Calculate the volume, surface area, face areas, face diagonals, space diagonal, and lateral area of a rectangular prism (box). Includes unit selector, presets, and reference table.
<p>The <strong>Rectangular Prism Volume Calculator</strong> computes the volume and all related measurements of a rectangular prism—also known as a cuboid or simply a box. Enter the length, width, and height, and the tool instantly returns the volume, total surface area, lateral area, individual face areas, face diagonals, and the space diagonal.</p> <p>Rectangular prisms are among the most common shapes in daily life. Shipping boxes, rooms, bricks, refrigerators, and storage containers are all rectangular prisms. Knowing their volume is essential for packing, shipping cost estimation, material ordering, and interior design. Surface area matters when you need to wrap, paint, or coat a box, while the space diagonal tells you the longest item that can fit diagonally inside.</p> <p>This calculator supports six common unit systems—millimeters, centimeters, inches, feet, meters, and yards—so you can work in whatever measurement system your project requires. Eight presets let you quickly load real-world examples like a shoebox, shipping box, room, or concrete slab. A visual bar chart compares the three face areas and four diagonals, and a reference table shows volumes of common everyday objects for context.</p> <p>All formulas are transparent: Volume = l × w × h, Surface Area = 2(lw + lh + wh), Space Diagonal = √(l² + w² + h²). Results update instantly as you type, making it fast to experiment with different dimensions.</p>
This calculator is useful when the main question starts with capacity but quickly expands into related box measurements. In one step you can check how much a prism holds, how much exterior material it needs, and how its faces and diagonals compare. That is valuable for shipping cartons, storage bins, room layouts, concrete pours, and manufacturing jobs where changing one dimension affects several downstream quantities.
Volume = l × w × h. Surface Area = 2(lw + lh + wh). Lateral Area = 2h(l + w). Space Diagonal = √(l² + w² + h²). Total Edge Length = 4(l + w + h).
Result: Volume = 7,776 in³, Surface Area = 2,376 in², Space Diagonal ≈ 34.99 in
For a 24 × 18 × 18 shipping box, volume is 24 × 18 × 18 = 7,776 in³. Surface area is 2(24×18 + 24×18 + 18×18) = 2(432 + 432 + 324) = 2,376 in². The space diagonal is √(24² + 18² + 18²) = √1,224 ≈ 34.99 in.
For a rectangular prism, volume answers the question of internal capacity, but it rarely stands alone. A box that holds a certain amount may still need a specific amount of cardboard, insulation, paint, or shelf space. That is why the related outputs in this calculator matter: surface area, lateral area, face areas, and diagonals all describe a different practical aspect of the same shape. Using them together gives a fuller picture than volume alone.
The face-area bars help you see which pair of faces dominates the prism. That is useful when choosing the orientation of a package label, deciding which side of a storage box rests on a shelf, or estimating exposure for heat transfer and coating. The diagonal comparison is equally practical. Base, front, and side diagonals describe the longest straight path across each face, while the space diagonal shows the longest object that can fit inside from corner to corner.
Rectangular prism calculations show up in warehouse planning, room design, cabinet building, product packaging, and material takeoffs. A contractor may estimate concrete or fill volume, a shipper may check carton size and internal clearance, and a teacher may use a simple box to introduce 3D measurement concepts. Because the formulas update instantly here, it is easy to test dimension changes and see which measurement is most sensitive to a design adjustment.
A rectangular prism (cuboid) is a 3D shape with six rectangular faces, 12 edges, and 8 vertices. All angles are right angles.
Surface area alone is not enough—you need at least two of the three dimensions plus one equation. Use known constraints to solve the system.
Surface area includes all six faces. Lateral area includes only the four side faces, excluding the top and bottom.
Yes—enter the same value for length, width, and height, and it works for a cube. Use this as a practical reminder before finalizing the result.
Enter dimensions in the desired unit. For example, enter cm for cm³ output, or switch to inches for in³.
It tells you the longest straight object that can fit diagonally inside the box—useful for packaging rods, pipes, or umbrellas. Keep this note short and outcome-focused for reuse.