P=2(l+w)Variables
- l: length
- w: width
- P: perimeter
How to use this formula
Calculates the perimeter of a rectangle.
Important notes
- Perimeter uses linear units.
Quick example
For l=5,w=3, P=16.
Applicability, worked calculation, and verification
Domain and applicability
Apply Rectangle Perimeter only when the listed variables are defined, denominators are nonzero, and the problem satisfies the assumptions stated on this page.
Assumptions and domain checks
- Perimeter uses linear 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 Rectangle Perimeter when the stated lengths, angles, or geometric conditions do not match the figure or use inconsistent units.
Boundary and special cases
- For Rectangle Perimeter, check zero, negative, and extreme input values before relying on the result.
- When using Rectangle Perimeter, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form P=2(l+w) for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
For l=5 cm and w=3 cm, P=2(5+3)=16 cm.
- Add one length and one width: 5+3=8 cm.
- Double the sum to include opposite sides.
- Report 16 cm as a length.
Independent verification
Adding all four sides, 5+3+5+3, also gives 16.
Common mistakes
- Before substituting values into Rectangle Perimeter, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- For the Rectangle Perimeter, 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 Rectangle Perimeter 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
P=2(l+w). - 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 Rectangle Perimeter.
Verified against: OpenStax Algebra and Trigonometry
Automated quality check: Passed the core formula indexing gate.
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 Rectangle Perimeter used for?
Calculates the perimeter of a rectangle.
Can I copy this formula as LaTeX?
Yes. Copy P=2(l+w) 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.