Pythagorean Theorem Calculator


Our Pythagorean calculator calculates length of any omitted side of a right angle triangle given of course that you know the lengths of the remaining two sides.It includes computing the hypotenuse. The hypotenuse of the triangle is the opposing side of the right angle, also being the longest one.

This side can be determined with the formula for the hypotenuse. It is an alternative term for the Pythagoras theorem when it's resolving the hypotenuse. Bear in mind that a right angle triangle has an angle measuring 90 degrees. The rest of the two angles should also sum up to 90 degrees, as the sum of the angles of any given triangle is 180.

Designed for Math Students and Teachers, Physicists, Engineers and Mathematicians, our calculator does a fine job at computing the right angle values for you. This tool is free to use and doesn’t require user registration to our site either. We value our site visitors. Feel Free!

Pythagoras theorem:

The Pythagoras theorem explains how the three sides of a right angle triangle are relative in Euclidean geometry. In essence, it states that the total of the squares of the sides of a right angle triangle is equivalent to the square of the hypotenuse. You can also make of Pythagoras theorem as the hypotenuse formula. If the sides of a Pythagorean triangle are ‘a’ and ‘b’ respectively and z is hypotenuse, the formula would look like this:

$$a^2 + b^2 = c^2$$

The theorem was developed by the ancient Greek Mathematician and Philosopher Pythagoras in 6th century BCE. Even though it was previously employed by the Babylonians as well, but Pythagoras was the first to prove the theorem’s validity according to the excerpts from the classical antiquity.

Using the Pythagoras theorem

It’s actually really fun to use this theorem due to its elegance and simplicity.

  • Put in the two lengths that you already have, into the equation. For instance, suppose you know the values for ‘a’ and ‘b’ to be 6 and 10 respectively and want to determine the length of hypotenuse ‘c’.
  • After you put the values into the formula, you have 6²+ 10² = c²
  • Square each of these terms: 36 + 100 = 136 = c²
  • Now, take square root of both sides of the formula to get c = 11.6. Or you can simply save yourself this time consuming manual math stuff and just determine the calculation with our tool in a split second.

On a side note, in case you’re are solving for either a or b, don’t forget to readjust the formula to segregate the variable in question before conjoining similar terms and taking square root.

Our Pythagorean calculator would solve for the sides in the same manner as has been shown above.

Hypotenuse equation

The hypotenuse equation is simply the rearrangement of Pythagoras theorem to solve the hypotenuse, ‘c’. To do so, we basically take the square root of both the sides of the formula a² + b² = c² and determine ‘c’. When we do so, we obtain c = √(a² + b²). By definition, it’s an extension of the Pythagoras theorem.

Secondary considerations when dealing with triangles

You should bear in mind that the sides of a triangle have a definite degree of slope. You can use our slope calculator to find out the gradient of each side. In a right triangle, the sides that shape the right angle would have gradients whose product would be -1. The equation for slope is given below:

(y₂ - y₁)/(x₂ - x₁)

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