Triangle Calculator

Enter any 3 known values (sides/angles) to solve the triangle

Sides
Angles (degrees)

Leave unknown fields blank. Enter at least 3 values (at least one side required).

Area

About the Triangle Calculator

This triangle solver uses the law of sines and law of cosines to compute all missing sides and angles given any three known values (at least one must be a side). It validates the triangle inequality theorem and displays the perimeter and area using Heron's formula.

The Formula

Law of Cosines: c² = a² + b² − 2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Heron's Area: s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c))

FAQs

What is the triangle inequality theorem?

The sum of any two sides of a triangle must be greater than the third side. If this condition fails, a triangle cannot be formed with the given side lengths.

Can I solve a triangle with only angles?

No — knowing only angles gives the shape but not the size (similar triangles). You must know at least one side length to determine the triangle uniquely.