30-60-90 Triangle Calculator

About this calculator

A 30-60-90 triangle is a special right triangle whose angles are fixed at 30°, 60°, and 90°, which forces its three sides into a constant ratio of 1 : √3 : 2 — the side opposite 30° is always the shortest, the side opposite 60° is √3 times that length, and the hypotenuse (opposite the right angle) is exactly twice the shortest side. Because the ratio never changes, knowing the length of just one side is enough to derive the other two, along with the triangle's area and perimeter.

This calculator takes any one known side, lets you specify which of the three it is, and solves for the remaining sides, area, and perimeter using that fixed ratio. Geometry and trigonometry students, and tradespeople such as carpenters and framers use 30-60-90 triangles constantly — they arise naturally from bisecting an equilateral triangle and show up in roof framing, stair stringers, and any layout involving a 30° or 60° angle.