Item Fits

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DOESN'T FIT

It doesn't fitby 4.5 in too large

Will a sleeper sofa (107x91x86 cm) fit in a space?

sleeper sofa· 3 ft 6 in × 3 ft × 34 in

−4.5 in (−36%)too large at tightest point

Item being fitted

sleeper sofa3 ft 6 in × 3 ft × 34 in

Space clearance

Space31 in × 6 ft 8 in

Result

4.5 in too large

▸ width axis · binding

Expert analysis

A sleeper sofa measuring 42 in × 36 in × 34 in does not fit in a space, but it's about 4.5 in too large at the tightest point. The binding dimension is width: that is the axis where the sleeper sofa runs out of room. The persisted calculation steps support the reported tightest-point margin. One caveat: checked as one rigid piece: not compressed, bent, or taken apart.

How we verified this

Binding axis: Width
Tightest clearance: 4.5 in over
Result: Width does not clear

−4.5 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.

34 in vs 29 in

Overage −4.5 in (−15.3%) on the WIDTH axis

AAxis inequality · opening width✕ FAIL

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

↓ SUBSTITUTE

34 \;\overset{?}{\le}\; 29.5\quad(\text{opening width})

↓ EVALUATE

34\,\text{in} \;>\; 29.5\,\text{in} \;\Longrightarrow\; \Delta = {-4.5}\,\text{in}

Plain English: Along the opening width, the item is 34 in and the space allows 29.5 in — over by 4.5 in.

BAxis inequality · opening height✓ PASS

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

↓ SUBSTITUTE

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

↓ EVALUATE

42\,\text{in} \;\le\; 78.5\,\text{in} \;\Longrightarrow\; \Delta = {+36.5}\,\text{in}

Plain English: Along the opening height, the item is 42 in and the space allows 78.5 in — 36.5 in to spare.

CDiagonal clearance · Pythagorean✓ PASS

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

↓ SUBSTITUTE

\sqrt{34^2 + 42^2} \;\overset{?}{\le}\; \sqrt{29.5^2 + 78.5^2}

↓ EVALUATE

54.1\,\text{in} \;\le\; 83.9\,\text{in} \;\Longrightarrow\; \Delta = {+29.8}\,\text{in}

Plain English: Tilted corner-to-corner the face spans 54.1 in, inside the opening's 83.9 in diagonal — but a tilt only buys diagonal room, it can't widen the throat.

D3D space diagonal✓ PASS

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

↓ SUBSTITUTE

\sqrt{42^2 + 36^2 + 34^2}

↓ EVALUATE

64.9\,\text{in} \;\le\; 83.9\,\text{in} \;\Longrightarrow\; \Delta = {+18.9}\,\text{in}

Plain English: Corner to corner the item reaches 64.9 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

34 + 1.5 = 35.5

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

29.5 - 1.5 = 28

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

Orientation	Width	Height	Result	Note
34 in×42 in (front/back)	-4.5 in	36.5 in	✕	Too wide
34 in×36 in (sideways)	-4.5 in	42.5 in	✕	Too wide
36 in×34 in (sideways)	-6.5 in	44.5 in	✕	Too wide
36 in×42 in (laid flat)	-6.5 in	36.5 in	✕	Too wide
42 in×34 in (front/back)	-12.5 in	44.5 in	✕	Too wide
42 in×36 in (laid flat)	-12.5 in	42.5 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

5 ft sofa in a 29 in spaceDOESN'T FIT

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

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

3 ft sofa in a 33 in spaceDOESN'T FIT

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Will a sleeper sofa (107x91x86 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