Triangle Calculator
The Triangle Calculator solves for all missing sides, angles, area, and perimeter of a triangle from three known values, using the Law of Cosines and Law of Sines.
Triangle Solution
--
Side a--
Side b--
Side c--
Angle A--
Angle B--
Angle C--
Perimeter--
The formulas used
Given three sides (SSS), angles are found with the Law of Cosines:
cos(A) = (b² + c² − a²) / (2bc)
Given two sides and the included angle (SAS), the third side is found the same way, then the remaining angles use the Law of Sines:
a / sin(A) = b / sin(B) = c / sin(C)
Area is calculated with Heron's formula using the semi-perimeter s = (a+b+c)/2:
Area = √[s(s−a)(s−b)(s−c)]
Example: A triangle with sides 5, 6, and 7 has an area of about 14.7 square units and angles of roughly 44.4°, 57.1°, and 78.5°.
Triangle inequality
For three side lengths to form a valid triangle, the sum of any two sides must be greater than the third. This calculator checks that automatically for the SSS mode. See our Scientific Calculator for standalone trigonometric functions.