What Is a Rectangular Prism?
A rectangular prism, also called a cuboid or rectangular box, is a three-dimensional solid bounded by six rectangular faces meeting at right angles. It is defined by three dimensions: length (\(l\)), width (\(w\)), and height (\(h\)). Everyday examples include boxes, bricks, books, and rooms. This calculator computes the volume, surface area, and the space diagonal from those three measurements.
How to Use the Calculator
Enter the length, width, and height of your prism using any consistent unit (cm, m, inches, etc.). The volume is returned in cubic units, the surface area in square units, and the space diagonal in the same linear units you entered. Make sure all three dimensions use the same unit so the results are meaningful.
The Formulas Explained
The volume is simply the product of the three sides: $$V = l \times w \times h.$$ The surface area sums the areas of all six faces. Opposite faces are equal, so $$SA = 2(lw + lh + wh).$$ The space diagonal — the straight line between two opposite corners — comes from the 3D Pythagorean theorem: $$d = \sqrt{l^2 + w^2 + h^2}.$$
Worked Example
Suppose a box measures \(l = 5\), \(w = 4\), and \(h = 3\). The volume is $$5 \times 4 \times 3 = 60 \text{ cubic units}.$$ The surface area is $$2(5 \times 4 + 5 \times 3 + 4 \times 3) = 2(20 + 15 + 12) = 2 \times 47 = 94 \text{ square units}.$$ The space diagonal is $$\sqrt{25 + 16 + 9} = \sqrt{50} \approx 7.07 \text{ units}.$$
FAQ
Is a cube a rectangular prism? Yes. A cube is a special rectangular prism where all three dimensions are equal.
What units does it use? Any unit works as long as all three dimensions share the same unit. Volume comes out in cubic units and surface area in square units.
What is the space diagonal? It is the longest straight line inside the prism, connecting two opposite vertices through the interior.
