Calculate volume, surface area (total and lateral), face diagonals, and space diagonal of a rectangular prism (cuboid). Includes presets for common boxes, rooms, and shipping containers.
A rectangular prism — also called a cuboid or rectangular box — is a three-dimensional solid bounded by six rectangular faces. Every pair of opposite faces is congruent and parallel, and all internal angles are right angles. It is arguably the most common 3D shape in everyday life: shipping boxes, rooms, refrigerators, books, and bricks are all rectangular prisms.
The volume is simply length × width × height (V = lwh). The total surface area sums all six faces: SA = 2(lw + lh + wh). The lateral surface area excludes the top and bottom: LSA = 2h(l + w). These formulas are essential in packaging, construction, logistics, and storage planning.
Rectangular prisms have three distinct face diagonals — one per pair of faces — and a single space diagonal that runs from one corner to the opposite corner through the interior. The space diagonal is d = √(l² + w² + h²) and is the longest straight distance inside the box.
When all three dimensions are equal (l = w = h), the shape becomes a cube. When only two dimensions match, you have a square prism. This calculator takes length, width, and height as inputs and computes volume, all surface areas, every diagonal, and additional properties like the circumsphere radius. Presets for everyday objects — from shoeboxes to shipping containers — and a reference table let you compare those measurements against familiar examples.
A rectangular prism often needs more than one answer at the same time: capacity for storage, total area for wrapping or paint, and diagonal length for fit checks. This calculator keeps those measurements tied to the same dimensions, so you do not have to recompute the solid through several separate formulas. It is useful for packaging decisions, room planning, construction estimates, shipping, and geometry work where a box-shaped solid must be analyzed from several angles at once.
Volume: V = l × w × h
Total Surface Area: SA = 2(lw + lh + wh)
Lateral Surface Area: LSA = 2h(l + w)
Face Diagonal (l×w): d₁ = √(l² + w²)
Face Diagonal (l×h): d₂ = √(l² + h²)
Face Diagonal (w×h): d₃ = √(w² + h²)
Space Diagonal: d = √(l² + w² + h²)
Circumsphere Radius: R = d / 2Result: Volume = 11,250 cm³, Total Surface Area = 3,150 cm², Space Diagonal ≈ 41.83 cm
For a 30 × 25 × 15 rectangular prism, the volume is 30 × 25 × 15 = 11,250 cm³. The total surface area is 2(30×25 + 30×15 + 25×15) = 2(750 + 450 + 375) = 3,150 cm². The space diagonal is √(30² + 25² + 15²) = √1,750 ≈ 41.83 cm.
Rectangular prisms invite several different questions, and each one points to a different formula. If you want to know how much the box can hold, volume is the right measure. If you are wrapping, painting, laminating, or insulating the outside, surface area matters instead. If you only care about the side walls, lateral surface area is the useful figure. Keeping those measurements separate prevents the common mistake of using the right dimensions with the wrong formula.
The diagonal measurements are more than geometry extras. A face diagonal tells you the longest straight line that fits across one face, which is helpful for braces, panels, or cuts across a rectangular sheet. The space diagonal goes corner to corner through the interior and tells you whether a long object can fit inside the box at an angle. That is important when checking luggage, shelving, packaging inserts, or equipment storage.
Because this calculator also identifies cubes and square prisms, it helps you recognize when a special case simplifies the geometry. A cube has equal edges and matching face diagonals everywhere, while a square prism has one repeated side pair and a different height. Those distinctions matter when comparing storage containers, designing product packaging, estimating coating materials, or analyzing room dimensions in building and remodeling work.
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Volume = length × width × height (V = lwh). All three dimensions are multiplied together.
Space diagonal = √(l² + w² + h²). It runs from one corner to the diagonally opposite corner through the interior.
Total surface area counts all six faces. Lateral surface area counts only the four vertical faces (excluding the top and bottom), useful for wrapping or painting walls.
Yes. Cuboid and rectangular prism are synonyms. Both refer to a box-shaped solid with six rectangular faces and right angles.
If you know two dimensions, divide the volume by their product to find the third: h = V / (l × w). With only volume, you need at least two measurements or ratios.
Absolutely. Rooms, containers, tanks, and storage units are all rectangular prisms. Use the presets for common sizes.
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