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Rectangular Prism (Cuboid) Calculator
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Enter length, width, and height to instantly calculate the base area, lateral surface area, total surface area, volume, and total edge length of a rectangular prism.
Formulas
Surface Area: S = 2(ab + ah + bh)
Volume: V = abh
Total Edge Length: L = 4(a + b + h)
Space Diagonal: d = √(a² + b² + h²)
All dimensions (length, width, height) must be positive numbers.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
A rectangular prism (also called a cuboid or rectangular box) has three edge dimensions meeting at right angles. Enter its length, width, and height using the same selected unit. The calculator reports the three face areas, total surface area, volume, total edge length, and the space diagonal.
Area results use the selected unit squared; volume uses it cubed; edge length and diagonal use the selected length unit. For 8 cm × 5 cm × 3 cm, the outputs are face areas 40, 24, and 15 cm²; total surface area 158 cm²; volume 120 cm³; total edge length 64 cm; and diagonal about 9.8995 cm. The [OpenStax geometry lesson](https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area) explains the prism area and volume relationships.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Fill in length, width, and height. A blank, invalid, zero, or negative value cannot produce a valid measurement set.
Choose millimeters, centimeters, meters, inches, or feet. All three entered values are interpreted in that unit; the calculator does not convert separate input units individually.
Select a precision option for the displayed values. This changes formatting, while calculations use the underlying dimension values.
Use squared units for face areas and surface area, cubic units for volume, and the original length unit for edge total and space diagonal.
Use cases
See how the tool fits into real work and everyday tasks.
For dimensions 8 cm, 5 cm, and 3 cm, compare the displayed 120 cm³ volume and 158 cm² total area with a hand calculation. The three different face areas help locate a missed side.
Use outer dimensions to estimate the box’s geometric volume or total outside face area. Use inner dimensions if the question is the space available inside; the tool does not infer wall thickness.
For a room or storage bay with perpendicular sides, enter the three dimensions in one unit to estimate enclosed volume and total rectangular surface area.
Q&A
Find concise answers to common questions and confusing cases.
Volume measures the space enclosed and is expressed in cubic units. Surface area adds all six faces and is expressed in square units.
No. Pick one unit and express all three dimensions in it before entering them. The unit selector labels outputs but does not convert each input separately.
It is the straight-line distance through the solid between opposite corners, calculated from the three perpendicular dimensions with the three-dimensional Pythagorean relationship.
Notes
Review scope, result limitations, and important precautions before use.
The formulas describe a rectangular solid with straight perpendicular edges. They do not account for taper, rounded corners, cutouts, internal dividers, or material thickness. A package capacity estimate should use interior dimensions; outside dimensions can overstate usable space.
The decimal-place selector controls how many digits are shown, not the accuracy of the measurements. Input measurement error carries into area, volume, and diagonal results. The value displayed in scientific notation for exceptionally small or large results is still based on the entered dimensions.
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