Rectangle Calculator
Calculate rectangle area, perimeter, and diagonal from length and width. Solve for missing sides from area or diagonal. Includes aspect ratio, golden rectangle check, and inscribed circle radius.
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Area
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Perimeter —
Diagonal —
Extended More scenarios, charts & detailed breakdown ▾
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units
Area
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Perimeter —
Diagonal —
Professional Full parameters & maximum detail ▾
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units
Circles
Inscribed Circle Radius —
Circumscribed Circle Radius —
Proportions
Aspect Ratio —
Golden Rectangle? —
Scale Factor to Golden —
How to Use This Calculator
- Enter Length and Width to get area, perimeter, and diagonal instantly.
- Use the From Area & One Side tab to find the other side when area is known.
- Use the From Diagonal & Side tab when diagonal is known.
- The Professional tab adds inscribed/circumscribed circle radii, aspect ratio, and golden rectangle check.
Formula
Area = L × W | Perimeter = 2(L + W) | Diagonal = √(L² + W²)
Example
L=8, W=5 → Area = 40, Perimeter = 26, Diagonal ≈ 9.43 units.
Frequently Asked Questions
- The area of a rectangle equals its length multiplied by its width: A = L × W. For an 8×5 rectangle: A = 8 × 5 = 40 square units. Units of area are always square units (cm², m², in², ft²). If length is in meters and width is in centimeters, convert both to the same unit first. Area represents the amount of 2D space enclosed within the rectangle and is used for floor coverage, painting, tiling, and land measurement.
- The diagonal of a rectangle is found using the Pythagorean theorem, since the diagonal and two sides form a right triangle: d = √(L² + W²). For an 8×5 rectangle: d = √(64 + 25) = √89 ≈ 9.434 units. A square (L = W) has diagonal d = L√2. The diagonal bisects the rectangle into two congruent right triangles. Both diagonals of a rectangle have equal length, which is a distinguishing property — parallelograms in general have unequal diagonals.
- A golden rectangle has a length-to-width ratio equal to the golden ratio φ ≈ 1.61803. If you remove a square from a golden rectangle, the remaining smaller rectangle is itself a golden rectangle — this self-similar property makes it unique. The golden ratio appears naturally in Fibonacci proportions: as you go further in the sequence (1, 1, 2, 3, 5, 8, 13, …), consecutive ratios (8/5, 13/8, …) approach φ. The calculator tells you how close your rectangle is to golden proportions.
- The largest circle that fits entirely inside a rectangle has its diameter equal to the shorter side (it is tangent to both longer sides). Its radius is: r = min(L, W) / 2. For an 8×5 rectangle, the inscribed circle has r = 5/2 = 2.5 and diameter = 5, touching both long sides but leaving gaps at the ends. The circumscribed circle (the smallest circle containing the rectangle) passes through all four corners and has radius equal to half the diagonal: r_circ = d/2 = √89/2 ≈ 4.717.
- If you know the area A and one side, the missing side = A ÷ known side. Formula: L = A ÷ W or W = A ÷ L. Example: Area = 60, Width = 6 → Length = 60 ÷ 6 = 10. Another: Area = 75 square meters, Length = 12.5 m → Width = 75 ÷ 12.5 = 6 m. The "From Area and One Side" tab automates this. If you know area and the diagonal instead, you need two equations: A = L×W and d² = L² + W², which the Professional tab solves simultaneously.