45-45-90 Triangle Calculator

About this calculator

A 45-45-90 triangle is a right triangle whose two non-right angles are both 45 degrees, which means its two legs are always equal in length. Because of that symmetry, the hypotenuse is always the leg length multiplied by the square root of two, a shortcut that saves reaching for the full Pythagorean theorem every time.

This exact triangle shape is what you get by cutting a square along its diagonal, so it comes up constantly in carpentry and design when mitering a 45-degree corner or bracing a square frame. It is also one of the two "special right triangles" taught in geometry classes, alongside the 30-60-90 triangle, precisely because its side ratios are fixed and easy to memorize.