Triangle Hypotenuse Calculator

Calculate the length of the hypotenuse in a right triangle using two sides or one side and one angle with the calculator below.

Solve Using:

Solution:

Hypotenuse c =  


How to Calculate the Hypotenuse of a Right Triangle

The hypotenuse is the side in a right triangle that is opposite the 90° right angle. It’s also the longest side of the triangle.

The hypotenuse is side c in the illustration of a right triangle shown below.

diagram of a triangle showing sides a & b and hypotenuse c

The hypotenuse can be solved using one of the following formulas.

Solve the Hypotenuse using Two Sides

The Pythagorean theorem can be used to solve the hypotenuse using two sides. The Pythagorean theorem states a² + b² = c².

This formula can be rewritten to solve for the hypotenuse c.

c = a² + b²

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

diagram of a triangle showing two sides used to solve the hypotenuse

Solve the Hypotenuse using One Side and the Adjacent Angle

Given one side and the adjacent angle, the following formula can be used to find the hypotenuse.

c = acos(β)

The hypotenuse c is equal to side a divided by the cosine of the adjacent angle β.

diagram of a triangle showing side a and adjacent angle b

Solve the Hypotenuse using One Side and the Opposite Angle

Given one side and the opposite angle, the following formula can be used to solve the hypotenuse.

c = asin(α)

The hypotenuse c is equal to side a divided by the sine of the opposite angle α.

diagram of a triangle showing side a and opposite angle a