Rectangle Calculator Online
Calculate rectangle area, perimeter, diagonal, and circumcircle with step-by-step geometry formulas.
Input Parameters
Live Result
Details
Steps
Length L = 8 m, Width W = 5 m
Area Formula: A = L · W = 8 · 5 = 40 m²
Perimeter Formula: P = 2(L + W) = 2(8 + 5) = 26 m
Diagonal Formula: d = √(L² + W²) = √(64 + 25) = √89 ≈ 9.434 m
Circumscribed Circle: Radius R = d / 2 = 4.717 m, Area = π · R² ≈ 69.9004 m²
Quick Answer & Understanding Your Result
A rectangle is a quadrilateral with four right angles (90°), where the area is A = L · W, the perimeter is P = 2(L + W), and the diagonal is d = √(L² + W²).
Key Geometric Formulas
- Area: The two-dimensional surface enclosed: A = L · W.
- Perimeter: The total boundary distance: P = 2 · (L + W).
- Diagonal: Length of corner-to-corner hypotenuse: d = √(L² + W²) via Pythagorean theorem.
- Circumcircle: Circle enclosing all 4 vertices with radius R = d / 2 and area A_c = π · R².
Common Architectural & Design Applications
- Flooring & Carpeting: Computing square footage and perimeter baseboard lengths for room remodeling.
- Screen Displays & Monitors: Analyzing aspect ratios (e.g. 16:9, 4:3) and screen diagonal sizing.
- Land Plotting & Real Estate: Measuring rectangular lot boundaries, set-backs, and total acreage.
Enter your length and width measurements in the calculator above to get instant area, perimeter, and diagonal metrics.
Formula & Calculation Logic
Mathematical FormulaL represents length and W represents width. The diagonal creates two congruent right-angled triangles whose hypotenuse is calculated via the Pythagorean theorem.
Step-by-Step Guide
Enter Length & Width
Input the two perpendicular side dimensions into the Length and Width fields.
Select Unit
Choose your unit of measure (meters, centimeters, millimeters, inches, or feet).
Instant Computation
View the primary area hero card along with perimeter, diagonal, and circumscribed circle metrics.
Examine Step-by-Step Proofs
Review each calculation step including Pythagorean theorem expansion.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Standard Room: 8m by 5m | Area = 8 · 5 = 40 m², Perimeter = 2(8 + 5) = 26 m, Diagonal = √(64 + 25) = √89 ≈ 9.434 m. | ||
| Display Aspect: 16cm by 9cm | Area = 16 · 9 = 144 cm², Perimeter = 50 cm, Diagonal = √(256 + 81) = √337 ≈ 18.358 cm. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Wolfram MathWorld - Rectangle
NIST Handbook of Mathematical Functions
Standard: Rectangle Dimensions & Diagonal
Formula: Area = L · W
Last Reviewed: August 21, 2026
Primary Source: Wolfram MathWorld - Rectangle
Reference Document: NIST Handbook of Mathematical Functions
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.