45-45-90 Triangle Calculator

Enter a leg or the hypotenuse of a 45-45-90 triangle to calculate the other two sides.

How to Use the 45-45-90 Triangle Calculator

Choose whether the value you know is a Leg or the Hypotenuse, enter it, and the remaining two sides, area, and perimeter fill in below.

Slice a square in half along its diagonal and both resulting triangles are 45-45-90s — a right angle with two equal 45° angles on either side, and legs that are, by definition, equal to each other. That symmetry fixes the ratio between the legs and the hypotenuse permanently:

leg : leg : hypotenuse = 1 : 1 : √2

√2 ≈ 1.41421, so a leg of 5 always pairs with a hypotenuse of about 7.071 — never anything else. Compare that to a general right triangle, where the Pythagorean theorem needs two known sides before it can solve for the third; here, one side is always enough.

Area and Perimeter

area = ½ × leg²
perimeter = 2 × leg + hypotenuse

Since both legs are identical, area simplifies to half the square of a single leg rather than the usual ½ × base × height with two different numbers.