## Summary

To calculate the longest side (the hypotenuse) of a right triangle in Excel, you can use a formula based on the Pythagorean theorem, adapted to use Excel's math operators and functions. In the example shown, the formula in D5, copied down, is:

``````=SQRT(B5^2+C5^2)
``````

which returns the length of the hypotenuse, given lengths of side a and aside b, given in column B and C respectively.

## Explanation

The Pythagorean theorem is a key principle in Euclidean geometry. It states that the square of the longest side of a right triangle (the hypotenuse) is equal to the sum of the squares of the other two sides. The theorem is written as an equation like this:

a2 + b2 = c2

When any two sides are know, this equation can be used to solve for the third side. When a and b are known, the length of the hypotenuse can be calculated with:

When b and c are known, the length of side a can be calculated with:

When a and c are known, length of side b can be calculated with:

To translate the above into Excel formula syntax, use the exponentiation operator (^) and the SQRT function, as seen below. The Pythagorean theorem can be written as:

``````=a^2+b^2=c^2 // pythagorean theorem
``````

And the formulas below can be used to solve for each of the three sides:

``````c=SQRT(a^2+b^2) // hypotenuse
a=SQRT(c^2-b^2) // side a
b=SQRT(c^2-a^2) // side b
``````

Instead of the exponentiation operator, you can also use the POWER function like this:

``````c=SQRT(POWER(a,2)+POWER(b,2))
a=SQRT(POWER(c,2)-POWER(b,2))
b=SQRT(POWER(c,2)-POWER(a,2))
``````

The formulas above are an example of nesting one function inside another. Author ### Dave Bruns

Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.