Right Isosceles Triangle Calculator (Area, Hypotenuse)

Enter one value, the leg, hypotenuse, or area, to find the area, hypotenuse, perimeter, height, inradius, and circumradius of a right isosceles triangle.

Input

Enter the leg, hypotenuse, or area of a right isosceles triangle to find its area, hypotenuse, perimeter, height, inradius, and circumradius all at once.

Value to enter

Leg a

Result

Leg a

Hypotenuse c

14.142136

Area S

Perimeter L

34.142136

Height to hypotenuse h

7.071068

Inradius r

2.928932

Circumradius R

7.071068

The three angles are always 45, 45, and 90 degrees.

Lengths use the same unit as your input, and the area uses that unit squared.

How it works

With a leg length of a, the hypotenuse is c = a×√2 by the Pythagorean theorem.
The area is S = a²÷2, because the two equal legs meet at the right angle, so both the base and height equal a.
The perimeter is L = 2a + a√2.
The height drawn to the hypotenuse is h = a÷√2.
The three angles are always 45, 45, and 90 degrees.
The inradius is r = a×(2 − √2)÷2, and the circumradius is R = hypotenuse÷2 = a√2÷2.
To work backward from the hypotenuse use a = c÷√2, and from the area use a = √(2S).

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