Pythagorean Theorem Calculator — Right Triangle Solver
Solve right triangles with the Pythagorean theorem. Find any side, angles, area, perimeter, altitude, inradius, circumradius, and detect special triples.
Diagonal of a Rectangle Calculator
Calculate the diagonal of a rectangle from its length and width using the Pythagorean theorem. Also find area, perimeter, diagonal angle, and aspect ratio.
The longer side of the rectangle
mm
The shorter side of the rectangle
mm
Diagonal (d)⧉
363.7430 mm
d = √(297.00² + 210.00²) = √(88,209.00 + 44,100.00) = 363.7430
Area⧉
62,370.0000 mm²
A = 297.00 × 210.00 = 62,370.0000
Perimeter⧉
1,014.0000 mm
P = 2(297.00 + 210.00) = 1,014.0000
Diagonal Angle (α)⧉
35.2630°
Angle between diagonal and length side: α = arctan(width / length)
Complementary Angle (β)⧉
54.7370°
Angle between diagonal and width side: β = 90° − α
Half Diagonal⧉
181.8715 mm
Distance from center to corner
Aspect Ratio⧉
1.4143
≈ 99:70
Diagonal-to-Perimeter⧉
0.3587
d / P ratio
Pythagorean Theorem
d² = a² + b²
a² = 297.00² = 88,209.00
b² = 210.00² = 44,100.00
d² = 88,209.00 + 44,100.00 = 132,309.00
d = √132,309.00 = 363.7430 mm
Dimension Comparison
Length (a)
297.00 mm
Width (b)
210.00 mm
Diagonal (d)
363.74 mm
Half Diagonal
181.87 mm
Area vs. Perimeter Ratio
Length contribution
58.6%
Width contribution
41.4%
Common Rectangles Reference
| Object | Length | Width | Diagonal | Aspect Ratio |
|---|---|---|---|---|
| Business Card | 89 mm | 51 mm | 102.6 mm | 1.75:1 |
| A4 Paper | 297 mm | 210 mm | 363.7 mm | 1.41:1 |
| Letter Paper | 279.4 mm | 215.9 mm | 353.1 mm | 1.29:1 |
| Passport Photo | 45 mm | 35 mm | 57.0 mm | 1.29:1 |
| Credit Card | 85.6 mm | 53.98 mm | 101.2 mm | 1.59:1 |
| 24" Monitor (16:9) | 531 mm | 299 mm | 609.4 mm | 1.78:1 |
| 55" TV (16:9) | 1218 mm | 685 mm | 1,397.4 mm | 1.78:1 |
| Tennis Court | 23770 mm | 10970 mm | 26,179.3 mm | 2.17:1 |
| Football Field (US) | 109700 mm | 48800 mm | 120,064.7 mm | 2.25:1 |
| Soccer Field | 105000 mm | 68000 mm | 125,096.0 mm | 1.54:1 |
Planning notes, formulas, and examples
About the Diagonal of a Rectangle Calculator
The Diagonal of a Rectangle Calculator uses the Pythagorean theorem to compute the diagonal length of any rectangle from its length and width. In addition to the diagonal, it calculates area, perimeter, the angle the diagonal makes with each side, the aspect ratio, and the half-diagonal (center-to-corner distance).
The diagonal of a rectangle is one of the most commonly needed measurements in everyday life. When you shop for a television, the advertised size is the screen diagonal. When builders check if a room is square, they measure the diagonals. When designers create layouts, they need to know how the diagonal relates to the sides for spacing and alignment.
The formula is elegantly simple — d = √(a² + b²) — but it gives much more than a bare number. It shows a step-by-step Pythagorean theorem breakdown so students can follow the math, displays complementary angles in degrees or radians, and computes the aspect ratio with a simplified integer approximation.
Eight presets let you load common rectangles such as A4 paper, letter paper, credit cards, TV screens, smartphones, and sports fields. The reference table lists diagonals and aspect ratios for objects you encounter every day. Visual bars compare length, width, diagonal, and half-diagonal at a glance. Whether you are a student, engineer, designer, or curious learner, the page makes rectangle geometry quick and intuitive.
When This Page Helps
The Diagonal of a Rectangle Calculator is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Diagonal (d), Area, Perimeter in one pass, with conversions and derived values shown together.
How to Use the Inputs
- Choose the unit of measurement for your rectangle dimensions.
- Select whether you want angles displayed in degrees or radians.
- Enter the length (longer side) of the rectangle.
- Enter the width (shorter side) of the rectangle.
- Read the diagonal and all other properties in the output grid.
- Review the Pythagorean theorem step-by-step breakdown below the outputs.
- Click a preset button to load dimensions of common rectangular objects.
- Scroll down to see comparison bars and the reference table.
Formula used
Diagonal d = √(a² + b²) where a is the length and b is the width. Angle α = arctan(b / a). Area = a × b. Perimeter = 2(a + b).Example Calculation
Result: 363.7 mm
An A4 sheet of paper (297 × 210 mm) has a diagonal of √(297² + 210²) = √(88,209 + 44,100) = √132,309 ≈ 363.7 mm. The diagonal angle is arctan(210/297) ≈ 35.26°.
Tips & Best Practices
- TV and monitor sizes are measured along the diagonal — use this calculator to find the actual width and height from a diagonal and aspect ratio.
- To check if a room is perfectly rectangular, measure both diagonals — they should be equal.
- The diagonal of a rectangle is always longer than either side but shorter than the perimeter halved.
- For a square (where length = width), the diagonal equals the side length × √2 ≈ 1.414 × side.
How This Diagonal of a Rectangle Calculator Works
Where It Helps In Practice
Diagonal of a Rectangle Calculator calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Accuracy And Setup Tips
Sources & Methodology
Last updated:
Frequently Asked Questions
Use the Pythagorean theorem: d = √(length² + width²). For example, a 3 × 4 rectangle has a diagonal of √(9 + 16) = √25 = 5.
The diagonal is the advertised size (e.g., 55"). To find width and height from the diagonal and ratio, use w = d × 16/√(16² + 9²) and h = d × 9/√(16² + 9²).
No. By the Pythagorean theorem, the diagonal is always strictly longer than either side since d = √(a² + b²) > max(a, b).
The angle between the diagonal and the length is α = arctan(width / length). The angle with the width is 90° − α.
For a square with side s, the diagonal is d = s√2 ≈ 1.4142 × s.
Yes. A rectangle (and any parallelogram with right angles) always has two diagonals of equal length, and they bisect each other.
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