What Is the Surface Area of a Rectangular Prism?
A rectangular prism (also called a cuboid) is a three-dimensional box-shaped solid with six rectangular faces. Its surface area is the total area of all six faces added together. This calculator computes that total instantly from the prism's length, width, and height, and also reports the volume for convenience.
How to Use the Calculator
Enter the three dimensions of your box — length (\(l\)), width (\(w\)), and height (\(h\)) — using any consistent unit (cm, m, inches, etc.). The result is given in square units of whatever unit you used. For example, dimensions in centimeters yield a surface area in square centimeters (cm²).
The Formula Explained
A rectangular prism has three pairs of identical faces. One pair has area \(l \times w\), another \(l \times h\), and the third \(w \times h\). Summing one of each and doubling gives the full surface area:
$$A = 2(lw + lh + wh)$$
This accounts for the front and back, top and bottom, and the two sides of the box.
Worked Example
Suppose a box is 5 units long, 4 units wide, and 3 units tall. Then:
\(lw = 5 \times 4 = 20\), \(lh = 5 \times 3 = 15\), \(wh = 4 \times 3 = 12\). Sum \(= 47\). Surface area \(= 2 \times 47 =\) 94 square units. Its volume is \(5 \times 4 \times 3 = 60\) cubic units.
FAQ
What's the difference between surface area and volume? Surface area measures the total outer skin (in square units); volume measures the space inside (in cubic units).
Does a cube use the same formula? Yes. A cube is a special prism where \(l = w = h = s\), so \(A = 6s^2\).
What units does the result use? Whatever unit you input, squared. Inputs in meters give a surface area in square meters.
