Rectangular Prism Volume: worked example
| Length | 6 |
|---|---|
| Width | 4 |
| Height | 3 |
| Volume | 72 |
| Surface area | 108 |
| Space diagonal | 7.8 |
Rectangular Prism Volume: formula
Enter the length, width and height of the box in the same unit, measuring the outside dimensions for surface coverings and the inside dimensions for capacity. If the box is a cube, enter the same number three times.
Rectangular Prism Volume: changing Length
| Length | Volume | Surface area | Space diagonal |
|---|---|---|---|
| 4.8 | 57.6 | 91.2 | 6.9 |
| 5.4 | 64.8 | 99.6 | 7.4 |
| 6 (example) | 72 | 108 | 7.8 |
| 6.6 | 79.2 | 116.4 | 8.3 |
| 7.2 | 86.4 | 124.8 | 8.8 |
Rectangular Prism Volume: compare input ranges
| Input | Tested from | To | Volume: low input | Volume: high input | Swing |
|---|---|---|---|---|---|
| Width | 3.6 | 4.4 | 64.8 | 79.2 | 14.4 (20%) |
| Length | 5.4 | 6.6 | 64.8 | 79.2 | 14.4 (20%) |
| Height | 2.7 | 3.3 | 64.8 | 79.2 | 14.4 (20%) |
Rectangular Prism Volume: individual input comparisons
| Input | Value | Volume | Surface area | Space diagonal |
|---|---|---|---|---|
| Length | 4.8 | 57.6 | 91.2 | 6.9 |
| 5.4 | 64.8 | 99.6 | 7.4 | |
| 6 | 72 | 108 | 7.8 | |
| 6.6 | 79.2 | 116.4 | 8.3 | |
| 7.2 | 86.4 | 124.8 | 8.8 | |
| Width | 3.2 | 57.6 | 93.6 | 7.4 |
| 3.6 | 64.8 | 100.8 | 7.6 | |
| 4 | 72 | 108 | 7.8 | |
| 4.4 | 79.2 | 115.2 | 8 | |
| 4.8 | 86.4 | 122.4 | 8.2 | |
| Height | 2.4 | 57.6 | 96 | 7.6 |
| 2.7 | 64.8 | 102 | 7.7 | |
| 3 | 72 | 108 | 7.8 | |
| 3.3 | 79.2 | 114 | 7.9 | |
| 3.6 | 86.4 | 120 | 8.1 |
Rectangular Prism Volume: combined input changes
| Length / Width | 3.2 | 4 | 4.8 |
|---|---|---|---|
| 4.8 | 46.1 | 57.6 | 69.1 |
| 5.4 | 51.8 | 64.8 | 77.8 |
| 6 | 57.6 | 72 | 86.4 |
| 6.6 | 63.4 | 79.2 | 95 |
| 7.2 | 69.1 | 86.4 | 103.7 |
Rectangular Prism Volume: which assumptions move the result?
Rectangular Prism Volume: values and definitions
| Quantity and definition | Value used |
|---|---|
| Length | 6 |
| Width | 4 |
| Height | 3 |
| Volume | 72 |
| Surface area | 108 |
| Space diagonal | 7.8 |
Rectangular Prism Volume: half and double Width
| Width | Volume |
|---|---|
| 2 | 36 |
| 4 | 72 |
| 8 | 144 |
Common error: Reading surface area as volume because both come from the same three numbers. One is measured in square units and the other in cubic units, and they answer different questions.
Wall thickness makes inside dimensions smaller than outside, so capacity is less than the outside volume. Rounded corners and lids reduce usable space. Units are cubed for volume, so convert every dimension to the same unit.
Irregular shapes need to be split into boxes.
Geometry calculators: Triangle Third Side Calculator, Arc Length and Sector Area Calculator, Ellipse Area Calculator, Pyramid Volume Calculator, Right Triangle & Pythagorean Calculator, Aquarium Volume Calculator.
A box has three numbers and three different jobs for them. Multiply all three for how much it holds. Add up its six faces for how much wrapping, paint or insulation covers it.
Take the diagonal for the longest straight object that fits inside. A 6 by 4 by 3 box holds 72 cubic units, needs 108 square units of surface and swallows a rod up to about 7.8 units long.
Use one unit for all three sides before you calculate. Mixing inches and feet gives a volume that is wrong by a factor no one will spot on sight.
Convert to gallons or liters on the unit conversion pages, calculate a cube on the cube calculator, and other solids on the cylinder, pyramid and triangular prism pages. The concrete and paint calculators in the trades categories use volume and area, and the pallet loading page packs boxes.
How do I calculate the volume of a box?
Multiply length by width by height. A 6 by 4 by 3 box holds 72 cubic units.
What is the space diagonal used for?
It is the longest straight line that fits inside the box, useful for checking whether a long item, such as a rod, will fit.
How do I find the surface area of a box?
Add the areas of the six faces: two of length times width, two of length times height and two of width times height.