45-45-90 Triangle Calculator
Solve any triangle from three known values — SSS, SAS, ASA, AAS or SSA — and get every side, every angle, the area, the perimeter and the heights, with the law of sines and cosines steps written out and a scaled diagram.
Result
The 45-45-90 triangle is the isosceles right triangle: two equal legs, two 45° angles and a right angle between the legs. Its sides always come in the exact ratio 1 : 1 : √2, so the hypotenuse is the leg times √2 ≈ 1.41421 — no matter the size of the triangle.
This page opens the calculator with that minimal example prefilled: legs 1 and 1 with the included 90° angle. Solving it returns the hypotenuse √2, the two 45° base angles, an area of exactly 0.5 and the heights, drawn on a diagram with the right angle marked. Replace the two legs with your own length to scale the whole triangle.
You meet this shape whenever a square is cut along its diagonal: rafters and braces at 45°, mitre cuts, chamfers, and the diagonal of any square floor plan (side × √2). Since only ratios are involved, one solved 45-45-90 triangle answers every other one by simple multiplication.