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Diagonal of Rectangle Calculator

Geometry

Diagonal Length

10.0000 m

Angle with Width (α)

53.1301°

Angle with Height (β)

36.8699°

Area

48.0000 m²

Perimeter

28.0000 m

Rectangle Diagram

w = 6.00 mh = 8.00 md = 10.00 mα = 53.13°

About This Tool

Diagonal of Rectangle Calculator – Find d from Width and Height

The diagonal of a rectangle is the straight line connecting two opposite corners, splitting the rectangle into two congruent right triangles. This calculator finds the diagonal from a rectangle's width and height, or reverses the process to solve for a missing side when the diagonal and one side are already known — along with the angles the diagonal forms, the area, and the perimeter.

The Core Diagonal Formula

Because a rectangle's diagonal, width, and height form a right triangle, the Pythagorean theorem applies directly:

d = √(w² + h²)

For example, a rectangle with a width of 6 m and a height of 8 m has a diagonal of d = √(6² + 8²) = √(36 + 64) = √100 = 10 m. This is the classic 6-8-10 right-triangle relationship, a multiple of the well-known 3-4-5 triple.

Finding a Missing Side

If the diagonal and one side are already known, the other side can be found by rearranging the same formula:

h = √(d² − w²)
w = √(d² − h²)

For instance, with a diagonal of 10 m and a known width of 6 m, the height is h = √(10² − 6²) = √(100 − 36) = √64 = 8 m. The diagonal must always be strictly greater than either known side — otherwise the values cannot form a valid rectangle.

Angles Formed by the Diagonal

The diagonal creates two angles with the rectangle's sides, commonly called alpha (α) and beta (β):

α = arctan(h / w) — the angle between the diagonal and the width side
β = arctan(w / h) — the angle between the diagonal and the height side

These two angles always sum to exactly 90 degrees, since the diagonal and the two sides form a right triangle. For the 6-8-10 example above, α ≈ 53.13° and β ≈ 36.87°.

Watch the units
All calculations convert your inputs to a common unit before applying the formula. Mixing units (e.g., width in meters and height in feet) is handled automatically when you select a single display unit for both values.

Area and Perimeter

Alongside the diagonal, the calculator reports the rectangle's area and perimeter for convenience:

Area = w × h
Perimeter = 2(w + h)

Common Applications

  • Construction and carpentry — checking that a frame, door, or wall section is square by comparing measured diagonals
  • Screens and displays — verifying an advertised diagonal size (e.g., a 15.6-inch laptop screen) from its physical width and height
  • Flooring and tiling — measuring a room's diagonal to plan diagonal tile layouts or estimate cable and baseboard runs
  • Architecture and engineering — validating rectangular layouts on drawings and site plans
  • Everyday tasks — sizing picture frames, boxes, or furniture that must fit through a doorway diagonally

Why a Rectangle's Diagonals Are Equal

A rectangle has two diagonals of equal length, both computed with the same formula, because opposite sides of a rectangle are equal and all four corners are right angles. This property is often used as a practical check for squareness: if two diagonals measured across a frame or opening are equal, the corners are true right angles.

Precision and Accuracy

All calculations use standard 64-bit floating-point arithmetic, accurate to about 15 significant digits. Displayed values are rounded to your chosen precision, from 0 to 10 decimal places.

Frequently Asked Questions

Is the Diagonal of Rectangle Calculator free?

Yes, Diagonal of Rectangle Calculator is totally free :)

Can I use the Diagonal of Rectangle Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Diagonal of Rectangle Calculator?

Yes, any data related to Diagonal of Rectangle Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

How does this diagonal of rectangle calculator work?

Enter a rectangle's width and height to compute its diagonal using the Pythagorean theorem (d = √(w² + h²)). You can also switch to reverse mode and enter the diagonal plus one known side to solve for the missing side. The calculator also shows the angles the diagonal forms with each side, along with the rectangle's area and perimeter.

What is the formula for the diagonal of a rectangle?

The diagonal formula is d = √(w² + h²), where w is the width and h is the height. This comes directly from the Pythagorean theorem, since a rectangle's diagonal splits it into two right triangles with legs equal to the width and height.

How do I find a missing side if I know the diagonal?

If you know the diagonal (d) and one side, the other side is found by rearranging the Pythagorean theorem: missing side = √(d² − known side²). The diagonal must always be greater than either individual side, otherwise no valid rectangle exists.

What are the angles alpha and beta in the results?

Alpha (α) is the angle the diagonal makes with the width side, calculated as arctan(height / width). Beta (β) is the angle the diagonal makes with the height side, calculated as arctan(width / height). Alpha and beta always add up to 90 degrees.

Can I use this calculator for screens, tiles, or rooms?

Yes. The same formula applies whether you're measuring a television or monitor's screen size, a tile or picture frame, or a rectangular room's floor diagonal — just enter the width and height in your preferred unit and choose the appropriate unit from mm, cm, m, km, in, ft, or yd.

How accurate are the results?

Calculations use standard 64-bit floating-point arithmetic (IEEE 754), accurate to about 15 significant digits. Displayed values are rounded to your chosen precision, from 0 to 10 decimal places.