V=lwhVariables
- V: volume
- l: length
- w: width
- h: height
How to use this formula
Calculates volume from length, width, and height.
Important notes
- All dimensions must use compatible units.
- The formula applies to right rectangular prisms.
Quick example
A 2×3×4 prism has volume 24 cubic units.
Applicability, worked calculation, and verification
Domain and applicability
Apply Rectangular Prism Volume only when the listed variables are defined, denominators are nonzero, and the problem satisfies the assumptions stated on this page.
Assumptions and domain checks
- All dimensions must use compatible units.
- Use one consistent unit system and confirm whether lengths, areas, volumes, and angles use the dimensions implied by the formula.
Do not use this formula when
- Do not use Rectangular Prism Volume when the stated lengths, angles, or geometric conditions do not match the figure or use inconsistent units.
Boundary and special cases
- For Rectangular Prism Volume, check zero, negative, and extreme input values before relying on the result.
- When using Rectangular Prism Volume, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form V=lwh for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
A prism with dimensions 2×3×4 has volume V=24 cubic units.
- Use mutually perpendicular length, width, and height.
- Multiply 2×3=6.
- Multiply 6×4=24 and use cubic units.
Independent verification
The prism contains 4 layers of 6 unit cubes.
Common mistakes
- Before substituting values into Rectangular Prism Volume, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- For the Rectangular Prism Volume, do not report a length, area, or volume with the wrong unit dimension, and keep intermediate precision until the final rounding step.
Continue the workflow
Use Rectangular Prism Volume in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
V=lwh. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked workflow, and verification method for Rectangular Prism Volume.
Verified against: OpenStax Algebra and Trigonometry
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Rectangular Prism Volume used for?
Calculates volume from length, width, and height.
Can I copy this formula as LaTeX?
Yes. Copy V=lwh or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.