What is the law of cosines?

c² = a² + b² - 2ab cos(C). It generalizes the Pythagorean theorem for any triangle.

When do I use SSS vs SAS?

Use SSS when you know all three sides. Use SAS when you know two sides and the angle between them.

Law of Cosines Calculator

Enter three sides (SSS) or two sides and the included angle (SAS) to solve the triangle. Finds all angles, area, and perimeter using the law of cosines: c^2 = a^2 + b^2 - 2ab cos(C).

Inputs

Mode

Side a

Side b

Side c / Angle C (°)

Results

Side a

Side b

Side c

Angle A

44.0486°

Angle B

52.6168°

Angle C

83.3346°

Area

27.8107 sq units

Perimeter

Frequently Asked Questions

Related Calculators

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Triangle Calculator

Calculate triangle area, perimeter, and angles from three side lengths using Heron's formula and the law of cosines.

Pythagorean Theorem Calculator

Find the missing side of a right triangle using a² + b² = c².