Enter one side of a 30-60-90 triangle to calculate the other two, using its fixed side ratio.

How to Use the 30-60-90 Triangle Calculator

Pick which side you know — the Short Leg, Long Leg, or Hypotenuse — then enter its length. The other two sides, plus area and perimeter, update immediately.

A 30-60-90 triangle is a right triangle whose acute angles are locked at exactly 30° and 60°, which locks its side lengths into a fixed ratio no matter how big the triangle is:

short leg : long leg : hypotenuse = 1 : √3 : 2

That ratio is what makes the triangle useful as a shortcut — half of an equilateral triangle, split down its own height, is always a 30-60-90, so its exact side lengths never need a calculator at all once one side and the ratio are known. Cut a square along its diagonal instead and the other common special right triangle appears, 45-45-90, with its own fixed ratio.

Area and Perimeter

area = ½ × short leg × long leg
perimeter = short leg + long leg + hypotenuse

Because every side collapses to a multiple of the short leg (call it x: the sides are x, x√3, and 2x), area and perimeter both reduce to a single-variable formula once any one measurement is known — no ambiguity or second solution the way a general triangle sometimes has.