Quick answer
A rectangular prism has volume lwh, surface area 2(lw + lh + wh) and space diagonal √(l² + w² + h²). A 2 × 3 × 4 box has volume 24, surface area 52 and diagonal 5.3852.
Enter length, width and height. The calculator returns volume, surface area and space diagonal.
Related tools: Prism Volume Calculator: Volume of any prism from base area and height. Triangular Prism Volume Calculator: Volume of a triangular prism. Volume of a Hemisphere Calculator: Volume and surface area of a hemisphere.
How to use the Rectangular Prism Volume Calculator
- Enter length (above 0).
- Enter width (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Length | A number | > 0 |
| Width | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
V = lwh; SA = 2(lw + lh + wh); space diagonal = √(l² + w² + h²)
IEEE-754 double precision; shown to at most 6 decimal places.
Standard rectangular prism formulas.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Length = 2; Width = 3; Height = 4.
| Result | Value |
|---|---|
| Volume | 24 |
| Surface area | 52 |
| Space diagonal | 5.385165 |
Example 2
Inputs: Length = 1; Width = 1; Height = 1.
| Result | Value |
|---|---|
| Volume | 1 |
| Surface area | 6 |
| Space diagonal | 1.732051 |
The first line is the headline result (volume). Below it the rectangular Prism Volume Calculator lists surface area and space diagonal, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Reading the result
Volume 2 × 3 × 4 = 24 cubic units. The six faces total 2 × (6 + 8 + 12) = 52. A rod up to 5.385 units fits corner to corner.
Applications
Shipping boxes, tanks and rooms. Convert cubic feet to cubic yards by dividing by 27, and cubic centimetres to litres by dividing by 1,000. Dimensions must be positive and in one unit.
How the result changes with length
Holding every other input at the first worked example, this table changes only length. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Length | Volume | Surface area | Space diagonal |
|---|---|---|---|
| 1 | 12 | 38 | 5.09902 |
| 2 | 24 | 52 | 5.385165 |
| 4 | 48 | 80 | 6.403124 |
| 8 | 96 | 136 | 9.433981 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Length: entering "0" shows "Length must be greater than 0." beside that field and no result.
Choosing between the Rectangular Prism Volume Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Prism Volume Calculator](/math/prism-volume-calculator/) | base area and height | Volume |
| [Triangular Prism Volume Calculator](/math/triangular-prism/) | triangle base, triangle height and prism length | Volume |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | radius | Volume |
| [Aquarium Tank Volume Calculator](/math/aquarium-tank-volume-calculator/) | length, width and water height | Volume |
| [Cylinder Volume Calculator](/math/cylinder-volume-calculator/) | radius and height | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive dimensions
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for length to confirm this.
Frequently asked questions
What is the volume of a 10 × 10 × 10 box?
A 10 × 10 × 10 box has volume 1,000 cubic units and surface area 600.
Is it the same as a cuboid?
Yes. A rectangular prism is the same solid as a cuboid.
How do I find height from volume?
Divide by length × width.
What does the Rectangular Prism Volume Calculator calculate?
Volume of a rectangular prism (box). It returns Volume, Surface area and Space diagonal.
What formula does the Rectangular Prism Volume Calculator use?
V = lwh; SA = 2(lw + lh + wh); space diagonal = √(l² + w² + h²). Standard rectangular prism formulas.
What do I need to enter in the rectangular Prism Volume Calculator?
You enter Length, Width and Height.
What is an example of a rectangular Prism Volume result?
With length 2, width 3 and height 4, the volume is 24.
Related calculators
- Prism Volume Calculator — Volume of any prism from base area and height.
- Triangular Prism Volume Calculator — Volume of a triangular prism.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- Aquarium Tank Volume Calculator — Volume of a rectangular tank in litres and US gallons.
- Cylinder Volume Calculator — Volume of a cylinder.
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Polar to Rectangular Converter — x and y from radius and angle.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.