Rectangular Prism Calculator
A 2 by 3 by 4 rectangular prism has a volume of 24 and a surface area of 52. This rectangular prism calculator finds the volume, total surface area, lateral surface area, and space diagonal of a box from its length, width, and height. A rectangular prism is also called a cuboid. Enter the three dimensions to get every result at once.
Quick answer
Volume is the space inside the prism, found by multiplying length, width, and height.
What this tells you
- •Volume is the space inside the prism, found by multiplying length, width, and height.
- •Surface area is the total area of all six faces.
- •The space diagonal is the straight-line distance between two opposite corners.
- •Results are rounded to 4 decimal places.
How to Use
- 1Enter the length of the rectangular prism.
- 2Enter the width and the height in the same units.
- 3Click Calculate to get the volume, surface area, lateral surface area, and diagonal.
How It Works
Formula
V = l x w x h, SA = 2(lw + lh + wh), diagonal = sqrt(l^2 + w^2 + h^2)Volume multiplies the three dimensions together. Surface area adds the areas of the three distinct face pairs and doubles the total. The space diagonal uses the 3D Pythagorean theorem on the length, width, and height. For a 2 by 3 by 4 prism, the volume is 24, the surface area is 52, and the diagonal is about 5.39.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Volume and surface area of a 2 x 3 x 4 prism
Volume is 2 x 3 x 4 = 24. Surface area is 2 x (2x3 + 2x4 + 3x4) = 2 x 26 = 52. The space diagonal is the square root of (4 + 9 + 16), which is about 5.39.
A cube with 5-unit sides
A cube is a rectangular prism with equal sides. Volume is 5 x 5 x 5 = 125, and surface area is 6 x (5 x 5) = 150.
Example Rectangular Prisms
Volume and surface area for sample dimensions.
| Length x Width x Height | Volume | Surface Area |
|---|---|---|
| 2 x 3 x 4 | 24 | 52 |
| 5 x 5 x 5 | 125 | 150 |
| 10 x 4 x 2 | 80 | 136 |
| 1 x 1 x 1 | 1 | 6 |
Common mistakes
- Confusing volume with surface area. Volume measures the space inside in cubic units, while surface area measures the outside faces in square units.
- Forgetting to use the same units for all three dimensions. Mixing inches and feet gives a wrong result, so convert everything to one unit first.
- Using the face diagonal instead of the space diagonal. The space diagonal goes corner to corner through the prism and uses all three dimensions, not just two.