Triangle Solver

Solve any triangle from sides and angles with visual diagrams

SSS (3 sides)

SSS: a=3, b=4, c=5
Side a
3
Side b
4
Side c
5
Angle α
36.8699°
Angle β
53.1301°
Angle γ
90°
Area
6
Perimeter
12
Triangle with sides a=3.00, b=4.00, c=5.00 and angles α=36.9°, β=53.1°, γ=90.0°Triangle with sides a=3.00, b=4.00, c=5.00 and angles α=36.9°, β=53.1°, γ=90.0°A (36.9°)B (53.1°)C (90°)c=5a=3b=4

About this calculator

Solve any triangle given sides and/or angles using the law of sines and cosines. See the triangle drawn to scale with all sides, angles, area, and perimeter calculated and labeled.

How to solve a triangle

  1. Choose the input combination that matches what you know (SSS, SAS, ASA, AAS, or SSA).
  2. Enter the sides in fields a, b, c and angles in fields alpha, beta, gamma.
  3. Read the missing sides and angles, plus area and perimeter, in the results section.
  4. Check the proportional diagram to verify the triangle looks right.

Common examples

  • Sides 3-4-5: right triangle, area = 6
  • Sides 5-5-5: equilateral, angles = 60° each
  • Side 10, angles 45°-90°-45°
  • Sides 7-8-9: scalene triangle
  • Sides 6-6-8: isosceles triangle

Frequently asked questions

What input combinations can solve a triangle?

Any of SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), AAS (two angles and a non-included side), or SSA (two sides and an angle opposite one of them). At least one side is required because angles alone do not fix the size.

What is the SSA ambiguous case?

When you specify two sides and an angle opposite one of them, there can be zero, one, or two valid triangles. The calculator shows both solutions side by side whenever both are valid, rather than guessing which one you meant.

Which formulas are used?

The Law of Sines (a/sin A = b/sin B = c/sin C) and the Law of Cosines (c² = a² + b² − 2ab cos C) cover every supported case. Sides are labeled a, b, c and the angle opposite each side is α (alpha), β (beta), γ (gamma).

What if the inputs do not form a real triangle?

If the side lengths violate the triangle inequality or the angles do not sum to 180°, the calculator shows a clear invalid-triangle message instead of an arbitrary numeric result.