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Triangle Calculator

Solve any triangle from three sides or angles: SSS, SAS, ASA, AAS and the two-triangle SSA case.

Result

Enter your values and select Calculate to see the result.

Runs in your browser — nothing you enter is sent to a server.

How the Triangle Calculator works

Enter any three of the six values — sides a, b, c and the angles A, B, C opposite them — including at least one side. The calculator works out the rest, the area and perimeter, and names the triangle (for example "scalene, right"). With two sides and an angle that isn't between them there can be two different triangles; both are shown.

Formulas

Law of cosines

c² = a² + b² − 2ab cos C

Law of sines

a ÷ sin A = b ÷ sin B = c ÷ sin C

Heron's area

area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Examples

Two sides and the angle between

a = 5, b = 7 and C = 60° give c ≈ 6.245.

The ambiguous case

a = 6, b = 8 and A = 35° fit two triangles: B ≈ 49.89° or B ≈ 130.11°.

Frequently asked questions

Why can't I solve with three angles?

Three angles give the shape but not the size — every enlargement fits. One side fixes it.

Why does it say no triangle exists?

Each side must be shorter than the other two together, the angles must add up to less than 180°, or (for SSA) the side opposite the angle may be too short to reach.

Degrees or radians?

Degrees.

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