Item Fits

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DOESN'T FIT

It doesn't fitby 1.5 in too large

Will a sofa (170x102x74 cm) fit in a space?

sofa· 5 ft 7 in × 3 ft 4 in × 29 in

−1.5 in (−131%)too large at tightest point

Item being fitted

sofa5 ft 7 in × 3 ft 4 in × 29 in

Space clearance

Space29 in × 6 ft 8 in

Result

1.5 in too large

▸ width axis · binding

Expert analysis

A sofa measuring 67 in × 40 in × 29 in does not fit in a space, but it's about 1.5 in too large at the tightest point. The binding dimension is width: that is the axis where the sofa runs out of room. The persisted calculation steps support the reported tightest-point margin. One caveat: item is rigid and cannot be compressed, bent, or disassembled.

How we verified this

Binding axis: Width
Tightest clearance: 1.5 in over
Result: Width does not clear

−1.5 in over

· ON THE WIDTH AXIS

It exceeds the opening at the tightest point.

The width axis runs out of room.
A 1.5 in handling allowance is already subtracted.

29 in vs 28 in

Overage −1.5 in (−5.4%) on the WIDTH axis

AAxis inequality · opening width✕ FAIL

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

↓ SUBSTITUTE

29 \;\overset{?}{\le}\; 27.5\quad(\text{opening width})

↓ EVALUATE

29\,\text{in} \;>\; 27.5\,\text{in} \;\Longrightarrow\; \Delta = {-1.5}\,\text{in}

Plain English: Along the opening width, the item is 29 in and the space allows 27.5 in — over by 1.5 in.

BAxis inequality · opening height✓ PASS

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

↓ SUBSTITUTE

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

↓ EVALUATE

67\,\text{in} \;\le\; 78.5\,\text{in} \;\Longrightarrow\; \Delta = {+11.5}\,\text{in}

Plain English: Along the opening height, the item is 67 in and the space allows 78.5 in — 11.5 in to spare.

CDiagonal clearance · Pythagorean✓ PASS

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

↓ SUBSTITUTE

\sqrt{29^2 + 67^2} \;\overset{?}{\le}\; \sqrt{27.5^2 + 78.5^2}

↓ EVALUATE

73\,\text{in} \;\le\; 83.2\,\text{in} \;\Longrightarrow\; \Delta = {+10.2}\,\text{in}

Plain English: Tilted corner-to-corner the face spans 73 in, inside the opening's 83.2 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{67^2 + 40^2 + 29^2}

↓ EVALUATE

83.3\,\text{in} \;>\; 83.2\,\text{in} \;\Longrightarrow\; \Delta = {-0.1}\,\text{in}

Plain English: Corner to corner the item reaches 83.3 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

29 + 1.5 = 30.5

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

27.5 - 1.5 = 26

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

Orientation	Width	Height	Result	Note
29 in×67 in (front/back)	-1.5 in	11.5 in	✕	Too wide
29 in×40 in (sideways)	-1.5 in	38.5 in	✕	Too wide
40 in×29 in (sideways)	-12.5 in	49.5 in	✕	Too wide
40 in×67 in (laid flat)	-12.5 in	11.5 in	✕	Too wide
67 in×29 in (front/back)	-39.5 in	49.5 in	✕	Too wide
67 in×40 in (laid flat)	-39.5 in	38.5 in	✕	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

7 ft Standard 3-seat sofa in a 7 ft spaceFITS

7 ft Standard 3-seat sofa in a 31 ft spaceFITS

3 ft sleeper sofa in a 31 in spaceDOESN'T FIT

3 ft sofa in a 33 in spaceDOESN'T FIT

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Will a sofa (170x102x74 cm) fit in a space?

Expert analysis

It exceeds the opening at the tightest point.

Dimensions

Space geometry

Handling

Other assumptions

Similar calculations

Run your own fit check