×176.5 + 227.5 = 580.5 mm → below 600 mm warning. Reduce step count or widen run to fix.
Example 3: Loft stair, total rise 2,000 mm (public threshold applied)
Public: R ≤ 180 mm. round(2000÷175) = 11 steps. R = 2000÷11 ≈ 181.8 mm → exceeds 180 mm warning. Increasing to 12 steps: R = 166.7 mm, T = 620−2×166.7 = 286.6 mm → both limits met. Angle = 30.2°.
Frequently asked questions
What is the Blondel formula?
The Blondel formula (2R + T = 600–640 mm) was proposed by 17th-century French architect François Blondel to describe the ergonomic stride length on stairs. When this range is satisfied, climbing feels natural without overstretching or shuffling. This calculator uses 620 mm as the target and warns when the value falls outside 600–640 mm.
Why does the actual riser differ from the preferred value I entered?
The tool rounds total rise ÷ preferred riser to the nearest integer to ensure every step is equal height. The actual riser (total rise ÷ rounded step count) will therefore differ slightly from your preferred value. Always verify the displayed 'actual riser' before drafting construction drawings.
Why is the tread auto-calculated when I leave total run blank?
Without a measured run, the Blondel formula T = 620 − 2R provides a recommended starting tread depth. This is useful in early design when only the floor-to-floor height is known. Enter the actual total run once the stair footprint is fixed to get precise tread dimensions.
Where are the Korean building-code stair dimensions specified?
Building Act Enforcement Decree Article 48 and the Rules on Evacuation and Fire-Protection Structures Article 15 set stair dimensional requirements in Korea. This tool applies: residential (within dwelling unit) R ≤ 200 mm / T ≥ 240 mm; public (common areas / public buildings) R ≤ 180 mm / T ≥ 280 mm. Always verify current local authority requirements before permit submission.
How do I design stair width (clear width)?
Korean code minimums: residential ≥ 750 mm, public ≥ 1,200 mm clear width. This calculator covers riser, tread, and step count only — stair width design should be confirmed with a licensed architect. Handrail requirements (height ≥ 900 mm) should also be reviewed.
Can this calculator be used for outdoor stairs?
The geometry formulas apply equally to indoor and outdoor stairs, but outdoor stairs benefit from wider treads (to shed rainwater) and anti-slip finishes. In freeze-thaw climates, keeping risers at 150 mm or below reduces ice-accumulation risk. Structural footings for exterior stair stringers are a separate design consideration.
Cautions
- •This tool references Korean Building Act Enforcement Decree Art. 48 as a guide. Final design and permit approval must be confirmed with a licensed architect and the local authority having jurisdiction.
- •Stair width (clear width), headroom (≥ 2,100 mm), and handrail requirements are not calculated here.
- •Total rise must reflect finished-floor-to-finished-floor height, including floor finish and stair tread thickness. Structural shell height will differ.
- •Step count is determined by rounding, so actual riser may differ from the preferred value. Use the displayed actual riser for all drawings.
- •Cutting a stair opening through floor joists requires double headers and trimmer/rim joists — consult a structural engineer.
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Last reviewed: 2026-06-17