Triangle Calculator

Solve the remaining sides and angles with the laws of sines and cosines. Includes area, perimeter, heights, inradius, circumradius, and a diagram drawn to scale.

Measurements

Mode

Enter all three sides. Angles come from the Law of Cosines and the area from Heron's formula.

Angle unit

Side a

Side b

Side c

Side a is opposite angle A, side b opposite angle B, and side c opposite angle C.

Diagram

Drawn roughly to scale — vertices, sides, and angle arcs labeled.

The math behind it

Law of Cosines


              c² = a² + b² − 2ab·cos(C)

Used to find the third side from SAS, or angles from SSS.

Law of Sines


              a / sin(A) = b / sin(B) = c / sin(C)

Used to find remaining sides once two angles are known (ASA, SSA).

Heron's formula


              s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c))

Area from the three sides; SAS area uses ½ab·sin(C) directly.

Radii and heights


              r = Area / s, R = a / (2·sin(A)), hₐ = 2·Area / a

Inradius from area over the semi-perimeter, circumradius from any side and its opposite angle, heights from twice the area over a side.