Triangle Calculator
Give it three known values from any triangle and it figures out everything else - all sides, all angles, area, and perimeter. Uses the Law of Sines and Cosines under the hood so it works for any triangle, not just right-angled ones.
How to use
- Choose what you already know: three sides (SSS), two sides and an angle (SAS), or two angles and a side (ASA).
- Enter those values into the fields that appear.
- Everything else - missing sides, angles, area, perimeter - fills in automatically.
Related tools:
Any triangle is fully defined once you know 3 of its 6 elements (3 sides, 3 angles) - as long as at least one is a side. Three angles alone do not fix the triangle (infinitely many similar triangles share the same angles). The law of sines (a/sin A = b/sin B = c/sin C) and the law of cosines (c^2 = a^2 + b^2 - 2ab cos C) together can solve any case.
The calculator works with any valid combination of inputs: SSS (all three sides), SAS (two sides and the included angle), or ASA (two angles and the side between them). It also handles AAS and SSA, though SSA (two sides and a non-included angle) can sometimes yield two solutions - the ambiguous case.
Frequently Asked Questions
When is the SSA case ambiguous?
When the given angle is acute and the side opposite to it is shorter than the adjacent known side, two different triangles can satisfy the given measurements. The calculator will show both solutions if they exist.
What is Heron formula for triangle area?
If you know all three sides (a, b, c), area = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 (the semi-perimeter). No need to find height first.
What is the sum of angles in a triangle?
Always 180 degrees for a flat (Euclidean) triangle. In spherical geometry (like navigation on a globe), angles sum to more than 180. In hyperbolic geometry, less than 180. This calculator assumes flat geometry.