How to Calculate Diagonal Length and Width

Using geometry allows you to find the length of the diagonals in a rectangle or square without measuring. A diagonal reaches from one corner of the shape to the corner farthest from it. A rectangle or square has two diagonals of equal length; thus, diagonal length and diagonal width are two terms expressing the same thing. Since the diagonal splits a shape into two right triangles, you can use the Pythagorean theorem to find the length of the diagonal.

Things You'll Need

• Ruler or measuring tape
• Calculator

Instructions

1. Measure the length of one short side and one long side for a rectangle, or the length of one side for a square. Record the measurements in inches. Skip this step if the lengths are given to you in a math problem.

2. Square the length of a long side and the length of a short side for a rectangle. Square the length of one side for a square. For example, (5 inches)^2 = 25 square inches.

3. Add the squared lengths together for a rectangle. For example, 25 square inches + 16 square inches = 41 square inches.

   For a square, multiply the squared length by two. For example, (25 square inches)*2 = 50 square inches.

4. Take the square root of the result to find the length of the diagonal. For example, the square root of 41 square inches equals 6.4 inches.

Tips & Warnings

• Multiply the length of one side of a square by the square root of two to find the diagonal length.

References

• Western Kentucky University; The Pythagorean Theorem; Bettina Richmond; January 2008
• University of Georgia; Applications of the Pythagorean Theorem and Special Right Triangles; Jim Wilson

Resources

• The Geometry Center; Textbook Problems