Pythagorean Theorem Calculator

Enter the lengths of any two sides of a right triangle, and the calculator will determine the unknown side using the Pythagorean theorem equation: \(a^2 + b^2=c^2\).

Solve for:

Hypotenuse b

Area c

Perimeter:

Side:

a = c² - b²

Related

Pythagorean Theorem Calculator

Use this calculator to find unknown sides of a right triangle using the Pythagorean theorem. It also provides calculations for Area, Perimeter, Angles, and Altitude for a complete triangle analysis.

Pythagorean Theorem Formula

\(a^2 + b^2 = c^2\)

c = Hypotenuse (the triangle's longest side)
a = One leg of the triangle
b = Other leg of the triangle

Finding the Hypotenuse (c):

\(c = \sqrt{a^2 + b^2}\)

Finding a Leg (a):

\(a = \sqrt{c^2 - b^2}\)

Finding a Leg (b):

\(b = \sqrt{c^2 - a^2}\)

Additional Calculations

Area: \(A = \frac{a \cdot b}{2}\)
Perimeter: \(P = a + b + c\)
Angle α: \(\alpha = \arctan\left(\frac{a}{b}\right)\)
Angle β: \(\beta = \arctan\left(\frac{b}{a}\right)\)
Altitude from Hypotenuse: \(h = \frac{a \cdot b}{c}\)

About the Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right triangle. It states:

"The square of the hypotenuse equals the sum of the squares of the other two sides."

This theorem was first attributed to the Greek mathematician Pythagoras around 500 BC and is widely used in mathematics, engineering, and physics.