Rectangular Prism Surface Area

SA = 2(lw + lh + wh). Box / cuboid surface.

Inputs

Result

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How to use this calculator

  • Enter length, width, height.
  • Read total surface area.

About this calculator

A rectangular prism has 6 faces in 3 pairs: top/bottom (lw each), front/back (lh), left/right (wh). SA = 2(lw + lh + wh). For shipping cost calculations: surface area drives material cost (cardboard); volume drives weight + space. The optimal box for a given volume is a cube (minimizes SA).

Frequently asked

When is open-top SA useful?+
For boxes without a lid: subtract one lw face. SA = lw + 2(lh + wh).
Wallpaper / paint estimate?+
Most rooms need just 4 walls (lh + lh + wh + wh = 2(lh + wh)) plus ceiling (lw). Subtract doors/windows separately.
Why cube minimizes SA?+
For fixed volume, equal sides spread out the surface โ€” proven by AM-GM inequality applied to 3 numbers.
How is this used in shipping?+
DIM weight calculations: airlines and parcel carriers charge by max(actual weight, dimensional weight). SA proxies for cargo footprint.
Open box (vs. closed) calc?+
Subtract one face area for any opening. This calc shows individual face areas in the breakdown โ€” easy to subtract.

Related calculators

Cube Surface Area Calculator
SA = 6sยฒ. Six identical square faces.
Cylinder Surface Area Calculator
SA = 2ฯ€rยฒ + 2ฯ€rh. Two circular ends + lateral wrap.
Sphere Surface Area Calculator
SA = 4ฯ€rยฒ. Exactly 4ร— the area of a great circle of the same radius.
Rectangular Prism Volume
V = l ร— w ร— h. Box / cuboid volume.
Cube Volume Calculator
V = sยณ. Six equal square faces.
Rectangle Perimeter Calculator
P = 2(l + w). Length plus width, doubled.

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