Triangle calculator
Enter the three values you know and leave the rest empty. Sides a, b, c are opposite angles A, B, C. For a right triangle, enter C = 90.
Result
- Perimeter
- 12
- Type
- right, scalene
- Heights ha, hb, hc
- 4 · 3 · 2.4
- Medians ma, mb, mc
- 4.272 · 3.60555 · 2.5
- Inradius r
- 1
- Circumradius R
- 2.5
law of cosines: a² = b² + c² − 2bc·cos A
law of sines: a / sin A = b / sin B = c / sin C = 2R
Heron: Area = √(s(s−a)(s−b)(s−c))
How to solve a triangle
A triangle is fixed by three values, at least one of which is a side. Three sides (SSS), or two sides and the angle between them (SAS), are solved with the law of cosines. A side and two angles (ASA, AAS) use the law of sines, since the third angle is 180° minus the other two.
Two sides and an angle that is not between them (SSA) is the ambiguous case: two different triangles may fit, or one, or none. The tool then shows both solutions.
Right triangles
Enter C = 90 and two other values. For example, legs a = 3 and b = 4 give a hypotenuse c = 5 (Pythagoras).
Common questions
What units do I use for angles?
Degrees. Sides can be in any unit, as long as they all use the same one; the area comes out in that unit squared.
Why are there two results?
Two sides and the angle opposite one of them can fit both an acute and an obtuse triangle.