Triangle Angles From Sides Calculator

Enter the three sides a, b and c of a triangle to find all three interior angles using the law of cosines, plus area and a diagram.

Input

Enter the three side lengths of a triangle to find all three interior angles with the law of cosines.

Side a

Length

Side b

Length

Side c

Length

Three interior angles

Angle A (opposite side a)

36.86989765 deg

Angle B (opposite side b)

53.13010235 deg

Angle C (opposite side c)

90 deg

Area

Perimeter

Angle sum

180 deg

Angles are shown in degrees. Length values use the same unit as your input.

Each angle comes from the law of cosines. For side a the opposite angle A is cosA=(b²+c²−a²)/(2bc), and B and C follow the same pattern.
The area uses Heron formula S=√(s(s−a)(s−b)(s−c)) where s is half the perimeter.
A triangle is valid only when every side is positive and the sum of any two sides is greater than the third side (triangle inequality).
The three interior angles sum to 180 degrees in theory, so the displayed total is a handy check of the result.

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