Will a couch (180x89x76 cm) Fit Through a 76 cm Door?

−1.5 in over

· ON THE WIDTH AXIS

It exceeds the opening at the tightest point.

The width axis runs out of room.
Checked all 6 orientations — none fits.
A 1.5 in handling allowance is already subtracted.

30 in vs 29 in

Overage −1.5 in (−5.2%) on the WIDTH axis

AAxis inequality · opening width✕ FAIL

d_{\text{item}} \;\le\; d_{\text{space}}

↓ SUBSTITUTE

30 \;\overset{?}{\le}\; 28.5\quad(\text{opening width})

↓ EVALUATE

30\,\text{in} \;>\; 28.5\,\text{in} \;\Longrightarrow\; \Delta = -1.5\,\text{in}

Plain English: Along the opening width, the item is 30 in and the space allows 28.5 in — over by 1.5 in.

BAxis inequality · opening height✓ PASS

d_{\text{item}} \;\le\; d_{\text{space}}

↓ SUBSTITUTE

71 \;\overset{?}{\le}\; 78.5\quad(\text{opening height})

↓ EVALUATE

71\,\text{in} \;\le\; 78.5\,\text{in} \;\Longrightarrow\; \Delta = +7.5\,\text{in}

Plain English: Along the opening height, the item is 71 in and the space allows 78.5 in — 7.5 in to spare.

CDiagonal clearance · Pythagorean✓ PASS

\sqrt{a^2 + b^2} \;\le\; \sqrt{a_{\text{sp}}^2 + b_{\text{sp}}^2}

↓ SUBSTITUTE

\sqrt{30^2 + 71^2} \;\overset{?}{\le}\; \sqrt{28.5^2 + 78.5^2}

↓ EVALUATE

77\,\text{in} \;\le\; 83.5\,\text{in} \;\Longrightarrow\; \Delta = +6.5\,\text{in}

Plain English: Tilted corner-to-corner the face spans 77 in, inside the opening's 83.5 in diagonal — but a tilt only buys diagonal room, it can't widen the throat.

D3D space diagonal✕ FAIL

\mathcal{D}_{3D} = \sqrt{L^2 + W^2 + H^2}

↓ SUBSTITUTE

\sqrt{71^2 + 35^2 + 30^2}

↓ EVALUATE

84.6\,\text{in} \;>\; 83.5\,\text{in} \;\Longrightarrow\; \Delta = -1.1\,\text{in}

Plain English: Corner to corner the item reaches 84.6 in — keep that swing room in mind for the turn after.

EMinimum required space · opening width✕ FAIL

d_{\text{req}} = d_{\text{item}} + t

↓ SUBSTITUTE

30 + 1.5 = 31.5

Plain English: Smallest space on the limiting axis that would admit this item (with handling tolerance).

FLargest item that fits · opening width✕ FAIL

d_{\max} = d_{\text{space}} - t

↓ SUBSTITUTE

28.5 - 1.5 = 27

Plain English: Largest item dimension this space admits on the limiting axis (after handling tolerance).

Orientation	Width	Height	Result	Note
30×71" (front/back)	0"	9"	✕	Too wide
30×35" (sideways)	0"	45"	✕	Too wide
35×30" (sideways)	-5"	50"	✕	Too wide
35×71" (laid flat)	-5"	9"	✕	Too wide
71×30" (front/back)	-41"	50"	✕	Too wide
71×35" (laid flat)	-41"	45"	✕	Too wide

How the door-passage check works

A door is a 2D opening — width and height matter; depth (path length through the doorway) doesn’t.

Generate all 6 dimension permutations of the item (3 axes × 2 flips).
For each permutation, apply the door constraint: item_width ≤ door_width AND item_height ≤ door_height.
Subtract 1.5 in handling clearance from each axis to leave room for human movement.
Pick the permutation with the largest minimum-axis margin — that’s the orientation a mover would choose.
Verdict ladder (verdict-tiers.js): FITS if margin ≥ 2 in; FITS_TIGHT if 0.5–2 in; FITS_VERY_TIGHT if 0–0.5 in; DOESN'T_FIT below.

Tolerance ±¼ in (6 mm) is applied implicitly (band promotion to FITS_VERY_TIGHT) — see the note below the orientation matrix.

Similar calculations

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Will a couch (180x89x76 cm) fit through a 76 cm door?

Expert analysis

It exceeds the opening at the tightest point.

Dimensions

Space geometry

Handling

Similar calculations

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