45-45-90 Triangle Calculator

How it is calculated

You enter the length of one leg, a, and the other leg is the same because the two acute angles are both 45°. The hypotenuse is c = a × √2, which follows from the Pythagorean theorem c² = a² + a² = 2a². The area is A = a² / 2, half of the square built on the leg. The hypotenuse comes out in the same unit as the leg, and the area in that unit squared. Both results are rounded to two decimals, so a very small leg, such as 0.001, shows as 0.00. The leg must be above zero. The tool starts from a leg only. If you know the hypotenuse, divide it by √2, about 1.4142, to get the leg first.

Common mistakes

• Entering the hypotenuse as the leg. The input is one of the two equal short sides, so a diagonal of 11.31 must be divided by √2 first.
• Multiplying by 2 instead of √2. The hypotenuse is about 1.414 times the leg, not double it.
• Forgetting that the area is half of leg squared. A square on the same leg has area a², and the triangle is half of that.
• Using the tool for a right triangle whose legs differ. It always assumes the two legs are equal and both angles are 45°.
• Reading a rounded 0.00 for a tiny leg as a real zero. The results have only two decimals, so scale up the units, for example millimetres instead of metres.