Pythagorean Theorem Calculator – with Steps to Solve

Use the Pythagorean theorem to solve the length of an edge of a right triangle or its area by entering known leg or hypotenuse values.

Solve For:

Solution and Steps:

a=4

a= c² - b²
a= 5² - 3²
a= 25 - 9
a=16
a=4


What is the Pythagorean Theorem?

illustration showing the formula for the Pythagorean theorem and its relation to a right triangle

The Pythagorean theorem, sometimes called Pythagoras’ theorem, is an equation used to solve the length of the hypotenuse in a right triangle. The equation defines the relationship between the length of the three sides of a right triangle.

The Pythagorean theorem can be used to solve any side if the length of the other two sides is known.

The Pythagorean theorem states that the length of the hypotenuse squared is equal to the sum of the squares of each leg.

Pythagorean Theorem Formula

The Pythagorean theorem is expressed using the following equation:

a² + b² = c²

Thus, the length of edge a squared plus the length of edge b squared is equal to the length of the hypotenuse c squared.

How to use the Pythagorean Theorem for Right Triangles

Given the length of any two edges of a right triangle, the Pythagorean theorem is used to solve the length of the third edge. To solve, replace the values of a, b, or c in the formula with the two known values and solve the equation.

The following formulas are derived from the Pythagorean theorem to solve for any edge of a right triangle.

Solve the Length of Edge a

The length of leg a can be found using the following formula:

a = c² – b²

The length of leg a is equal to the square root of c squared minus b squared.

Solve the Length of Edge b

The length of leg b can be found using the following formula:

b = c² – a²

The length of leg b is equal to the square root of c squared minus a squared.

Solve the Length of Hypotenuse c

The length of hypotenuse c can be found using the following formula:

c = a² + b²

The hypotenuse c is equal to the square root of a squared plus b squared.

To calculate the angles, area, or perimeter try our right triangle calculator.