ABC Triangle Calculator

General triangle solver. Enter any 3 known values (sides and/or angles) to solve the entire triangle.

Enter Any 3 Known Values

A B C a b c
Fill in exactly 3 fields (leave the other 3 empty). The calculator auto-detects the case (SSS, SAS, ASA, AAS, SSA).
Sides
opposite A
opposite B
opposite C
Angles (degrees)
opposite a
opposite b
opposite c
Fields filled: 0 / 3

Result

Enter any 3 known values and click Solve Triangle.

Solving Triangles: A Complete Overview

What This Calculator Does

This general triangle solver accepts any combination of three known values and computes all unknowns. Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.

The Five Solvable Cases

1. SSS (Side-Side-Side)

All three sides are known. Use the law of cosines to find each angle:

A = arccos[(b² + c² - a²) / (2bc)]

2. SAS (Side-Angle-Side)

Two sides and the included angle. Use the law of cosines:

a² = b² + c² - 2bc × cos(A)

3. ASA (Angle-Side-Angle)

Two angles and the included side. Find the third angle, then use the law of sines.

4. AAS (Angle-Angle-Side)

Two angles and a non-included side. Equivalent to ASA after finding the third angle.

5. SSA -- The Ambiguous Case

Two sides and a non-included angle can yield 0, 1, or 2 valid triangles. This calculator shows all valid solutions.

The Law of Cosines

c² = a² + b² - 2ab × cos(C)

The Law of Sines

a / sin(A) = b / sin(B) = c / sin(C) = 2R

Area Formulas

  • Area = ½ ab sin(C)
  • Heron's: Area = √[s(s-a)(s-b)(s-c)]

Triangle Classification

  • By sides: Equilateral, Isosceles, Scalene
  • By angles: Acute, Right, Obtuse