Rectangular Prism Calculator

Built and fact-checked by the DocNectar team — see our editorial standards

Thanks for rating!

Key Features

Instant Calculation

Get accurate results in real time with our optimized algorithm.

Mobile Friendly

Fully responsive design. Works on all devices & screen sizes.

Privacy Focused

Your data stays on your device. We don't store any inputs.

100% Free

No hidden costs. This tool is completely free forever.

A rectangular prism (also called a cuboid or a box) is fully described by just three numbers — its length, width, and height — from which volume, total surface area, and the space diagonal all follow directly. This is one of the most practically useful 3D shape calculators there is: shipping boxes, rooms, shelving units, aquariums, and storage containers are all rectangular prisms, and knowing the volume (for capacity), surface area (for materials like paint, wrapping, or cardboard), and diagonal (for checking if something long will fit inside) covers most everyday sizing questions.

How it works

Enter length (l), width (w), and height (h). Volume is simply the product of all three dimensions, V = lwh. Surface area sums the areas of all six rectangular faces — there are three pairs of matching opposite faces (top/bottom = lw each, front/back = lh each, left/right = wh each) — giving A = 2(lw+lh+wh). The space diagonal, running corner-to-corner through the box's interior, comes from applying the Pythagorean theorem twice: first finding the diagonal across the base, then combining that with the height, giving d = √(l²+w²+h²).

Enter length.
Enter width.
Enter height.
Click Calculate to see your results.

Examples

l=5, w=4, h=3

V = 5×4×3 = 60. A = 2(5×4+5×3+4×3) = 2(20+15+12) = 2(47) = 94. d = √(25+16+9) = √50 ≈ 7.07.

l=10, w=10, h=2 (a shallow, wide box)

V = 10×10×2 = 200. A = 2(100+20+20) = 280. d = √(100+100+4) = √204 ≈ 14.28.

Common mistakes to avoid

Swapping length/width/height values, which doesn't change volume or diagonal but can cause confusion about which faces the surface-area terms represent.
Forgetting the factor of 2 in the surface area formula (computing only half the actual surface area).
Using the space diagonal formula for just the base diagonal (forgetting the height term) by mistake.

Frequently asked questions

A cube is a special rectangular prism where length, width, and height are all equal — this tool handles the general case where they can all differ, which is the more common real-world scenario for boxes and rooms.

A box has six faces, but they come in three matching pairs (top/bottom, front/back, left/right); each pair shares the same area (lw, lh, or wh), so instead of summing six terms, the formula sums the three unique pair-areas and doubles the total.

It tells you the longest straight line that fits inside the box — useful for checking whether a rod, pole, or other elongated object of a given length can fit diagonally inside a container even if it's too long to fit along any single edge.

Not for the final volume, surface area, or diagonal values, since all three formulas treat l, w, and h symmetrically — but it does matter if you're trying to identify which physical face of the box corresponds to which pair of dimensions.

Free Rectangular Prism Calculator