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Rectangular prism (cuboid) - area and volume

 

Online calculator — enter the values and get the result instantly, with the formula and a worked example.

Photo
Rectangular prism
Formula & notes
A=2·(a·b+b·c+c·a) V=a·b·c

A = Area

V = volume

a = side "a"

b = side "b"

c = side "c"

What is it?

A rectangular prism, also called a cuboid, is a three-dimensional solid bounded by six flat faces that are all rectangles. It has twelve edges and eight vertices, and exactly three edges meet at every corner. Opposite faces are congruent and parallel, so the shape is fully described by just three measurements: its length, width, and height. Every angle where faces or edges meet is a right angle, which gives the prism its neat, box-like regularity. When all three dimensions happen to be equal, the rectangular prism becomes a cube, its most symmetric special case. This is one of the most common shapes in everyday life, appearing in bricks, cardboard boxes, books, rooms, shipping containers, and countless packaged products. Because it is so easy to measure and stack, it is a favourite in engineering, architecture, and logistics, where knowing its volume and surface area helps with packing, material estimates, and design.

Calculator
cm
cm
cm

Volume V

Surface area S

Space diagonal u

Sum of edges
Dimensions a · b · c
Interactive graph

Drag the point a · b · c Re-center

a b c

Discover more
Worked example

The side a of the cuboid is, for example, 8 cm, side b is, for example, 6 cm, and side c is 4 cm.

Thus

a = 8,

b = 6,

c = 4

area of the cuboid:

We use the formula

A = 2(ab) + 2(bc) + 2(ca)

thus

A = 2(8*6) + 2(6*4) + 2(4*8)

A = 208 cm²

volume of the cuboid:

We use the formula

V = a * b * c

thus

V = 8 * 6 * 4

V = 192 cm³



 

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