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Math • Diagonal of a Rectangle Calculator

Diagonal of a Rectangle Calculator

Calculate the diagonal length of a rectangle from its length and width using the Pythagorean theorem.

Area (A = l × w)
60.00
Perimeter (P = 2(l+w))
32.00
Diagonal (d = √(l²+w²))
11.66
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Calculation Guide & Reference

Rectangle Diagonal Mathematics

Diagonal of a rectangle calculator computes the diagonal length from a rectangle's length and width using the Pythagorean theorem.

Standardized Mathematical Formula
d = √(l² + w²)

A rectangle's diagonal splits it into two right triangles, with the diagonal as the hypotenuse and the length and width as the two legs — so the diagonal follows directly from the Pythagorean theorem.

Variables:
l:Length of the rectangle
w:Width of the rectangle
How It Works (Step-by-Step)
  • 1Enter the rectangle's length (l) and width (w).
  • 2View the diagonal length, area, and perimeter.
Real-World Numerical Example
A Rectangle 10 × 6

A rectangular door measures 10 units long and 6 units wide.

•Diagonal: √(10² + 6²) = √(100 + 36) = √136 ≈ 11.66 units.
Result: The diagonal of the rectangle is approximately 11.66 units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Yes — a square is just a special rectangle where length equals width, so the same formula applies: d = √(s² + s²) = s√2.

By the Pythagorean theorem, the hypotenuse of a right triangle is always longer than either leg, since it's the square root of the sum of both legs squared — the diagonal can never be shorter than the longest side.

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