# Sweeping curved staircase — calculation notes

The supplied photograph is treated as shape inspiration only. Its room, dimensions and stair geometry were not assumed.

## Established vertical dimensions

- Ground-floor clear ceiling height: **2750 mm**.
- Assumed timber floor / ceiling build-up above ground floor: **280 mm**.
- Ground-to-first finished-floor height: **3030 mm**.
- Basement clear ceiling height: **2350 mm**.
- Assumed ground-floor slab / build-up above basement: **250 mm**.
- Basement-to-ground finished-floor height: **2600 mm**.

The build-ups are explicit design assumptions because the existing concept plans state clear ceiling heights but not structural floor thicknesses.

## Ground to first

- 18 equal risers.
- Riser height: 3030 / 18 = **168.3 mm**.
- 17 walking-line goings.
- Going: **290 mm**.
- Step rule: 2 × 168.3 + 290 = **626.6 mm**.
- Developed walking length: 17 × 290 = **4930 mm**.
- Half-turn angle: 180°.
- Walking-line radius: 4930 / π = **1569 mm**.

## Basement to ground

- 16 equal risers.
- Riser height: 2600 / 16 = **162.5 mm**.
- 15 walking-line goings.
- Going: **290 mm**.
- Step rule: 2 × 162.5 + 290 = **615 mm**.
- Developed walking length: 15 × 290 = **4350 mm**.
- Using the same 1569 mm walking-line radius produces approximately **158.8°** of rotation.

## Plan geometry

- Clear flight width: **1000 mm**.
- Walking line positioned 400 mm from the inner handrail.
- Inner radius: 1569 − 400 = **1169 mm**.
- Outer radius: 1169 + 1000 = **2169 mm**.
- Required outside diameter: **4338 mm**.
- Central open-well diameter: **2338 mm**.

## Fit against the approved plan

The current concept core is approximately 3000 × 3300 mm. The photo-like comfortable sweep therefore needs roughly:

- **1338 mm additional width**.
- **1038 mm additional depth**.

A compressed version can be drawn inside the current core, but it would no longer achieve the selected 290 mm going at the walking line. The safer plan-faithful alternative is the earlier soft-horseshoe option: straight uniform treads with curved landing edges, stringers and handrails.

## Status

This is a scale-controlled art-direction and spatial-feasibility study. Final headroom, structural thickness, baluster spacing, fire strategy, walking-line rules and approval must be resolved by the project architect, structural engineer and qualified staircase builder.