45-45-90 Triangle Calculator
Solve a 45-45-90 triangle from a leg or the hypotenuse. Get both equal legs, the hypotenuse, area, and perimeter with instant results.
Formula
If each leg = x, then hypotenuse = x√2
A 45-45-90 triangle is exactly half of a square cut along its diagonal, which permanently locks the two legs to the same length and makes the hypotenuse equal to the leg multiplied by √2. Both 45° angles are identical, so the triangle is isosceles as well as right-angled. Because the hypotenuse is the diagonal of the underlying square, this triangle appears whenever a square corner or grid layout needs to be measured diagonally.
Frequently Asked Questions
What is a 45-45-90 triangle?
A 45-45-90 triangle is an isosceles right triangle. Its two legs are equal, and the hypotenuse is always the leg multiplied by √2.
What is the side ratio for a 45-45-90 triangle?
If each leg is x, then the hypotenuse is x√2. The fixed side ratio is 1 : 1 : √2.
Where is this triangle used?
45-45-90 triangles appear in squares, diagonal measurements, drafting, layout work, and many geometry and trigonometry problems.
How do I find the hypotenuse of a right triangle?
Use the Pythagorean theorem: hypotenuse = square root of (a squared + b squared), where a and b are the two legs. For a 45-45-90 triangle with legs of length 5, the hypotenuse is 5 times the square root of 2, or approximately 7.07.
What is the difference between a 45-45-90 and a 30-60-90 triangle?
A 45-45-90 triangle has two equal legs with hypotenuse = leg times sqrt(2). A 30-60-90 triangle has sides in the ratio 1 : sqrt(3) : 2, where the shortest side is opposite the 30-degree angle. Both are special right triangles with fixed side ratios.
How do I calculate the area of a triangle?
The basic formula is area = (1/2) times base times height. For a right triangle, the two legs serve as base and height. For a 45-45-90 triangle with legs of length a, the area is (1/2) times a squared.