120
units³
158
units²
9.8995
units
120
units³
158
units²
9.8995
units
The Rectangular Prism Calculator computes the volume, surface area, and space diagonal of a rectangular prism (also called a cuboid or rectangular box). A rectangular prism is a three-dimensional solid with six rectangular faces, where opposite faces are congruent and parallel. It is the most common solid shape encountered in everyday life—from shipping boxes to rooms to bricks.
Given length $$l$$, width $$w$$, and height $$h$$:
Volume:
$$V = l \times w \times h$$
The volume equals the product of the three edge lengths. It measures how much space the box encloses.
Surface Area:
$$SA = 2(lw + lh + wh)$$
The surface area sums all six rectangular faces. There are three pairs of congruent opposite faces: two of area $$lw$$, two of area $$lh$$, and two of area $$wh$$.
Space Diagonal:
$$d = \sqrt{l^2 + w^2 + h^2}$$
The space diagonal connects two opposite vertices through the interior of the prism. It is derived by applying the Pythagorean theorem in three dimensions. First, the base diagonal is $$\sqrt{l^2 + w^2}$$, then the space diagonal extends this by the height: $$d = \sqrt{(\sqrt{l^2 + w^2})^2 + h^2} = \sqrt{l^2 + w^2 + h^2}$$.
When all three dimensions are equal ($$l = w = h = a$$), the rectangular prism becomes a cube, and the formulas simplify to $$V = a^3$$, $$SA = 6a^2$$, $$d = a\sqrt{3}$$. When one dimension is very small compared to the others, the prism approximates a flat rectangular plate or slab.
Shipping and logistics: Dimensional weight (DIM weight) for freight pricing is based on the volume of the rectangular prism that encloses a package. Carriers use $$l \times w \times h$$ divided by a DIM factor to calculate billable weight.
Construction: Concrete volume for slabs, footings, and walls is calculated as rectangular prism volumes. A slab 10 m × 8 m × 0.15 m requires 12 m³ of concrete.
Interior design: Room volumes ($$l \times w \times h$$) determine HVAC sizing, since air conditioning capacity must match the volume of air to be cooled or heated.
Aquariums: The volume of a rectangular tank gives its water capacity. A 60 × 30 × 40 cm tank holds 72,000 cm³ = 72 liters.
Enter length, width, and height to compute all three properties at once.
Enter the three dimensions of the rectangular prism: length, width, and height. The calculator multiplies them for volume, sums the three face-pair areas for surface area, and applies the 3D Pythagorean theorem for the space diagonal.
Volume is in cubic units (e.g., m³, cm³). Surface area is in square units (e.g., m²). The space diagonal is the longest straight line that fits inside the box—useful for determining whether a long object (like a rod or a TV) can fit diagonally inside.
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A 60×40×30 cm box has volume 72,000 cm³ (72 liters), surface area 10,800 cm², and space diagonal ≈78.1 cm—meaning a 75-cm rod will not fit diagonally.
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A room 5×4×2.7 m has 54 m³ of air volume. Standard HVAC sizing uses approximately 30–40 BTU per m³.
They are the same shape. "Rectangular prism" is the term commonly used in American mathematics education, while "cuboid" is preferred in British English and many international textbooks.
Volume alone is insufficient—infinitely many combinations of $$l$$, $$w$$, $$h$$ produce the same volume. You need at least two additional constraints (e.g., ratios between dimensions or specific surface area).
The space diagonal $$d = \sqrt{l^2 + w^2 + h^2}$$ gives the length of the longest straight rod that fits inside. This is why the calculator computes it.
DIM weight = $$\frac{l \times w \times h}{\text{DIM factor}}$$. Common DIM factors are 5000 (cm/kg) or 139 (in/lb). The billable weight is the greater of actual weight and DIM weight.
Yes, by definition. A rectangular prism has six rectangular faces meeting at right angles. If the faces are not rectangles or the angles are not 90°, it is a more general parallelepiped.
If dimensions are in cm: divide volume in cm³ by 1000 for liters. If in inches: divide volume in in³ by 231 for US gallons. If in m: multiply m³ by 1000 for liters.
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