This all-in-one online Pythagorean Theorem Calculator helps to calculate the length of any side of a right triangle provided the lengths of its other two sides are known.
Pythagorean theorem
The Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides:
$$a^{2}+b^{2}=c^{2},$$
where \(c\) represents the length of the hypotenuse and \(a\) and \(b\) the lengths of the triangle’s other two sides.
So, if the lengths of both \(a\) and \(b\) are known, then \(c\) can be calculated as
$${\displaystyle c={\sqrt {a^{2}+b^{2}}}.}$$
If the length of the hypotenuse \(c\) and of one side (\(a\) or \(b\)) are known, then the length of the other side can be calculated as
$${\displaystyle a={\sqrt {c^{2}-b^{2}}}}$$
or
$${\displaystyle b={\sqrt {c^{2}-a^{2}}}.}$$
Using our Pythagorean Theorem Calculator makes any calculation based on the Pythagorean theorem a matter of a fraction of a second.
Related calculators
To calculate parameters of an arbitrary triangle check out our Triangle Calculator.