The diagonal of a square is a line drawn from one corner to the corner across and at the other side of the square. The length of the diagonal of any rectangle equals the square root of the sum of the squares of its length and width. A square is a rectangle with all sides of equal length, so the diagonal’s length is the square root of twice the square of a side, which simplifies to the square root of two multiplied by the length of a side. You can compute the length of the diagonal merely by multiplying the length of a side by this constant.

The square root of 2 is 1.414. You can quickly compute the diagonal length by multiplying 1.414 by the length of a side. In the example, you have 1.414 * 9 = 12.73.

In trigonometry, the number 1.414 equals both the secant and cosecant of 45 degrees. The diagonal of a square makes a 45-degree angle with all sides of the square. You can compute the diagonal’s length by multiplying the length of a side by the secant or cosecant.

Enter the number “2” on a scientific calculator.

Press the “square root” key, which typically has a radical symbol on it.

Multiply by the length of a side of the square. For example, if a side has length 9, then press “times” on the calculator, enter “9” and press “equal.” The answer is 12.73.

#### Tips

References

Tips

- The square root of 2 is 1.414. You can quickly compute the diagonal length by multiplying 1.414 by the length of a side. In the example, you have 1.414 * 9 = 12.73.
- In trigonometry, the number 1.414 equals both the secant and cosecant of 45 degrees. The diagonal of a square makes a 45-degree angle with all sides of the square. You can compute the diagonal's length by multiplying the length of a side by the secant or cosecant.

About the Author

Jim Dorsch has been a writer and editor since 1991. He has written for major newspapers, including "The Washington Post" and "Chicago Tribune," and is publisher and editor of "American Brewer" magazine. He holds a Bachelor of Science in mathematics from Rose-Hulman Institute of Technology and a Master of Science in statistics from Purdue University.

Photo Credits

Thinkstock/Comstock/Getty Images