Geometry desk
Rectangular Prism Volume Calculator
Calculate a rectangular prism's volume from length, width, and height.
Rectangular Prism Volume Calculator: Find the space occupied by a box-shaped solid from its length, width and height. Enter three perpendicular dimensions to compare cuboid volumes or estimate the internal capacity of a rectangular container when you have measured its inside dimensions. Runs 100% locally in your browser with zero server file uploads.
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- Calculators
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- Free · no sign-up
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Volume
384 cm³
Volume = length × width × height- All three dimensions are mutually perpendicular.
- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Volume = length × width × height
A worked example with sample values:
| Inputs | |
|---|---|
| Length | 12 cm |
| Width | 8 cm |
| Height | 4 cm |
| Results | |
|---|---|
| Volume | 384 cm³ |
Rows, columns and layers of cubes
For length L, width W and height h, volume V = L × W × h. The bottom layer covers L × W square units. Stacking such layers through the height produces cubic units. This model assumes a constant rectangular cross-section and right angles between the three dimensions; an irregular parcel may not fill its enclosing cuboid.
Take length 12 cm, width 8 cm and height 4 cm. First compute the base area: 12 × 8 = 96 cm². Multiply by the height: 96 × 4 = 384 cm³. The result sheet displays Volume = 384 cm³. Written as litres, this is 384 ÷ 1,000 = 0.384 litres.
OpenStax presents rectangular-solid volume (https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area) as a product of three perpendicular lengths. Reordering the dimensions leaves their product unchanged.
Mixed measurements and cubic conversions
If a box measures 0.12 m by 8 cm by 40 mm, convert it to 12 by 8 by 4 cm before entering those numbers with cm selected. A cubic metre contains 100 × 100 × 100 = 1,000,000 cubic centimetres, so the example is 0.000384 m³. A length conversion factor must be cubed when converting a finished volume. Doubling only one side doubles the capacity; doubling all three sides makes eight times the volume. The unit selector does not rewrite existing numbers, so update every dimension when switching measurement scales.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
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Frequently asked questions
Do I measure inside or outside a rectangular container?
Inside dimensions give usable geometric capacity; outside dimensions give the enclosing box volume. The calculator does not subtract walls, handles or compartments. Measure the dimensions appropriate to the space you want to describe.
How can I find the missing height of a cuboid?
Divide volume by length times width: h = V ÷ (L × W). A 384 cm³ volume with length 12 cm and width 8 cm has height 384 ÷ 96 = 4 cm. Neither length nor width may be zero.
Is cuboid volume the same as the total surface area?
No. Volume measures the interior space in cubic units. The area of all six faces is 2(LW + Lh + Wh), in square units, and is not an output of this tool. Wrapping a box and filling it are different calculations.
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