Furniture Doorway & Staircase Calculator
The Furniture Moving Puzzle: Geometry of Doorways and Corners
One of the most frustrating real-world geometry problems is determining whether furniture can physically fit through doorways and around corners. A piece that seems like it should fit often gets stuck mid-transit, requiring awkward angling, disassembly, or return trips. The solution lies in understanding the geometry of pivoting objects: as a sofa or mattress is rotated to thread through tight spaces, its effective reach extends diagonally, constrained by walls and door frames. This calculator applies the mathematics of diagonal spans and corner pivoting to determine whether your furniture can make it through.
The moving sofa problem—mathematically, whether a sofa of a given size can navigate a right-angle hallway corner—is a famous unsolved problem in pure mathematics. This calculator addresses the practical version: given your specific furniture dimensions and doorway/corner constraints, can it fit?
Geometry of Doorway Passage and Diagonal Constraint
For straight doorway passage, the furniture must fit through the rectangular opening. The critical constraint is the diagonal:
where w is doorway width and h is doorway height. The furniture's longest dimension (length when tilted optimally) must not exceed this diagonal. For right-angle corners in hallways, the constraint becomes a two-dimensional optimization: the sofa must pivot through the corner, and at some angle, its longest reach is limited by the geometry of two perpendicular walls.
Worked Example: Moving a Sofa Up a Staircase
A 200 cm long, 85 cm deep sofa must fit through a stairwell. The stairwell has 80 cm width, 210 cm ceiling height at the landing, and a 90° corner turn. Assess if it fits:
Step 1: Check straight doorway (assuming stairwell entrance) – Diagonal of 80 cm × 210 cm = √(6400 + 44100) = √50500 ≈ 225 cm. Sofa's 200 cm length fits.
Step 2: Check width constraint – Sofa is 85 cm deep; stairwell is 80 cm wide. The sofa cannot lay flat; it must tilt. At a 20° angle, the sofa's projected width becomes 85 cos(20°) ≈ 80 cm—tight but fitting.
Step 3: Check corner turn – With a 90° staircase corner, the sofa must rotate around the corner. If tilted to fit the width, and the stairwell landing allows 200 cm projection at an angle, the sofa can pivot around the corner by rotating incrementally.
Result: The sofa LIKELY FITS, but with minimal margin. Actual moving would require careful angling and potentially help; any obstructions (railings, pipes) could block passage.
Critical Dimensions for Different Furniture Types
The following table shows typical critical dimensions and doorway requirements:
| Furniture Type | Typical Length × Width × Height | Min Doorway Width | Min Diagonal (W×H) | Notes |
|---|---|---|---|---|
| Single mattress | 190 × 90 × 15 cm | 75 cm | 192 cm (for 75×210) | Often fits if tilted; diagonal is critical |
| Queen mattress | 200 × 150 × 15 cm | 85 cm | 218 cm (for 85×210) | Very tight; may not fit standing up |
| Standard sofa | 210 × 85 × 85 cm | 85 cm | 225 cm (for 85×210) | Requires angling; corner turns challenging |
| Large sectional | 250+ × 100+ × 90 cm | 100+ cm | 266+ cm (for 100×210) | May not fit up stairs; disassemble if possible |
| Upright piano | 150 × 65 × 120 cm | 75 cm | 226 cm (for 75×210) | Weight matters; use professional movers |
Using the Calculator
Enter your furniture's length, width (depth), and height in centimeters. Specify doorway width and height, and the type of passage (straight, right-angle corner, or staircase). The calculator determines whether the furniture's maximum diagonal or angled projection fits through the space. A result of "YES, it fits" means passage is geometrically possible; "NO, it won't fit" means it's blocked. Tight margins require careful maneuvering and possibly help.
Limitations and Practical Reality
This calculator assumes rigid furniture and ignores obstacles like railings, wall outlets, or light fixtures. Real-world moving involves surprises: stairs may have more complex geometry than perfect right angles, doors may not open fully against walls, or doorframes may have trim that reduces effective width. The calculation assumes optimal tilting and angling; furniture might be disassembled (legs removed, cushions separated) to improve fitment in actual moving. When in doubt, measure carefully, consult the furniture manufacturer's dimensions, and consider professional movers for expensive or large items.