Triangle Calculator
Solve the sides and angles of a triangle.
Tip: Give 3 values (sides or angles) and the calculator finds all the other values.
Did this tool help?
About this digital tool
The triangle calculator solves any triangle: from three given values it finds all the sides and angles, as well as the area and perimeter. It supports three modes: SSS (three sides), SAS (two sides and the angle between them) and AAS (two angles and one side).
The unknowns are calculated with the law of cosines and the law of sines, while the sum of the angles is always 180°. For a triangle with sides 3, 4 and 5, the area comes out as 6, the perimeter 12 and the angles 36.87°, 53.13° and 90°, so it is a right triangle. It is useful for school geometry, construction, surveying and any measurement where only a few elements of the triangle are known.
How to use
- Choose the mode: SSS (three sides), SAS (two sides + angle) or AAS (two angles + side).
- Enter the required data: sides a, b, c or angles in degrees.
- If an error appears, check that the sides satisfy the triangle inequality.
- Read the calculated sides, angles, area and perimeter.
Frequently asked questions
How many values are needed to solve a triangle?
At least 3, where at least one must be a side. E.g. 3 sides (SSS), 2 sides + 1 angle (SAS), or 1 side + 2 angles (ASA).
How is the area of a triangle calculated when three sides are known?
Heron's formula is used: S = √(p(p−a)(p−b)(p−c)), where p is half the perimeter. For 3, 4, 5: p = 6 and S = √(6 × 3 × 2 × 1) = 6.
What is the triangle inequality?
The sum of any two sides must be greater than the third side. Sides 2, 3 and 6 do not form a triangle because 2 + 3 < 6.
What is the sum of the angles of a triangle?
Always 180°. In AAS mode, if angles 50° and 60° are given, the third angle is 180° − 50° − 60° = 70°.