Right triangle

Calculation of a right triangle from a given side and angle

Calculate right triangle


This function calculates the most important parameters of a right triangle from a side length and the angle α. As a result, the cathetus, hypotenuse, height, circumference, area, hypotenuse sections and the angles are displayed.

To perform the calculation, select the side length you know and enter its values and the angle. Then click on the 'Calculate' button.


Right triangle calculator

 Input
Angle α
Decimal places
 Results
Cathete a
Cathete b
Hypotenuse c
Height h
Perimeter P
Area A
Segment p
Segment q
Angle α
Angle β

Formulas and description for right triangles


In a right angle, the cathets are the two sides that lie against the right angle. The hypotenuse is the side opposite the right angle. The height is measured from the right angle to the hypotenuse. The hypotenuse sections are the sections of the hypotenuse from the respective corner to the point where the line of height meets the hypotenuse.


Hypotenuse c

\(\displaystyle c=\sqrt{a^2+b^2} \)
\(\displaystyle c= \frac{a}{sin(α)}\)
\(\displaystyle c= \frac{b}{cos(α)}\)

Cathete a

\(\displaystyle a=\sqrt{c^2-b^2}\)
\(\displaystyle a=b·tan(α)\)
\(\displaystyle a=c·sin(α)\)

Cathete b

\(\displaystyle a=\sqrt{c^2-a^2} \)
\(\displaystyle b=\frac{a}{tan(α)}\)
\(\displaystyle b=c·cos(α)\)

Area A

\(\displaystyle A = \frac{ a · b}{2} \)
\(\displaystyle A = \frac{ c · h}{2} \)

Perimeter P

\(\displaystyle P=a+b+c \)

Height h

\(\displaystyle h = \frac{ a · b}{c} \)
\(\displaystyle h=\sqrt{ p · q} \)

Segment p

\(\displaystyle p= \frac{a^2}{c} \)

Segment q

\(\displaystyle q = \frac{b^2}{c} \)

Angle α

\(\displaystyle α = arcsin \left( \frac{a}{c} \right) \)
\(\displaystyle α = arccos \left( \frac{b}{c} \right) \)

Angle β

\(\displaystyle β = arcsin \left( \frac{b}{c} \right) \)
\(\displaystyle β = arccos \left( \frac{a}{c} \right) \)


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