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Cuboid surface area calculator

Measure a box, recover a missing edge, and compare the material area for a closed box and a box without its top.

Calculator

Closed surface area
52
Area without the top
46
Length
2
Width
3
Height
4
Space diagonal
5.38516
Face-pair contributions
PairShare of closed area (%)
Top and bottom23.07692308
Front and back30.76923077
Left and right46.15384615

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How this calculator works

Opposite faces form three equal-area pairs. The table shows which pair contributes most to the total. Removing the top subtracts one length-by-width face. Reverse area modes isolate one edge; the diagonal mode uses a spatial right triangle. These are geometric areas before seams, overlaps or cutting waste.

Formula

S = 2(lw + lh + wh); open-top area = lw + 2h(l + w); h = (S/2 - lw)/(l + w); d² = l² + w² + h².

Worked example

A 2 m by 3 m base and 4 m height give face pairs of 12, 16 and 24 m². The closed total is 52 m²; removing the 6 m² top leaves 46 m².

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Frequently asked questions

Which face is removed for an open box?

The top parallel to the length-by-width base. Rotate your measurements if a different face is open.

Can the area be too small?

Yes. For a positive height the total must exceed twice the base area.

Does the table include waste?

No. Its percentages describe the six ideal faces only.

Sources

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