Law of sines & cosines

Triangle Solver

Enter any three sides or angles — with at least one side — and solve every missing measurement instantly.

Fill in exactly three fields (at least one side), leave the rest blank.

Sides (opposite each matching angle)

Angles (degrees)

Side a
Side b
Side c
Angle A
Angle B
Angle C
Area
Perimeter

How it works

1

Enter three values

Fill in any three sides or angles — sides a, b, c line up with the opposite angles A, B, C.

2

Automatic case detection

The solver detects SSS, SAS, ASA, AAS or SSA and applies the right formula automatically.

3

Get every measurement

See every missing side, every missing angle, the area and the perimeter at once.

FAQ

How many values do I need to solve a triangle?

You need exactly three known values, and at least one must be a side length. Three angles alone only fix the triangle's shape, not its size.

What is the ambiguous SSA case?

When you know two sides and a non-included angle (SSA), there can be zero, one or two valid triangles. This tool returns one valid solution and flags when a second solution also exists.

Which formulas does this tool use?

It uses the law of cosines (c² = a² + b² − 2ab·cos C) to relate three sides and an angle, and the law of sines (a/sin A = b/sin B = c/sin C) to relate sides and their opposite angles.

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