Triangle Calculator

Solve any triangle by entering known values. Get all sides, angles, area, perimeter, and triangle classification.

Side-Angle-Side (SAS)

Length Unit:
The angle between sides a and b
The side between angles A and B
The side opposite to angle A
The angle opposite to side a (ambiguous case possible)
a b c A B C
Invalid triangle: The given values cannot form a valid triangle.

Sides

Side a --
Side b --
Side c --

Angles

Angle A --
Angle B --
Angle C --

Measurements

Perimeter --
Area --
Height (to c) --
Triangle Type --

Triangle Formulas

Law of Cosines

c² = a² + b² - 2ab·cos(C)
Find a side when you know two sides and the included angle

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)
Relates sides and their opposite angles

Heron's Formula

Area = sqrt(s(s-a)(s-b)(s-c))
Where s = (a+b+c)/2 is the semi-perimeter

Area (SAS)

Area = (1/2)·a·b·sin(C)
Area using two sides and included angle

Angle Sum

A + B + C = 180°
The sum of all angles in a triangle

Triangle Inequality

a + b > c (for all sides)
Sum of any two sides must exceed the third