How this calculator works
Equal legs imply equal acute angles. They share the 90° left after the right angle, so each measures 45°. Pythagoras makes the diagonal √2 times either leg. Reflecting across the diagonal forms a square with twice the triangle’s area. The altitude to the hypotenuse is half the hypotenuse and bisects it.
Formula
a=b; c=√2 a; K=a²/2=c²/4; P=(2+√2)a; h=c/2; square area=a²; R=c/2; r=a-c/2.
Worked example
Equal legs of 6 cm give c=6√2 cm, area 18 cm² and a completed square of 36 cm². A hypotenuse of 10 m gives each leg 5√2 m and triangle area 25 m².
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Frequently asked questions
Can either leg be entered?
Yes. Both have the same length, so there is no short-leg versus long-leg choice.
Why does area equal one quarter of c squared?
Substituting a=c/√2 into K=a²/2 gives K=c²/4.
What is the square-diagonal connection?
A square’s diagonal divides it into two congruent 45°-45°-90° triangles. Its side is a and diagonal is c.