How this instrument works
A rectangular prism has six faces arranged in three matching pairs: a length-by-width pair (top and bottom), a length-by-height pair (front and back), and a width-by-height pair (the two sides). Adding up all six — which is the same as doubling the sum of the three distinct face areas — gives the total surface area.
This site already has combined Rectangular Prism and Cuboid calculators that report volume and surface area (and, for the cuboid, the interior diagonal) together from the same three measurements. This page is a narrower, quicker convenience version for whenever only the surface area itself is needed — sizing wrapping paper or paint coverage, say, without also wanting the volume alongside it.
Surface area doesn't scale as simply as volume does: doubling every dimension of a box quadruples its surface area (since each face's area is a product of two scaled lengths) while actually multiplying its volume by eight — a distinction worth knowing whenever comparing a scaled-up version of the same box shape.
- Enter the box's length into the Length field.
- Enter its width into the Width field.
- Enter its height into the Height field.
- Read Total surface area: the combined area of all six faces.
Worked example — a 3 by 4 by 5 box
A box measuring 3 by 4 by 5 units has three distinct face areas: 3×4=12, 3×5=15, and 4×5=20. Doubling their sum gives the total surface area: 2×(12+15+20)=94 square units, covering all six faces (each of the three shapes appearing twice, once on each opposite side).
A cube 2 units on every edge has six identical 2×2=4 faces, giving a total of 6×4=24 — matching the general formula's 2×(4+4+4)=24 exactly. A thin slab measuring 1 by 10 by 10 has a surface area of 2×(10+10+100)=240, dominated by its two large 10-by-10 faces.
Questions
What is the formula for the surface area of a rectangular prism?
A = 2(lw + lh + wh), where l, w, and h are the length, width, and height — the sum of the three distinct face areas, doubled to account for each face's matching opposite.
How is this different from the Rectangular Prism or Cuboid calculators on this site?
Those pages return volume and surface area (and, for the cuboid, the interior diagonal) together from the same three inputs; this page is a narrower, single-figure version for whenever only the surface area itself is needed.
What happens to the surface area if I double every dimension?
It quadruples, not doubles — each of the three face areas is a product of two dimensions, so scaling every length by a factor scales every face area by that factor squared, unlike volume, which would multiply by that factor cubed instead.
How many faces does a rectangular prism have?
Six, arranged in three matching pairs of opposite faces — a top and bottom, a front and back, and two sides — each pair sharing the identical area as its opposite.
What's the surface area of a cube using this calculator?
Enter the same value for length, width, and height — since all six faces of a cube are identical squares, the general formula simplifies to six times that shared edge length squared.