Triangle Calculator
Solve any triangle — find all sides, angles, area, and perimeter from SSS, SAS, AAS, or right triangle inputs. Uses law of cosines and law of sines.
All calculations happen in your browser. No data is sent anywhere.
SSS — Three Sides Known
b / \ a
/___\
A c B
SAS — Two Sides & Included Angle
b / \ a
/___\
A c B
↑ enter a, b, and angle C
AAS — Two Angles & One Side
Angle C = 180° − A − B
Right Triangle
c² = a² + b²
How Triangle Solving Works
Law of Cosines (SSS and SAS)
Given three sides (SSS) or two sides and the included angle (SAS), the law of cosines finds the remaining measurements: c² = a² + b² − 2ab·cos(C). Once all sides are known, Heron's formula gives the area: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
Law of Sines (AAS and ASA)
Given two angles and one side (AAS), the law of sines finds the remaining sides: a/sin(A) = b/sin(B) = c/sin(C). The third angle is always C = 180° − A − B. For right triangles, the Pythagorean theorem applies directly: c² = a² + b².
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Open calculator →FAQ
What is the law of cosines?
c² = a² + b² − 2ab·cos(C). It relates three sides of a triangle to one of its angles. Used for SSS (find angles from three sides) and SAS (find the third side). When C = 90° it reduces to the Pythagorean theorem.
What is the law of sines?
a/sin(A) = b/sin(B) = c/sin(C). Each side divided by the sine of its opposite angle gives the same ratio. Used for AAS and ASA — when you know two angles and one side, this finds the remaining sides.
How do you find the area of a triangle?
Three methods: (1) Heron's formula from three sides: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. (2) ½·base·height. (3) ½·a·b·sin(C) when two sides and included angle are known. This calculator uses the appropriate method based on your inputs.
What does SSS, SAS, AAS mean?
SSS = three sides known. SAS = two sides and the angle between them. AAS = two angles and one side (opposite one of the known angles). ASA = two angles and the side between them (treated the same as AAS after finding the third angle). Any of these fully determines a unique triangle.