45-45-90 Triangle Calculator

Solve an isosceles right triangle from one leg or the hypotenuse using the exact 1 : 1 : sqrt(2) ratio.

Last updated: June 2026 | By Patchworkr Team

Leg (x)

Math check: leg : leg : hypotenuse = 1 : 1 : sqrt(2)

Result

Enter a positive side length to complete the triangle.

Ratios

1 : 1 : sqrt(2)

If one leg is 5, the other leg is also 5 and the hypotenuse is 5 sqrt(2) = 7.071068.

The area is 12.5 and the perimeter is about 17.071068.

This triangle always has two equal acute angles, each 45 degrees.

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