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How to use
A rectangular prism is a box with three independent edge lengths. With length, width and height the tool returns volume, total surface, space diagonal, base area, lateral area and total edge length. You can also supply a known volume instead of height to recover the missing height.
- Choose direct dimensions or known-volume mode.
- Enter length and width plus height or volume in a consistent base unit.
- Calculate; volume mode first recovers the height.
- Review volume, areas, diagonal and edge length with correct unit powers.
How it is calculated
Example
Example: a 6×4×3 cm box has volume 72 cm³, total surface 108 cm² and space diagonal √61 ≈ 7.810 cm. With volume 72, length 6 and width 4, the inverse mode recovers height 3.
Important notes
Use one underlying length unit. Volume is cubic and areas are squared. A rectangular prism is only a cube when all three dimensions are equal.
Worked examples and interpreting results
A rectangular box measuring 2 by 3 by 6 cm has volume 36 cm³, total surface area 72 cm² and space diagonal 7 cm. Volume multiplies three perpendicular dimensions rather than adding them.
| Case | Calculation | Result |
|---|---|---|
| Volume | 2 × 3 × 6 | 36 cm³ |
| Area of all six faces | 2 × (2×3 + 2×6 + 3×6) | 72 cm² |
| Space diagonal | √(2² + 3² + 6²) | 7 cm |
How to check the result
Total surface area assumes a closed box with six faces. Capacity needs internal dimensions. Convert all lengths to the same unit before multiplying to avoid mixing centimeters and meters in one volume.
Frequently asked questions
Face diagonal or space diagonal?
A face diagonal uses two dimensions; the space diagonal joins opposite corners through the solid and uses all three.
Can height be found from volume?
Yes, with positive known length and width: h=V÷(lw).
Does total surface include top and bottom?
Yes. It sums all six faces.