Rectangle Geometry & Aspect Ratio Calculator
Compute area, perimeter & diagonals, solve inverse side lengths from constraints, and size display aspect ratios & golden rectangles
Longer parallel horizontal side
Shorter perpendicular vertical side
Enclosed Surface Area & Boundary
144.000 cm²
Oblong Rectangle (16 : 9)
Perimeter (2l + 2w): 50.000 cm • Semi-perimeter: 25.000 cm
Diagonal Length (d = √(l² + w²))
18.358 cm
Corner-to-corner Euclidean chord
Diagonal Intersection Angle (θ)
58.72° (Acute)
121.28° supplementary pair
Circumcircle Radius (R = d / 2)
9.179 cm
Circumcircle Area: 264.67 cm²
Largest Inscribed Circle (r_max)
4.500 cm
Diameter = width (9.000 cm)
Extracted Dimensions (Length × Width)
16.000 × 9.000 units
Valid Geometric Solution
Quadratic Discriminant Δ: 49.000 (Two distinct sides)
Length / Base (l)
16.000 units
Primary major dimension
Width / Height (w)
9.000 units
Perpendicular minor dimension
Verified Diagonal (d)
18.358 units
√(l² + w²) verification
Resulting Aspect Ratio (l / w)
1.778 : 1 (16:9)
Normalized dimensional quotient
Nominal diagonal measurement (d)
Display Physical Dimensions
23.53 × 13.24 in
Surface Area: 311.51 sq in (2,009.7 cm²)
Active Horizontal Width
23.532 in
59.77 cm horizontal span
Active Vertical Height
13.237 in
33.62 cm vertical span
Golden Ratio Variance
+9.87% from φ
Difference relative to 1.618 : 1
Area Efficiency (vs Square Screen)
85.4%
Max area for 27 in diagonal: 364.5 in²