Volume of a Hollow Rectangular Prism

This calculator finds the volume of the material (or the enclosed space) in a hollow rectangular prism, such as a pipe, a box with walls, or a concrete block. You enter the outer length, width, and height, plus the wall thickness (or inner dimensions), and you get the volume of the solid shell in cubic units. It also shows the inner volume and the total outer volume, so you can see how they relate.

Formula

The volume of a hollow rectangular prism is the difference between the outer prism and the inner cavity. If the outer dimensions are L, W, and H (length, width, height), and the walls are uniformly thick with thickness t, then:

Shell volume = (L × W × H) − ((L − 2t) × (W − 2t) × (H − 2t))

• L = outer length (m, ft, etc.)
• W = outer width (m, ft, etc.)
• H = outer height (m, ft, etc.)
• t = uniform wall thickness (same unit as L, W, H)

The inner dimensions are L − 2t, W − 2t, and H − 2t because the wall occupies thickness on both opposite sides. The formula assumes the wall is equally thick on all six faces and that the cavity is a smaller rectangular prism centered inside.

Worked Example

Using the default inputs: outer length = 2 m, outer width = 1 m, outer height = 0.5 m, wall thickness = 0.05 m.

1. Outer volume = 2 × 1 × 0.5 = 1.000 m³
2. Inner length = 2 − 2×0.05 = 1.90 m
3. Inner width = 1 − 2×0.05 = 0.90 m
4. Inner height = 0.5 − 2×0.05 = 0.40 m
5. Inner volume = 1.90 × 0.90 × 0.40 = 0.684 m³
6. Shell volume = 1.000 − 0.684 = 0.316 m³

The calculator shows 0.316 m³, matching the step-by-step result.

When to Use This Calculation

This is useful in construction, manufacturing, and packaging. For example, you might need to know how much concrete is in a hollow concrete block, how much plastic is in a molded box, or how much space is inside a shipping container. It also helps estimate material weight: multiply the shell volume by the material density (e.g., 2400 kg/m³ for concrete) to get mass.

You can also use it to find the inner capacity of a box with known wall thickness—just use the inner volume result. That’s the space available for storing liquids, powders, or goods.

How to Choose Your Inputs

Measure the outside dimensions of the prism, not the inside. Wall thickness must be uniform; if the walls vary, use the average or the thinnest value depending on whether you need a safe estimate. If you only know inner dimensions and wall thickness, you can still use the formula by adding 2t to each inner dimension to get the outer ones.

Make sure all lengths are in the same unit. If you mix meters and centimeters, the result will be wrong. For instance, 5 cm = 0.05 m, not 5.

Common Mistakes and Misconceptions

• Forgetting to subtract twice the thickness: A common error is using L − t instead of L − 2t. Remember the wall is on both sides.
• Using inner dimensions as outer: If you measure the inside of a box and call it L and W, you get the cavity volume, not the shell volume.
• Unit mix-ups: Mixing mm and m gives results off by a factor of 10³ or 10⁶. Convert everything to one unit first.
• Assuming the formula works for non-uniform walls: If the bottom is thicker than the sides, the simple formula under- or overestimates.

Limits of the Formula

The formula assumes a perfectly rectangular prism with straight, flat faces and uniform wall thickness. Real objects may have rounded corners, tapered walls, or internal ribs—those require more complex calculations or CAD software. Also, the volume of the shell is not the same as the volume of material if the material is porous (like some concretes) or if it has internal voids. For such cases, use the material’s apparent density.

Frequently Asked Questions

What is the difference between volume and capacity?
Volume is the amount of space an object occupies, while capacity usually refers to how much it can hold inside. For a hollow prism, the inner volume is the capacity. The shell volume is the volume of the material itself.

Can I use this for a pipe with a rectangular cross-section?
Yes. A rectangular tube (like a duct) is a hollow rectangular prism. Enter the outer dimensions and wall thickness, and you get the volume of the metal or plastic per unit length. To get volume per meter, set the height (or length) to 1 m.

What if I only know the inner dimensions?
Add twice the wall thickness to each inner dimension to get the outer dimensions, then use the formula. For example, inner 1.9 m × 0.9 m × 0.4 m with t = 0.05 m gives outer 2.0 × 1.0 × 0.5 m.

How do I convert the volume to weight?
Multiply the shell volume by the material’s density. For instance, steel has a density around 7850 kg/m³, so 0.316 m³ of steel would weigh about 2480 kg. Check the actual density for your material.

Does the formula work for any unit?
Yes, as long as all dimensions are in the same unit. If you use feet, the volume is in cubic feet. To convert to cubic meters, multiply by 0.0283168.

Why is the wall thickness subtracted twice?
Because each wall has an inside and an outside face. For the length, you remove the left wall and the right wall, so you subtract 2t. The same applies to width and height.

Related

• Trip Planner Mileage Calculator: How It Works
• EST to IST Converter: Time Made Simple
• Energy Efficiency Formula in Physics

in L | Outer length | m | 2 | 0
in W | Outer width | m | 1 | 0
in H | Outer height | m | 0.5 | 0
in t | Wall thickness | m | 0.05 | 0
out shell | Shell volume | m³ | (L*W*H) - ((L-2*t)*(W-2*t)*(H-2*t)) | 3
out inner | Inner volume | m³ | (L-2*t)*(W-2*t)*(H-2*t) | 3
out outer | Outer volume | m³ | L*W*H | 3