What Is the Surface Area of a Rectangular Prism?
A rectangular prism, also called a cuboid, is a six-sided box where every face is a rectangle and opposite faces are equal. Its surface area is the total area of all six faces added together. This calculator instantly computes that total from the box'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 (\(h\)) — in any single unit of measurement (cm, m, inches, feet). The result is returned in square units of that same measurement. For example, if you enter centimeters, the surface area is in square centimeters and the volume in cubic centimeters.
The Formula Explained
The surface area formula is $$A = 2(lw + lh + wh)$$ A rectangular prism has three distinct pairs of identical faces: the two \(l \times w\) faces (top and bottom), the two \(l \times h\) faces (front and back), and the two \(w \times h\) faces (left and right). Summing one of each pair gives \(lw + lh + wh\), and multiplying by 2 accounts for both faces in each pair.
Worked Example
Suppose a box measures \(l = 5\), \(w = 4\), and \(h = 3\). Then \(lw = 20\), \(lh = 15\), and \(wh = 12\). Their sum is 47, and doubling it gives $$A = 2 \times 47 = 94 \text{ square units}$$ The volume is \(5 \times 4 \times 3 = 60\) cubic units.
FAQ
What units does the result use? Whatever unit you input — surface area comes out in those units squared, volume in those units cubed.
Is a cube a rectangular prism? Yes. A cube is a special case where \(l = w = h\), giving \(A = 6s^2\) for side length \(s\).
What is the difference between surface area and volume? Surface area measures the outer skin you would paint or wrap (square units); volume measures the space inside the box (cubic units).
