Law of cosines calculator

Find a triangle’s third side from two sides and the included angle: c² = a² + b² − 2ab cos C.

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First adjacent side

Second adjacent side

More inputs and assumptions

Included angle (degrees)

Answer

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Find a triangle’s third side from two sides and the included angle: c² = a² + b² − 2ab cos C.

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Formula and assumptions

The angle must sit between the entered sides and be strictly between 0° and 180°. All lengths use one unit. A stable equivalent expression reduces cancellation.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Law of cosines calculator

Find a triangle’s third side from two sides and the included angle: c² = a² + b² − 2ab cos C.

The angle must sit between the entered sides and be strictly between 0° and 180°. All lengths use one unit. A stable equivalent expression reduces cancellation.

Next: Triangle calculator

A worked example

Example inputs: first adjacent side = 3, second adjacent side = 4, included angle (degrees) = 90. Opposite side length = 5.

Before you use the result

The angle must sit between the entered sides and be strictly between 0° and 180°. All lengths use one unit. A stable equivalent expression reduces cancellation.

Example results for first adjacent side

These examples use Second adjacent side: 4; Included angle (degrees): 90. They are reference calculations, not recommended settings.

First adjacent side	Opposite side length
1.5	4.27200187266
3	5
6	7.21110255093

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