Rectangular Prism Calculator
Enter the length, width, and height to calculate volume, surface area, lateral area, and diagonal of a rectangular prism (cuboid).
What Is a Rectangular Prism?
A rectangular prism is a 3D shape with six rectangular faces, twelve edges, and eight vertices. You might also hear it called a cuboid or a box-shaped solid. Common real-world examples include shipping boxes, books, refrigerators, and storage bins.
If you need to find the volume of a box, the surface area of a cuboid, or the longest inside diagonal, this rectangular prism calculator gives fast and accurate results.
Formulas Used in This Calculator
1) Volume
Volume tells you how much 3D space the prism occupies.
- Formula: V = l × w × h
- Units: cubic units (for example cm3, m3, ft3)
2) Total Surface Area
Surface area is the total area of all six faces combined.
- Formula: SA = 2(lw + lh + wh)
- Units: square units (for example cm2, m2, ft2)
3) Lateral Surface Area
Lateral area includes the four side faces and excludes top and bottom.
- Formula: LSA = 2h(l + w)
4) Space Diagonal
The space diagonal is the line from one corner of the prism to the opposite corner through the interior.
- Formula: d = √(l2 + w2 + h2)
How to Use the Rectangular Prism Calculator
- Enter the prism’s length, width, and height.
- Select a unit like cm, m, in, or ft.
- Click Calculate to get all measurements instantly.
- Use Clear to reset and start a new calculation.
Worked Example
Suppose a box has:
- Length = 10 cm
- Width = 6 cm
- Height = 4 cm
Then:
- Volume = 10 × 6 × 4 = 240 cm3
- Surface Area = 2(60 + 40 + 24) = 248 cm2
- Lateral Surface Area = 2 × 4 × (10 + 6) = 128 cm2
- Space Diagonal = √(102 + 62 + 42) = 12.33 cm (approx.)
Where This Calculator Is Useful
Packaging and Shipping
Estimate carton volume for freight pricing and compare package dimensions for storage efficiency.
Construction and Design
Compute space, material coverage, and interior dimensions for cabinets, tanks, and rooms.
Education and Homework
Great for geometry practice when checking cuboid formulas and understanding dimension relationships.
Common Mistakes to Avoid
- Mixing units (for example, using cm for one side and m for another without converting).
- Using negative numbers or zero for dimensions.
- Confusing square units and cubic units.
- Rounding too early in multi-step calculations.
Quick FAQ
Is a rectangular prism the same as a cube?
A cube is a special rectangular prism where all three dimensions are equal.
Can I use decimal values?
Yes. The calculator supports integers and decimals for all dimensions.
Do I need all three dimensions?
Yes. Length, width, and height are all required to compute full prism properties.
Final Note
This rectangular prism calculator is a fast way to compute box geometry, whether you are solving math problems, planning storage, or estimating project materials. Save this page whenever you need a reliable cuboid volume and surface area tool.