Volume
V = lwh
Volume is base area lw multiplied by perpendicular height.
Rectangular Prism Calculator — Volume, Surface Area and Diagonal
Enter the Prism Dimensions
Rectangular Prism Results
Volume (V)—
Total surface area (SA)—
Space diagonal (d)—
Base area (lw)—
Lateral surface area—
Total edge length—
Base face diagonal—
l × h face diagonal—
w × h face diagonal—
Circumsphere radius—
Enter valid dimensions to see the formula substitutions.
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Rectangular Prism Formulas
A rectangular prism, cuboid, or rectangular box has length l, width w, and perpendicular height h. Opposite faces are congruent rectangles.
Total surface area
SA = 2(lw + lh + wh)
There are two faces of each size: l × w, l × h, and w × h.
Space diagonal
d = √(l² + w² + h²)
This is the straight-line distance between opposite vertices through the prism.
Lateral surface area
LSA = 2h(l + w)
This counts the four side faces and excludes the two l × w bases.
Face diagonals
dlw = √(l² + w²)
Similarly, dlh = √(l² + h²) and dwh = √(w² + h²).
Total edge length
E = 4(l + w + h)
A rectangular prism has four edges of each dimension.
Assumptions: All faces are rectangles, adjacent edges meet at right angles, and length times width is the chosen base. A zero dimension produces a degenerate shape, so this calculator requires all dimensions to be greater than zero.
How to Use the Rectangular Prism Calculator
- Enter the prism’s positive length, width, and perpendicular height.
- Choose a unit for each input. Mixed units are supported and converted before the formulas are applied.
- Choose the output unit and rounding precision, then select Calculate prism.
- Review the results and formula substitutions, or copy the summary and download a CSV file.
The result unit is squared for areas and cubed for volume. Changing an input unit reinterprets that input’s number; it does not rewrite the number in the field.
Worked Rectangular Prism Examples
5 cm × 4 cm × 3 cm prism
V = 5 × 4 × 3 = 60 cm³.
SA = 2(20 + 15 + 12) = 94 cm², and d = √50 ≈ 7.071 cm.
18 in × 12 in × 8 in box
V = 18 × 12 × 8 = 1,728 in³.
SA = 2(216 + 144 + 96) = 912 in².
Mixed-unit prism
2 m × 75 cm × 500 mm becomes 2 m × 0.75 m × 0.5 m.
The volume is 0.75 m³ and the surface area is 5.75 m².
Common Rectangular Prism Mistakes
Adding dimensions for volume
Volume multiplies all three dimensions: lwh. Adding them is part of the total edge-length formula, not volume.
Counting only three faces
lw + lh + wh counts one face of each size. Multiply by two to include the opposite faces.
Mixing units before multiplying
Convert dimensions to compatible units first. The calculator does this automatically using each input’s unit selector.
Rectangular Prism Calculator FAQs
How do you find the volume of a rectangular prism?
Multiply length by width by height: V = lwh. Convert the three measurements to compatible length units before multiplying.
How do you find the surface area of a rectangular prism?
Add the areas of all six faces: SA = 2(lw + lh + wh). Each pair of opposite rectangular faces has the same area.
How do you find the diagonal of a rectangular prism?
The corner-to-corner space diagonal is d = √(l² + w² + h²).
What is the lateral surface area of a rectangular prism?
When l × w is treated as the base, lateral surface area is the area of the four side faces: LSA = 2h(l + w).
Can the calculator use different units for length, width, and height?
Yes. Each dimension has its own metric or imperial unit selector. The calculator converts all three to the selected output unit before applying the formulas.
Is a rectangular prism the same as a cuboid?
Yes. A rectangular prism is also commonly called a cuboid or rectangular box. All six faces are rectangles and opposite faces are congruent.
Are my dimensions uploaded or saved?
No. The calculation runs locally in your browser and does not send or save your dimensions.
Calculation Notes
Last reviewed: July 30, 2026 by the Starlight Tools editorial team.
The calculator uses standard Euclidean geometry and exact metric-to-imperial conversion factors. Unrounded values are used throughout; the decimal-place setting affects display only. Inputs outside a conservative browser-number range are rejected to prevent overflow or underflow in squared and cubed results.