Pythagorean theorem calculator

Our Pythagorean Theorem Calculator can be used to find the missing side length of a right triangle by inputting the lengths of two known sides.

The calculator will then use the Pythagorean Theorem to determine the length of the missing side and display the result. As usual, some theory can be found below the calculator.

Side length of a right triangle

Digits after the decimal point: 2
Side length

Pythagorean theorem

The Pythagorean Theorem is a mathematical principle named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to calculate the length of any side of a right triangle as long as the lengths of the other two sides are known.

Fun fact: The Pythagorean Theorem was not actually proven by Pythagoras himself, but is named after him because he was known to have been familiar with it.

If we denote hypotenuse as c and two legs as a and b, we can write the following equation, often called the Pythagorean equation:
$a^2+b^2=c^2$

From this, we can quickly get the formulas for the unknown value.
In the calculator above, if you select the "two legs" option, then you are solving for the hypotenuse (c), and the hypotenuse is

$c=\sqrt{a^2+b^2}$

If you select the "leg and hypotenuse" option, then you are solving the remained leg, and if it is a, then it equals to

$a=\sqrt{c^2-b^2}$

If it is b, then it equals to

$b=\sqrt{c^2-a^2}$

Fun fact: The Pythagorean Theorem is over 2,000 years old and is considered one of the most important mathematical principles in the world. Wikipedia says there are 367 ways to prove the Pythagorean theorem.

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PLANETCALC, Pythagorean theorem calculator