Item Fits

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DOESN'T FIT

It doesn't fitby 1 ft 2 in too large

Will a round table (224x152x122 cm) fit in a space?

round table· 7 ft 4 in × 5 ft × 4 ft

−1 ft 2 in (−151%)too large at tightest point

Item being fitted

round table7 ft 4 in × 5 ft × 4 ft

Space clearance

Space35 in × 6 ft 8 in

Result

1 ft 2 in too large

▸ width axis · binding

Expert analysis

A round table measuring 7 ft 4 in × 5 ft × 4 ft does not fit in a space, but it's about 1 ft 2 in too large at the tightest point. The binding dimension is width: that is the axis where the round table 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 ft 2 in over
Result: Width does not clear

−1 ft 2 in over

· ON THE WIDTH AXIS

It exceeds the opening at the tightest point.

The width axis runs out of room.
A 1 in handling allowance is already subtracted.

4 ft vs 34 in

Overage −1 ft 2 in (−41.1%) on the WIDTH axis

round table · Axis inequality✕ FAIL

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

↓ SUBSTITUTE

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

↓ EVALUATE

48\,\text{in} \;>\; 34\,\text{in} \;\Longrightarrow\; \Delta = {-14}\,\text{in}

Plain English: Along the opening width, the item is 48 in and the space allows 34 in — over by 14 in.

round table · Axis inequality✕ FAIL

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

↓ SUBSTITUTE

88 \;\overset{?}{\le}\; 79\quad(\text{opening height})

↓ EVALUATE

88\,\text{in} \;>\; 79\,\text{in} \;\Longrightarrow\; \Delta = {-9}\,\text{in}

Plain English: Along the opening height, the item is 88 in and the space allows 79 in — over by 9 in.

round table · Diagonal clearance · Pythagorean✕ FAIL

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

↓ SUBSTITUTE

\sqrt{48^2 + 88^2} \;\overset{?}{\le}\; \sqrt{34^2 + 79^2}

↓ EVALUATE

100.2\,\text{in} \;>\; 86\,\text{in} \;\Longrightarrow\; \Delta = {-14.2}\,\text{in}

Plain English: Even tilted corner-to-corner the face spans 100.2 in, past the opening's 86 in diagonal — angling it doesn't recover the fit.

round table · 3D space diagonal✕ FAIL

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

↓ SUBSTITUTE

\sqrt{88^2 + 60^2 + 48^2}

↓ EVALUATE

116.8\,\text{in} \;>\; 86\,\text{in} \;\Longrightarrow\; \Delta = {-30.8}\,\text{in}

Plain English: Corner to corner the item reaches 116.8 in — keep that swing room in mind for the turn after.

round table · Minimum required space✕ FAIL

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

↓ SUBSTITUTE

48 + 1 = 49

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

round table · Largest item that fits✕ FAIL

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

↓ SUBSTITUTE

34 - 1 = 33

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

door · Axis inequality✓ PASS

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

↓ SUBSTITUTE

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

↓ EVALUATE

1.4\,\text{in} \;\le\; 34\,\text{in} \;\Longrightarrow\; \Delta = {+32.6}\,\text{in}

Plain English: Along the opening width, the item is 1.4 in and the space allows 34 in — 32.6 in to spare.

door · Axis inequality✓ PASS

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

↓ SUBSTITUTE

32 \;\overset{?}{\le}\; 79\quad(\text{opening height})

↓ EVALUATE

32\,\text{in} \;\le\; 79\,\text{in} \;\Longrightarrow\; \Delta = {+47}\,\text{in}

Plain English: Along the opening height, the item is 32 in and the space allows 79 in — 47 in to spare.

door · 3D space diagonal✕ FAIL

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

↓ SUBSTITUTE

\sqrt{32^2 + 1.4^2 + 80^2}

↓ EVALUATE

86.2\,\text{in} \;>\; 86\,\text{in} \;\Longrightarrow\; \Delta = {-0.2}\,\text{in}

Plain English: Corner to corner the item reaches 86.2 in — keep that swing room in mind for the turn after.

door · Minimum required space✓ PASS

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

↓ SUBSTITUTE

1.4 + 1 = 2.4

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

door · Largest item that fits✓ PASS

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

↓ SUBSTITUTE

34 - 1 = 33

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

Orientation	Width	Height	Result	Note
4 ft×7 ft 4 in (front/back)	-14 in	-9 in	✕	Too wide
4 ft×5 ft (sideways)	-14 in	19 in	✕	Too wide
5 ft×4 ft (sideways)	-26 in	31 in	✕	Too wide
5 ft×7 ft 4 in (laid flat)	-26 in	-9 in	✕	Too wide
7 ft 4 in×4 ft (front/back)	-54 in	31 in	✕	Too wide
7 ft 4 in×5 ft (laid flat)	-54 in	19 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

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Will a round table (224x152x122 cm) fit in a space?

Expert analysis

It exceeds the opening at the tightest point.

Dimensions

Space geometry

Handling

Similar calculations

Run your own fit check