Quick answer
A cuboid's surface area is 2(lw + lh + wh), its volume lwh and its space diagonal √(l² + w² + h²). For 2 × 3 × 4: surface area 52, volume 24 and diagonal 5.3852.
Enter length, width and height. The calculator returns surface area, volume and space diagonal.
Related tools: Surface Area Calculator: Surface area of a sphere, cube, cylinder, cone or box. Surface Area of a Cylinder Calculator: Surface area and volume of a cylinder. Hemisphere Surface Area Calculator: Curved and total surface area of a hemisphere.
How to use the Cuboid Surface Area 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 |
|---|---|
| Surface area | 52 |
| Volume | 24 |
| Space diagonal | 5.385165 |
Example 2
Inputs: Length = 1; Width = 1; Height = 1.
| Result | Value |
|---|---|
| Surface area | 6 |
| Volume | 1 |
| Space diagonal | 1.732051 |
The first line is the headline result (surface area). Below it the cuboid Surface Area Calculator lists volume and space diagonal, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Face by face
Three pairs of faces: 2 × 3 = 6, 2 × 4 = 8 and 3 × 4 = 12, each twice: 2 × (6 + 8 + 12) = 52. Painting or wrapping a box uses surface area; filling it uses volume.
Space diagonal
The longest straight line inside the box is √(4 + 9 + 16) = √29 = 5.385, which tells you whether a long rod fits. All dimensions must be positive 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 | Surface area | Volume | Space diagonal |
|---|---|---|---|
| 1 | 38 | 12 | 5.09902 |
| 2 | 52 | 24 | 5.385165 |
| 4 | 80 | 48 | 6.403124 |
| 8 | 136 | 96 | 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 Cuboid Surface Area 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 |
|---|---|---|
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Surface Area of a Cylinder Calculator](/math/surface-area-of-cylinder/) | radius and height | Surface area |
| [Hemisphere Surface Area Calculator](/math/area-of-hemisphere/) | radius | Curved surface area |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
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
Will a 5.3 unit rod fit in the box?
Yes, diagonally, as the diagonal is 5.385.
What is the difference from a cube?
A cube has all sides equal.
How much wrapping paper?
At least the surface area plus overlaps.
What does the Cuboid Surface Area Calculator calculate?
Surface area of a cuboid. It returns Surface area, Volume and Space diagonal.
What formula does the Cuboid Surface Area 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 cuboid Surface Area Calculator?
You enter Length, Width and Height.
What is an example of a cuboid Surface Area result?
With length 2, width 3 and height 4, the surface area is 52.
Related calculators
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Surface Area of a Cylinder Calculator — Surface area and volume of a cylinder.
- Hemisphere Surface Area Calculator — Curved and total surface area of a hemisphere.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Square Area Calculator — Area of a square.
- Parallelogram Area Calculator — Area of a parallelogram.
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.